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Preprint ARTICLE | doi:10.20944/preprints202401.1113.v8

Assembly Theory of Binary Messages (How to Assemble a Black Hole and Use it to Assemble New Binary Information?)

Szymon Łukaszyk, Wawrzyniec Bieniawski

Subject: Physical Sciences, Mathematical Physics Keywords: assembly theory; emergent dimensionality; black holes; shortest addition chains; P versus NP problem; ; quantum orthogonalization interval theorems; mathematical physics; binputation

Online: 15 April 2024 (04:22:22 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202401.1113.v7

Assembly Theory of Binary Messages (How to Assemble a Black Hole and Use it to Assemble New Binary Information?)

Szymon Łukaszyk, Wawrzyniec Bieniawski

Subject: Physical Sciences, Mathematical Physics Keywords: assembly theory; emergent dimensionality; black holes; shortest addition chains; P versus NP problem; ; quantum orthogonalization interval theorems; second law of infodynamics; mathematical physics; binputation

Online: 7 April 2024 (05:34:12 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202404.0394.v1

The Second-Order Features Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (2nd-FASAM-L): Mathematical Framework and Illustrative Application to an Energy System

Dan Gabriel Cacuci

Subject: Physical Sciences, Mathematical Physics Keywords: exact computation of first- and second-order sensitivities of model responses to features of model parameters; first- and second-level adjoint sensitivity systems; neutron slowing down and transport

Online: 5 April 2024 (11:01:27 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202403.1417.v2

New Estimates of the Potential Schrödinger Equation

Asset Durmagambetov

Subject: Physical Sciences, Mathematical Physics Keywords: Schrö; dinger equation; Poincaré; – Riemann– Hilbert boundary-value problem; unitary scattering operator; quantum scattering theory

Online: 4 April 2024 (12:35:41 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202404.0118.v1

New Solution of the Grain Boundary Grooving Problem in Polycrystalline Thin Films when Evaporation and Diffusion meet in Power Electronic Devices

Tayssir Hamieh, Ali Ibrahim, Zoubir Khatir

Subject: Physical Sciences, Mathematical Physics Keywords: Mathematical solution; evaporation-condensation; diffusion; groove formation; degradation; thermal fatigue; electronic devices

Online: 1 April 2024 (16:25:00 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202403.1873.v1

On complex dynamics in a Suris's integrable map

Yasutaka Hanada, Akira Shudo

Subject: Physical Sciences, Mathematical Physics Keywords: dynamical tunneling; integrable map; complex classical dynamics

Online: 1 April 2024 (10:14:39 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202403.1417.v1

New Estimates of the Potential Schrödinger Equation

Asset Durmagambetov

Subject: Physical Sciences, Mathematical Physics Keywords: Schrö; dinger equation; Poincaré; – Riemann– Hilbert boundary-value problem; unitary scattering operator; quantum scattering theory

Online: 26 March 2024 (11:14:11 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.1313.v1

Rotation Matrix of a Charged Symmetrical Body: One-Parameter Family of Solutions in Elementary Functions

Alexei A. Deriglazov

Subject: Physical Sciences, Mathematical Physics Keywords: Euler-Poisson equations; exact solutions in elementary functions; constrained systems; integrable systems; spinning body in external fields

Online: 26 March 2024 (03:02:20 CET)

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Preprint ARTICLE | doi:10.20944/preprints202401.1113.v6

Assembly Theory of Binary Messages (How to Assemble a Black Hole and Use it to Assemble New Binary Information?)

Szymon Łukaszyk, Wawrzyniec Bieniawski

Subject: Physical Sciences, Mathematical Physics Keywords: assembly theory; emergent dimensionality; black holes; complexity measures; P versus NP problem; ; quantum orthogonalization interval theorems; second law of infodynamics; mathematical physics; binputation

Online: 20 March 2024 (04:38:20 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.0977.v1

The Wave Equation for the Moving Source and the Moving Receiver

Hrvoje Dodig

Subject: Physical Sciences, Mathematical Physics Keywords: Standard wave equation; Wave propagation; Moving receiver; Moving source

Online: 18 March 2024 (10:08:28 CET)

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Preprint ARTICLE | doi:10.20944/preprints202401.1113.v5

Assembly Theory of Binary Messages (How to Assemble a Black Hole and Use it to Assemble New Binary Information?)

Szymon Łukaszyk, Wawrzyniec Bieniawski

Subject: Physical Sciences, Mathematical Physics Keywords: assembly theory; emergent dimensionality; holographic principle; black holes; complexity measures; P versus NP problem; Gö; del's incompleteness theorems; halting problem; elegant program; Fibonacci sequence; Collatz conjecture; addition chains; quantum orthogonalization interval theorems; second law of infodynamics; mathematical physics; binputation

Online: 14 March 2024 (10:02:52 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.0785.v1

The Computational Universe: EPR Paradox and Pre-Measure Reality, Actual Time in Spacetime, Free Will and the Classical Limit Problem in Quantum Loop Gravity, Causal Dynamical Triangulation and Holographic Principle

Piero Chiarelli, Simone Chiarelli

Subject: Physical Sciences, Mathematical Physics Keywords: EPR Paradox, Pre.existing reality, Quantum to classical coexsistence, Actual Time in Spacetime, Free Will,

Online: 13 March 2024 (14:09:14 CET)

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The Simulation analogy presented in this work enhances the accessibility of abstract quantum theories, specifically the stochastic hydrodyanimc model (SQHM), by relating them to our daily experiences. The SQHM incorporates the influence of fluctuating gravitational background, resembling dark energy, into quantum equations. This model successfully addresses key aspects of Objective-Collapse Theories, including resolving the 'tails' problem through the definition of quantum potential length in addition to the De Broglie length, beyond which coherent Schrödinger quantum behavior and wavefunction tails cannot be maintained. The SQHM emphasizes that an external environment is unnecessary, asserting that the quantum stochastic behavior leading to wave-function collapse can be an inherent property of a system in a spacetime with fluctuating metrics. Embedded in relativistic quantum mechanics, the theory establishes a coherent link between the uncertainty principle and the constancy of light speed, aligning seamlessly with finite information transmission speed. Within a fluctuating quantum system, the SQHM derives the indeterminacy relation between energy and time, offering insights into measurement processes impossible within a finite time interval in a truly quantum global system. Experimental validation is found in confirming the Lindemann constant for solid lattice melting points and the transition from fluid to superfluid states. The SQHM's self-consistency lies in its ability to describe wavefunction collapse and the measure process. Additionally, the theory resolves the Pre-existing Reality problem by showing that large-scale systems naturally decay into decoherent states stable in time. Continuing, the paper demonstrates that the physical dynamics of SQHM can be analogized to a computer simulation employing optimization procedures for realization. This perspective elucidates the concept of time in contemporary reality and enriches our comprehension of free will. The overall framework introduces an irreversible process impacting the manifestation of macroscopic reality at the present time, asserting that the multiverse exists solely in future states, with the past comprising the formed universe after the current moment. Decoherence at the present time functions as a reduction of the multiverse to a single universe. The macroscopic reality, characterized by fractal consistency where microscopic domains with quantum properties coexist, provides insights into how our consciousness apprehends dynamic reality, the spontaneous emergence of gravity in discrete spacetime evolution, and the attainment of the classical General Relativity limit in Quantum Loop Gravity and Causal Dynamical Triangulation. The Simulation Analogy highlights a strategy focused on minimizing information processing, facilitating the universal simulation in solving its predetermined problem. From within, reality becomes the manifestation of specific physical laws emerging from the inherent structure of the simulation devised to address its particular issue. In this context, the reality simulation appears to employ an entropic optimization strategy, minimizing information loss while efficiently compressing data in line with the simulation's intended purpose.

Preprint ARTICLE | doi:10.20944/preprints202401.1113.v4

Assembly Theory of Binary Messages (How to Assemble a Black Hole and Use it to Assemble New Binary Information?)

Szymon Łukaszyk, Wawrzyniec Bieniawski

Subject: Physical Sciences, Mathematical Physics Keywords: assembly theory; emergent dimensionality; holographic principle; black holes; complexity measures; P versus NP problem; Gö; del's incompleteness theorems; halting problem; elegant program; Fibonacci sequence; addition chains; quantum orthogonalization interval theorems; second law of infodynamics; mathematical physics; binputation

Online: 8 March 2024 (11:02:28 CET)

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Preprint COMMUNICATION | doi:10.20944/preprints202402.0599.v2

Quantum Hydrodynamics in External Magnetic Fields: From Nonrelativistic to Relativistic Regimes

Matthew James Stephenson

Subject: Physical Sciences, Mathematical Physics Keywords: nonrelativistic quantum electrodynamics; NRQED; background magnetic field; gauge invariance; Lagrangian; electron self-interactions; electromagnetic field interactions; path integral formalism; effective action; photon propagator; screening effects; density components; current components; Laurent expansions; hydrodynamic limit; equations of motion; Poiseuille-like flow; Navier-Stokes equation; relativistic hydrodynamics; linearized equations; nonrelativistic limit; quantum electrodynamical analysis

Online: 7 March 2024 (09:33:28 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.0289.v1

Gravity and the Riemannian Hypothesis

Junze Shi

Subject: Physical Sciences, Mathematical Physics Keywords: gravitation; Riemann hypothesis; Euler's formula

Online: 6 March 2024 (11:04:14 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.0311.v1

Fiber Structure and Stability Theorems for Symmetry Breaking Transitions

Eve Bodnia

Subject: Physical Sciences, Mathematical Physics Keywords: Fiber bundle, phase transitions, Lie groups, homotopy,
fundamental group, Stability Theorem, Stability Lemma, Fiber Structure
Theorem, superfluid Helium

Online: 6 March 2024 (10:15:05 CET)

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Preprint ARTICLE | doi:10.20944/preprints202401.1113.v3

Assembly Theory of Binary Messages (How to Assemble a Black Hole and Use it to Assemble New Binary Information?)

Szymon Łukaszyk, Wawrzyniec Bieniawski

Subject: Physical Sciences, Mathematical Physics Keywords: assembly theory; emergent dimensionality; holographic principle; black holes; complexity measures; P versus NP problem; Gö; del's incompleteness theorems; halting problem; elegant program; quantum orthogonalization interval theorems; second law of infodynamics; mathematical physics; binputation

Online: 5 March 2024 (06:39:56 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.0099.v1

The Equations and Their Effects

carlos eduardo ramos cardoso cardoso

Subject: Physical Sciences, Mathematical Physics Keywords: multiplication and addition equations; division equations; subtraction equations;
physical concepts

Online: 4 March 2024 (10:36:26 CET)

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Preprint ARTICLE | doi:10.20944/preprints202401.1113.v2

Assembly Theory of Binary Messages (How to Assemble a Black Hole and Use it to Assemble New Binary Information?)

Szymon Łukaszyk, Wawrzyniec Bieniawski

Subject: Physical Sciences, Mathematical Physics Keywords: assembly theory; emergent dimensionality; holographic principle; black holes; complexity measures; P versus NP problem; Gö; del's incompleteness theorems; halting problem; elegant program; quantum orthogonalization interval theorems; second law of infodynamics; mathematical physics

Online: 27 February 2024 (08:02:17 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.1320.v1

The Hermitian Solution to a New System of Commutative Quaternion Matrix Equations

Yue Zhang, Qing-Wen Wang, Lv-Ming Xie

Subject: Physical Sciences, Mathematical Physics Keywords: Commutative quaternion algebra; Matrix equations; Hermitian matrix; Complex representation

Online: 22 February 2024 (15:08:30 CET)

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Preprint COMMUNICATION | doi:10.20944/preprints202402.1290.v1

Non-Linear Coordinate Transformations at Homogeneous Electron Gases

Matthew James Stephenson

Subject: Physical Sciences, Mathematical Physics Keywords: Hydrodynamical limit; Homogeneous electron gases; Non-linear coordinate transformations; Infrared limit; Phenomenological hydrodynamics; Normal modes; Harmonic system

Online: 22 February 2024 (09:52:46 CET)

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Preprint COMMUNICATION | doi:10.20944/preprints202402.1200.v1

Quasinormal Modes at Electron Plasmas

Anna Maria Wojtyra, Matthew James Stephenson

Subject: Physical Sciences, Mathematical Physics Keywords: Lifshitz black holes; holography; quasinormal modes; shear sector modes; small star limit; Reissner-Nordströ; m-AdS; hydrodynamical modes; flux analysis; infrared limit; holographic techniques

Online: 22 February 2024 (01:44:00 CET)

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Preprint COMMUNICATION | doi:10.20944/preprints202402.1215.v1

Exact Renormalization Group Dynamics through Schrödinger-Type Equations

Anna Maria Wojtyra, Matthew James Stephenson

Subject: Physical Sciences, Mathematical Physics Keywords: Exact Renormalisation Group; Quantum Mechanics; Schrö; dinger-Type Equation; Wilsonian Renormalisation Group; Quantum Field Theory; Functional Quantum Mechanics; Inflation; Scalar Field

Online: 21 February 2024 (15:02:25 CET)

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Preprint COMMUNICATION | doi:10.20944/preprints202402.0604.v2

QUENCH: Quantum Unraveling in Enhanced Nonlinear CTP Hydrodynamics

Matthew James Stephenson

Subject: Physical Sciences, Mathematical Physics Keywords: Dissipative Hydrodynamics, Schwinger-Keldysh Field Theory, Navier-Stokes Equations, Long-Range Massless Modes, Fluid Dynamics, Volume-Preserving Diffeomorphisms, Closed-Time-Path Formalism, Hydrodynamic Correlation Functions, Effective Field Theory, Non-Relativistic Fluid Dynamics, Systematic Treatment, Second Order in Derivatives, Energy-Momentum Balance Equation, Hydrodynamic Transport, Gravitational Anomaly, Quasinormal Modes, Holography, Entropy Production, Conformal Invariance

Online: 21 February 2024 (09:20:45 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.1141.v1

Dirac field, van der Waals gas, Weyssenhoff fluid, Newton particle

Luca Fabbri

Subject: Physical Sciences, Mathematical Physics Keywords: Dirac spinor; polar form; effective approximation; thermodynamics; non-relativistic limit; classical limit

Online: 20 February 2024 (13:35:36 CET)

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Preprint ARTICLE | doi:10.20944/preprints202308.0515.v2

Induced Electrostatic Fields in the Presence of Conductors and Dielectrics: A Purely Laplace Equation-Based Treatment

George Bjornsen

Subject: Physical Sciences, Mathematical Physics Keywords: potential; field; uniqueness; Legendre polynomial

Online: 20 February 2024 (06:06:22 CET)

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Preprint COMMUNICATION | doi:10.20944/preprints202402.0215.v2

PRODIGY: Probing Resilience Of Domain-wall Interactions at Gauge Theory

Matthew James Stephenson

Subject: Physical Sciences, Mathematical Physics Keywords: axion-dilaton model; supergravity; domain walls; holographic vitrification action; gauge theories; periodic vacuum structures; QCD-like axion term; stabilizing dilaton; conductivity changes; weak disorder; perfect conductivity; leading-order conductivity correction; strong disorder; insulator state; comprehensive understanding; resilience; behavior; varying conditions

Online: 19 February 2024 (08:17:03 CET)

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Preprint COMMUNICATION | doi:10.20944/preprints202402.0767.v1

Analytic Resonance and Model Harmony in Non-linear Oscillators

Matthew James Stephenson

Subject: Physical Sciences, Mathematical Physics Keywords: Quantum Oscillators; Oscillons; Sine-Gordon Breather; Weak Coupling Limit; Semi-Classical Quantization; Stability Angles; Field Configurations; Mathematical Physics

Online: 14 February 2024 (09:40:55 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.0699.v1

In Quest of BRST Symmetry and Observables in 4D Topological Gauge-Affine Gravity

Oussama Abdelghafour BELARBI, Ahmed Meziane

Subject: Physical Sciences, Mathematical Physics Keywords: Topological models of gravity; topological gauge-affine gravity; Off-shell nilpotent BRST and anti-BRST algebra; Descent equations; Topological observables

Online: 13 February 2024 (08:07:00 CET)

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Preprint COMMUNICATION | doi:10.20944/preprints202402.0669.v1

Renormalization and Thermodynamics of Probe-D-Branes: Wilsonian RG Analysis and Infrared Regime Studies

Matthew James Stephenson

Subject: Physical Sciences, Mathematical Physics Keywords: Probe-D-Branes; Wilsonian Renormalization Group; Dirac-Born-Infeld Action; Holographic Renormalization; Infrared Regime; Thermodynamics; Grand Potential; RG Equation; String Theory; Higher-Dimensional Spacetime; Counter-Terms; Convergence; Renormalization Constants; Temperature Effects; Supergravity; AdS/CFT Correspondence; Mirror Symmetry

Online: 13 February 2024 (05:58:39 CET)

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Preprint COMMUNICATION | doi:10.20944/preprints202402.0604.v1

QUENCH: Quantum Unraveling in Enhanced Nonlinear CTP Hydrodynamics

Matthew James Stephenson

Subject: Physical Sciences, Mathematical Physics Keywords: Dissipative Hydrodynamics, Schwinger-Keldysh Field Theory, Navier-Stokes Equations, Long-Range Massless Modes, Fluid Dynamics, Volume-Preserving Diffeomorphisms, Closed-Time-Path Formalism, Hydrodynamic Correlation Functions, Effective Field Theory, Non-Relativistic Fluid Dynamics, Systematic Treatment, Second Order in Derivatives, Energy-Momentum Balance Equation, Hydrodynamic Transport, Gravitational Anomaly, Quasinormal Modes, Holography, Entropy Production, Conformal Invariance

Online: 10 February 2024 (17:50:22 CET)

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Preprint COMMUNICATION | doi:10.20944/preprints202402.0599.v1

Quantum Hydrodynamics in External Magnetic Fields: From Nonrelativistic to Relativistic Regimes

Matthew James Stephenson

Subject: Physical Sciences, Mathematical Physics Keywords: nonrelativistic quantum electrodynamics; NRQED; background magnetic field; gauge invariance; Lagrangian; electron self-interactions; electromagnetic field interactions; path integral formalism; effective action; photon propagator; screening effects; density components; current components; Laurent expansions; hydrodynamic limit; equations of motion; Poiseuille-like flow; Navier-Stokes equation; relativistic hydrodynamics; linearized equations; nonrelativistic limit; quantum electrodynamical analysis

Online: 9 February 2024 (16:07:16 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.0539.v1

Restricted Singular Value Decomposition for a Tensor Triplet under T-product and Its Applications

Chong-Quan Zhang, Qing-Wen Wang, Xiang-Xiang Wang, Zhuo-Heng He

Subject: Physical Sciences, Mathematical Physics Keywords: Multilinear algebra; restricted singular value decomposition; tensor SVD

Online: 9 February 2024 (10:03:47 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.0425.v1

Direct Link Between Energy and Information via Fisher’s Measure

F. Pennini, Angelo Plastino

Subject: Physical Sciences, Mathematical Physics Keywords: Fisher information; Poisson distribution; energy variance

Online: 7 February 2024 (08:12:48 CET)

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Preprint ARTICLE | doi:10.20944/preprints202401.1963.v2

How Much Cosmic Time Does It Take for a Star to Collapse Forming a Black Hole?

Jaume Haro

Subject: Physical Sciences, Mathematical Physics Keywords: gravitational contraction; cosmic time; event horizon; black holes

Online: 7 February 2024 (08:11:14 CET)

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Preprint COMMUNICATION | doi:10.20944/preprints202402.0419.v1

Exploring Dilaton Dynamics: Gravitational Lensing and Cosmological Implications

Matthew James Stephenson

Subject: Physical Sciences, Mathematical Physics Keywords: entanglement; quantum geometry; gauge/gravity duality; Ryu-Takayanagi formula; quantum error correction; primordial fluctuations; quantum magnetism; Casimir effect; topological quantum computation; condensed matter physics; dark matter; weak gravitational lensing, quantum chaos; black hole thermodynamics; lattice QCD; entanglement entropy; renormalization group; asymptotic freedom; holographic dualities; non-abelian Berry curvature

Online: 7 February 2024 (08:10:02 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.0385.v1

On the Conjecture over Dimensions of Associated Lie Algebra to the Isolated Singularities

Naveed Hussain, Ahmad N. Al-Kenani, Muhammad Asif

Subject: Physical Sciences, Mathematical Physics Keywords: hypersurface singularity; inequality conjecture.; derivation Lie algebra; fewnomial isolated singularities; Lie algebra

Online: 6 February 2024 (15:34:01 CET)

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Preprint REVIEW | doi:10.20944/preprints202401.0992.v2

The Language of Spheres in Physics

Jean-Pierre Gazeau

Subject: Physical Sciences, Mathematical Physics Keywords: Numbers; Symmetry; Group Theory; Spheres

Online: 6 February 2024 (09:39:19 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.0316.v1

The Dual Quaternion Matrix Equation AXB=C with Applications

Yan Chen, Qing-Wen Wang, Lv-Ming Xie

Subject: Physical Sciences, Mathematical Physics Keywords: Dual Quaternion; Moore-Penrose inverse; ϕ-Hermitian solution; matrix equations

Online: 6 February 2024 (09:14:30 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.0280.v1

General Relativistic Hydrodynamics in Discrete Spacetime: Perfect Fluid Accretion onto Static and Spinning Black Holes

Jonathan Gorard

Subject: Physical Sciences, Mathematical Physics Keywords: General Relativity; Relativistic Hydrodynamics; Discrete Spacetime; Black Hole Accretion

Online: 5 February 2024 (15:35:16 CET)

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We study the problem of a spherically-symmetric distribution of a perfect relativistic fluid accreting onto a (potentially spinning) black hole within a fully discrete spacetime setting. This problem has previously been studied extensively in the context of continuum spacetimes, beginning with the purely analytic work of Bondi in the spherically-symmetric Newtonian case, Michel in the spherically-symmetric general relativistic case, and Petrich, Shapiro and Teukolsky in the axially-symmetric general relativistic case relevant for spinning black holes. However, the purpose of the present work is to determine the effect of discretization of the underlying spacetime upon the mass/energy and momentum accretion rates, the overall morphology and characteristics of the accretion flow, and the drag force exerted on the black hole in the case of non-zero spin. In order to achieve this, we first develop a novel formulation of the equations of general relativistic hydrodynamics that is more directly amenable to rigorous analysis within a discrete spacetime setting, and we then proceed to implement this formulation into the \textsc{Gravitas} computational general relativity framework. Through a combination of mathematical analysis and explicit numerical simulation in \textsc{Gravitas}, we discover that the mass/energy and momentum accretion rates both decrease monotonically as functions of the underlying spacetime discretization scale, with this effect becoming more pronounced for higher values of the black hole spin parameter, higher fluid temperatures, and stiffer equation of state parameters. We also find that the exerted drag force is highly sensitive to the value of the underlying discretization scale in the case of spinning black hole spacetimes, with certain instabilities becoming significantly more pronounced at certain critical values of the discretization parameter. We discuss some potentially observable consequences of these results, as well as some directions for future theoretical investigation.

Preprint COMMUNICATION | doi:10.20944/preprints202402.0215.v1

PRODIGY: Probing Resilience Of Domain-wall Interactions at Gauge Theory

Matthew James Stephenson

Subject: Physical Sciences, Mathematical Physics Keywords: axion-dilaton model; supergravity; domain walls; holographic vitrification action; gauge theories; periodic vacuum structures; QCD-like axion term; stabilizing dilaton; conductivity changes; weak disorder; perfect conductivity; leading-order conductivity correction; strong disorder; insulator state; comprehensive understanding; resilience; behavior; varying conditions

Online: 5 February 2024 (10:57:24 CET)

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Preprint ARTICLE | doi:10.20944/preprints202401.1963.v1

How Much Cosmic Time Does It Take for a Star to Collapse Forming a Black Hole?

Jaume Haro

Subject: Physical Sciences, Mathematical Physics Keywords: gravitational contraction; cosmic time; event horizon; black holes

Online: 29 January 2024 (04:00:29 CET)

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Preprint ARTICLE | doi:10.20944/preprints202401.1419.v1

Fisher Information for a System of a Combination of Similar Potential Models

Clement Atachegbe Onate, I.B. Okon, E.S. Eyube, Ekwevugbe Omugbe, K.O Emeje, M.C Onyeaju, Olumide Ajani, Jacob Akinpelu

Subject: Physical Sciences, Mathematical Physics Keywords: Bound state; Wave equation; Eigensolution; Fisher information; Potential model

Online: 18 January 2024 (12:25:39 CET)

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Preprint ARTICLE | doi:10.20944/preprints202305.0066.v4

Interpretation of Entropy by Complex Fluid Dynamics

Seiji Fujino

Subject: Physical Sciences, Mathematical Physics Keywords: entropy; complex fluid dynamics; Boltzmann principle; Planck law

Online: 16 January 2024 (13:49:34 CET)

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Preprint ARTICLE | doi:10.20944/preprints202401.1113.v1

Assembly Theory of Binary Messages (How to Assemble a Black Hole and Use it to Assemble New Binary Information?)

Szymon Łukaszyk, Wawrzyniec Bieniawski

Subject: Physical Sciences, Mathematical Physics Keywords: assembly theory; emergent dimensionality; holographic principle; black holes; complexity measures; P versus NP problem; quantum orthogonalization interval theorems; second law of infodynamics; mathematical physics

Online: 15 January 2024 (07:39:14 CET)

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Preprint ARTICLE | doi:10.20944/preprints202305.0066.v3

Interpretation of Entropy by Complex Fluid Dynamics

Seiji Fujino

Subject: Physical Sciences, Mathematical Physics Keywords: Entropy; Complex Fluid Dynamics; Boltzmann principle; Planck law

Online: 14 January 2024 (16:05:26 CET)

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Preprint REVIEW | doi:10.20944/preprints202401.0992.v1

The Language of Spheres in Physics

Jean-Pierre Gazeau

Subject: Physical Sciences, Mathematical Physics Keywords: Numbers; Symmetry; Group Theory; Spheres

Online: 12 January 2024 (09:16:28 CET)

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Preprint ARTICLE | doi:10.20944/preprints202203.0371.v7

Entropy and Its Application to Number Theory

Seiji Fujino

Subject: Physical Sciences, Mathematical Physics Keywords: Entropy; Boltzmann principle; Planck's law; Dynamical system; Logistic function; ; fine structure constant; Von Koch's inequality; Riemann Hypothesis; abc conjecture

Online: 8 January 2024 (17:00:00 CET)

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Preprint ARTICLE | doi:10.20944/preprints202203.0371.v6

Entropy and Its Application to Number Theory

Seiji Fujino

Subject: Physical Sciences, Mathematical Physics Keywords: Entropy; Boltzmann principle; Planck's law; Dynamical system; Logistic function; ; fine structure constant; Von Koch's inequality; Riemann Hypothesis; abc conjecture

Online: 30 December 2023 (16:24:49 CET)

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Preprint ARTICLE | doi:10.20944/preprints202312.2191.v1

An Extended Version of the _r+1R_s;k(B;C; z) Matrix Function

Ayman Shehata

Subject: Physical Sciences, Mathematical Physics Keywords: _r+1R_s,k(B, C, z) matrix function; k-fractional integral operators; k-fractional derivative operators; Riemann-Liouville k-fractional integral; k-Gamma matrix function; k-Beta matrix function

Online: 28 December 2023 (15:17:30 CET)

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Preprint ARTICLE | doi:10.20944/preprints202312.2129.v1

Lax Pairs for the Modified KdV Equation

Georgy I. Burde

Subject: Physical Sciences, Mathematical Physics Keywords: integrable equations; Lax pairs; direct method

Online: 28 December 2023 (10:10:24 CET)

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Preprint ARTICLE | doi:10.20944/preprints202203.0371.v5

Entropy and Its Application to Number Theory

Seiji Fujino

Subject: Physical Sciences, Mathematical Physics Keywords: Entropy; Boltzmann principle; Planck's law; Dynamical system; Logistic function; ; fine structure constant; Von Koch's inequality; Riemann Hypothesis; abc conjecture

Online: 18 December 2023 (10:28:51 CET)

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Preprint ARTICLE | doi:10.20944/preprints202312.0939.v1

On a Hierarchy of Vector Derivative Nonlinear Schrodinger Equations

Aleksandr O. Smirnov, Eugeni A. Frolov, Lada L. Dmitrieva

Subject: Physical Sciences, Mathematical Physics Keywords: Spectral curve; Derivative NLS equation; Vector NLS equation; Gerdjikov-Ivanov equation; Multi-phase solution

Online: 13 December 2023 (11:00:38 CET)

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Preprint ARTICLE | doi:10.20944/preprints202305.0066.v2

Interpretation of Entropy by Complex Fluid Dynamics

Seiji Fujino

Subject: Physical Sciences, Mathematical Physics Keywords: Entropy; Complex Fluid Dynamics; Boltzmann principle; Planck law

Online: 11 December 2023 (12:08:12 CET)

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Preprint ARTICLE | doi:10.20944/preprints202203.0371.v4

Entropy and Its Application to Number Theory

Seiji Fujino

Subject: Physical Sciences, Mathematical Physics Keywords: Entropy; Boltzmann principle; Planck's law; Dynamical system; Logistic function; ; fine structure constant; Von Koch's inequality; Riemann Hypothesis; abc conjecture

Online: 29 November 2023 (10:59:25 CET)

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Preprint ARTICLE | doi:10.20944/preprints202311.1673.v1

Quaternion Algebra on 4D Spacetime: The Lorentz Gauge Is a Door to the Invisible World of Dark Matter and Dark Energy

Valeriy Sbitnev

Subject: Physical Sciences, Mathematical Physics Keywords: Navier-Stokes equation; vorticity equation; ; toroidal vortex; irrotational velocity; solenoidal velocity; spiral galaxies; dark matter; dark energy

Online: 27 November 2023 (07:48:01 CET)

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Preprint ARTICLE | doi:10.20944/preprints202311.1244.v1

Exact Response Theory for Time-Dependent and Stochastic Perturbations

Lamberto Rondoni, Leonardo Iannella

Subject: Physical Sciences, Mathematical Physics Keywords: Nonequilibrium phenomena; Dissipation; Time Reversal Invariance; molecular dyanmics

Online: 20 November 2023 (13:55:30 CET)

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Preprint BRIEF REPORT | doi:10.20944/preprints202311.0784.v2

Parameterization of Quantum Interactions

Lester Ingber

Subject: Physical Sciences, Mathematical Physics Keywords: path integral; quantum systems; multiscale modeling; supercomputer

Online: 17 November 2023 (07:56:21 CET)

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Preprint ARTICLE | doi:10.20944/preprints202310.1909.v1

A Quantum Geometric Approach for the Generalization of Spacetime Curvature

Abdel Nasser Tawfik, Tahia Dabash

Subject: Physical Sciences, Mathematical Physics Keywords: noncommutative differential geometry; discretized curved spacetime; gravitized quantum mechanics; quantized general relativity

Online: 30 October 2023 (10:29:30 CET)

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Preprint ARTICLE | doi:10.20944/preprints202310.1482.v1

Dynamics of the Static Star Differential System from the Mathematical and Physical Point of Views

Joan C. Artés, Jaume Llibre, Nicolae Vulpe

Subject: Physical Sciences, Mathematical Physics Keywords: Static star; polynomial vector fields; evolution

Online: 24 October 2023 (07:54:07 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202310.1399.v1

Phase Transitions in the Making of an Elementary Master Equation

Angelo Plastino, Diana Monteoliva

Subject: Physical Sciences, Mathematical Physics Keywords: master equation; phase transitions; entropy; disequilibrium

Online: 23 October 2023 (10:05:46 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202212.0045.v17

The Imaginary Universe

Szymon Łukaszyk

Subject: Physical Sciences, Mathematical Physics Keywords: emergent dimensionality; imaginary dimensions; natural units; fine-structure constant; black holes; neutron stars; white dwarfs; patternless binary messages; complex energy; complex force; Hawking radiation; extended periodic table; general relativity; photon sphere; entropic gravity; gravitational observations; holographic principle; mathematical physics

Online: 20 October 2023 (04:33:33 CEST)

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Maxwell's equations in vacuum provide the negative speed of light -c, which leads to imaginary Planck units. However, the second, negative fine-structure constant $\alpha_2^{-1} \approx -140.178$, present in the Fresnel coefficients for the normal incidence of electromagnetic radiation on monolayer graphene, establishes the different, negative speed of light in vacuum $c_2 \approx -3.06 \times 10^8~\text{[m/s]}$, which introduces imaginary Planck units different in magnitude from those parametrized with $c$. Furthermore, algebraic relations between the fine-structure constant hint that the fine-structure constant does not vary over time. It follows that electric charges are the same in real and imaginary dimensions. We model neutron stars and white dwarfs, emitting perfect black-body radiation, as \textit{objects} having energy exceeding their mass-energy equivalence ratios. We define complex energies in terms of real and imaginary natural units. Their imaginary parts, inaccessible for direct observation, store the excess of these energies. It is conjectured that the maximum atomic number $Z=238$. A black-body \textit{object} is in the equilibrium of complex energies if its radius $R_\text{eq} \approx 1.3833~R_{\text{BH}}$, which is close to the photon sphere radius $R_{\text{ps}}=1.5~R_{\text{BH}}$, and marginally greater than a locally negative energy density bound of $4/3~R_{\text{BH}}$. The complex force between real masses and imaginary charges leads to the black-body object's surface gravity and generalized Hawking radiation temperature, which includes its charge. Furthermore, this force agrees with the physical parameters of the hydrogen atom. The proposed model takes into account the value(s) of the fine-structure constant(s), which is/are otherwise neglected in general relativity, and explains the registered (GWOSC) high masses of neutron stars' mergers and the associated fast radio bursts (CHIME) without resorting to any hypothetical types of exotic stellar \textit{objects}.

Preprint ARTICLE | doi:10.20944/preprints202310.1216.v1

Measuremnt Problem in Statistical Signal Processing

Miloš Milovanović

Subject: Physical Sciences, Mathematical Physics Keywords: experimental mathematics; general measurement; time operator; frame wavelets; optimal decomposition.

Online: 19 October 2023 (07:02:10 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202309.0454.v2

Biased Random Process of Randomly Moving Particles with Fixed Mean and Curl

Baodan Bai, Tao Guo

Subject: Physical Sciences, Mathematical Physics Keywords: Randomly Moving Particles; Biased Motion; Special Relativistic-like Effects; Curl

Online: 17 October 2023 (09:36:38 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202301.0342.v4

Biased Random Process of Randomly Moving Particles with Fixed Mean and Group Velocities

Tao Guo

Subject: Physical Sciences, Mathematical Physics Keywords: biased random process; randomly moving particles; special relativity effect; lorentz-like factor

Online: 16 October 2023 (08:45:20 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202310.0377.v1

Galilean Non-invariance of Maxwell Equations Revisited

Hrvoje Dodig

Subject: Physical Sciences, Mathematical Physics Keywords: Maxwell equations; Lienard-Wiechert fields; Galilean invariance; Galilean transformation; Lorentz transformation

Online: 9 October 2023 (02:56:28 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202212.0045.v16

The Imaginary Universe

Szymon Łukaszyk

Subject: Physical Sciences, Mathematical Physics Keywords: emergent dimensionality; imaginary dimensions; natural units; fine-structure constant; black holes; neutron stars; white dwarfs; patternless binary messages; complex energy; complex force; Hawking radiation; extended periodic table; general relativity; photon sphere; entropic gravity; gravitational observations; holographic principle; mathematical physics

Online: 3 October 2023 (11:53:49 CEST)

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Maxwell's equations in vacuum provide the negative speed of light -c, which leads to imaginary Planck units. However, the second, negative fine-structure constant $\alpha_2^{-1} \approx -140.178$, present in the Fresnel coefficients for the normal incidence of electromagnetic radiation on monolayer graphene, establishes the different, negative speed of light in vacuum $c_2 \approx -3.06 \times 10^8~\text{[m/s]}$, which introduces imaginary Planck units different in magnitude from those parametrized with $c$. Furthermore, algebraic relations between the fine-structure constant hint that the fine-structure constant does not vary over time. It follows that electric charges are the same in real and imaginary dimensions. We model neutron stars and white dwarfs, emitting perfect black-body radiation, as \textit{objects} having energy exceeding their mass-energy equivalence ratios. We define complex energies in terms of real and imaginary natural units. Their imaginary parts, inaccessible for direct observation, store the excess of these energies. It is conjectured that the maximum atomic number $Z=238$. A black-body \textit{object} is in the equilibrium of complex energies if its radius $R_\text{eq} \approx 1.3833~R_{\text{BH}}$, which is close to the photon sphere radius $R_{\text{ps}}=1.5~R_{\text{BH}}$, and marginally greater than a locally negative energy density bound of $4/3~R_{\text{BH}}$. The complex force between real masses and imaginary charges leads to the black-body object's surface gravity and generalized Hawking radiation temperature, which includes its charge. Furthermore, this force agrees with the physical parameters of the hydrogen atom. The proposed model takes into account the value(s) of the fine-structure constant(s), which is/are otherwise neglected in general relativity, and explains the registered (GWOSC) high masses of neutron stars' mergers and the associated fast radio bursts (CHIME) without resorting to any hypothetical types of exotic stellar \textit{objects}.

Preprint ARTICLE | doi:10.20944/preprints202310.0137.v1

Research on Repeated Quantum Games with Public Goods under Strong Reciprocity

Simo Sun, Yadong Shu, Jinxiu Pi, Die Zhou

Subject: Physical Sciences, Mathematical Physics Keywords: Public goods; Repeated game; Strong reciprocity; Quantum entanglement; Pareto

Online: 3 October 2023 (09:32:35 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202310.0076.v1

Exotic Particle Dynamics using Novel Hermitian Spin Matrices

Timothy Ganesan

Subject: Physical Sciences, Mathematical Physics Keywords: exotic particle dynamics; generalized hermitian spin matrices; Pauli matrices; electrodynamics; fermionic quantum Heisenberg model; bosonic spin systems

Online: 3 October 2023 (05:40:19 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202309.2126.v1

Periodic Flows in a Viscous Stratified Fluid in a Homogeneous Gravitational Field

Yuli D. Chashechkin, Artem A. Ochirov

Subject: Physical Sciences, Mathematical Physics Keywords: heterogeneous fluid; stratification; viscosity; compressibility; linear models; complete description; dispersion relations

Online: 30 September 2023 (10:54:13 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202309.1955.v1

Is Bell’s Experiment Really Telling Us Something?

Han Geurdes

Subject: Physical Sciences, Mathematical Physics Keywords: Bell’s correlation formula; Bell’s experiment; basic probability theory

Online: 28 September 2023 (06:42:38 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202309.1831.v1

Phase Shift and Infinitesimal Wave Energy Loss Equations

Soumendra Nath Thakur, Deep Bhattacharjee

Subject: Physical Sciences, Mathematical Physics Keywords: Phase Shift, Phase Angle, Time Distortion, Wave Energy Loss, Wave Phenomena

Online: 27 September 2023 (05:00:38 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202309.1370.v1

Continuous Measure of Symmetry as a Dynamic Variable: a New Glance on the Three-Body Problem

Mark Frenkel, Shraga Shoval, Edward Bormashenko

Subject: Physical Sciences, Mathematical Physics Keywords: three-body problem; Lagrange triangle; continuous measure of symmetry; gravity; Coulomb interaction; asymptotic value

Online: 20 September 2023 (10:38:50 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202309.1221.v1

Anisotropic Fractional Cosmology: K-Essence Theory

J. Socorro, J Juan Rosales, L Toledo Sesma

Subject: Physical Sciences, Mathematical Physics Keywords: Fractional derivative; Fractional Quantum Cosmology; K-essence formalism; Classical and Quantum exact solutions

Online: 19 September 2023 (15:23:55 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202309.0985.v1

Implementation of Elzaki HPM for Semi-Analytical Solution upon Two-Dimensional Fuzzy Fractional Heat Equation

Mamta Kapoor, Prakasha D. G., Veeresha P., Nasser Bin Turki, Nehad Ali Shah

Subject: Physical Sciences, Mathematical Physics Keywords: Elzaki transform; Homotopy Perturbation Method; 2D fuzzy fractional Heat equation.

Online: 14 September 2023 (13:55:10 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202309.0454.v1

Biased Random Process of Randomly Moving Particles with Fixed Mean and Curl

Tao Guo

Subject: Physical Sciences, Mathematical Physics Keywords: Randomly Moving Particles; Biased Motion; Special Relativistic-like Effects; Curl

Online: 7 September 2023 (11:22:12 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202301.0342.v3

Biased Random Process of Randomly Moving Particles with Fixed Mean and Group Velocities

Tao Guo

Subject: Physical Sciences, Mathematical Physics Keywords: Biased Random Process; Randomly Moving Particles; Special Relativity Effect; Lorentz-like factor

Online: 6 September 2023 (10:37:58 CEST)

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Preprint REVIEW | doi:10.20944/preprints202309.0171.v2

Structural Identification of Control Objects—A Review

Nikolay Karabutov

Subject: Physical Sciences, Mathematical Physics Keywords: excitation constancy; geometric structure; Lyapunov exponent; structural identification; structural identifiability; S-synchronization

Online: 6 September 2023 (09:45:35 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202309.0309.v1

On the Variational Treatment of a Class of Double-Well Oscillators

Francisco Fernandez, Javier Garcia

Subject: Physical Sciences, Mathematical Physics Keywords: Double-well oscillator; upper bounds; Rayleiigh-Ritz; Gram-Schmidt

Online: 6 September 2023 (02:37:18 CEST)

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Preprint REVIEW | doi:10.20944/preprints202309.0171.v1

Structural Identification of Control Objects. Review

Nikolay Karabutov

Subject: Physical Sciences, Mathematical Physics Keywords: excitation constancy; geometric structure; Lyapunov exponent; structural identification; structural identifiability; S-synchronization

Online: 5 September 2023 (05:05:17 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202308.2071.v1

Riemann–Hilbert Problems, Polynomial Lax Pairs, Integrable Equations and Their Soliton Solutions

Vladimir Stefanov Gerdjikov, Aleksander Aleksiev Stefanov

Subject: Physical Sciences, Mathematical Physics Keywords: Riemann--Hilbert problem; polynomial Lax pair; integrable equations; soliton solutions

Online: 30 August 2023 (10:18:12 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202308.1564.v2

Spinors and Spatial Vectors Are Part of the Number System; They Are Extensions of Complex Numbers into Three-Dimensional Space

Srinivasa Mugeraya

Subject: Physical Sciences, Mathematical Physics Keywords: Spinor; vector; complex vector; spin; quantum mechanics; isotropic vectors; Hilbert space; division of vector; inversion of vector; three-dimensional number; quaternion; ket (physics); inner product; outer product; cross product; dot product; geometric algebra; vector projection; Stern-Gerlach analyzer; Bloch sphere; General quantum state vector

Online: 30 August 2023 (02:36:14 CEST)

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Spinors are used for the computation of probability in quantum mechanics. They are treated as elements of a complex vector space in contrast to a real vector space. Spinor theory is abstract mathematics with an ambiguous interpretation. The overall phase of spinors does not affect the computation of probability in quantum mechanics. If two spinors have an overall phase of imaginary number i, then they can be treated like vectors in a real vector space. The square of the magnitude of the number, which is the sum of dot product and the term having basis vector i of cross product of two such vectors, is equal to the probability computed using the corresponding spinors. Therefore, the geometry of such spinors can be easily depicted in a three-dimensional space like vectors in a real vector space. Spinors are not isotropic vectors in Hilbert space. The sum of dot product and cross product of two complex numbers is equivalent to the quotient of the division of one complex number by another. Similarly, the sum of dot product and cross product of two vectors is the quotient of the division of one vector by another. Using the rules of division of vectors, we can find the rules of multiplication of vectors. The rules of multiplication and division of basis vector i match the rules of multiplication and division of imaginary number i. Therefore, basis vector i is nothing but imaginary number i. Multiplication of dot and cross product of two vectors to the second vector will give us the components of the first vector that are parallel and orthogonal to the second vector. Vectors are also made up of complex numbers like spinors. The reason for finding dot product of complex numbers in the process of computing the probability is to ignore the overall phase in contrast to the phase difference. This is misconstrued as complex vector space in quantum mechanics. 3-D number which is nothing but a spinor with new notation is an extension of vector algebra. It can have a real number as a term in addition to the terms i, j and k. In all other respects, it is a vector. 3-D numbers are part of the number system like real numbers and complex numbers. The real numbers are one dimensional numbers, the complex numbers are two-dimensional numbers and the 3-D numbers as well as vectors and spinors are three-dimensional numbers. As polarisation and spin are one and the same, we can straight away apply 3-D numbers to polarisation of light. 3-D numbers will greatly simplify the study of areas of science where three-dimensional space is involved.

Preprint ARTICLE | doi:10.20944/preprints202308.1564.v1

Spinors and Spatial Vectors Are Part of the Number System; They Are Extensions of Complex Numbers into Three-Dimensional Space

Srinivasa Mugeraya

Subject: Physical Sciences, Mathematical Physics Keywords: Spinor; vector; complex vector; spin; quantum mechanics; isotropic vectors; Hilbert space; division of vector; inversion of vector; three-dimensional number; quaternion; ket (physics); inner product; outer product; cross product; dot product; geometric algebra; vector projection; Stern-Gerlach analyzer; Bloch sphere; General quantum state vector

Online: 23 August 2023 (02:53:55 CEST)

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Spinors are used for the computation of probability in quantum mechanics. They are treated as elements of a complex vector space in contrast to a real vector space. Spinor theory is abstract mathematics with an ambiguous interpretation. The overall phase of spinors does not affect the computation of probability in quantum mechanics. If two spinors have an overall phase of imaginary number , then they can be treated like vectors in a real vector space. The square of the magnitude of the number, which is the sum of dot product and the term having basis vector of cross product of two such vectors, is equal to the probability computed using the corresponding spinors. Therefore, the geometry of such spinors can be easily depicted in a three-dimensional space like vectors in a real vector space. Spinors are not isotropic vectors in Hilbert space. The sum of dot product and cross product of two complex numbers is equivalent to the quotient of the division of one complex number by another. Similarly, the sum of dot product and cross product of two vectors is the quotient of the division of one vector by another. Using the rules of division of vectors, we can find the rules of multiplication of vectors. The rules of multiplication and division of basis vector match the rules of multiplication and division of imaginary number . Therefore, basis vector is nothing but imaginary number . Multiplication of dot and cross product of two vectors to the second vector will give us the components of the first vector that are parallel and orthogonal to the second vector. Vectors are also made up of complex numbers like spinors. The reason for finding dot product of complex numbers in the process of computing the probability is to ignore the overall phase in contrast to the phase difference. This is misconstrued as complex vector space in quantum mechanics. 3-D number which is nothing but a spinor with new notation is an extension of vector algebra. It can have a real number as a term in addition to the terms , and . In all other respects, it is a vector. 3-D numbers are part of the number system like real numbers and complex numbers. The real numbers are one dimensional numbers, the complex numbers are two-dimensional numbers and the 3-D numbers as well as vectors and spinors are three-dimensional numbers. As polarisation and spin are one and the same, we can straight away apply 3-D numbers to polarisation of light. 3-D numbers will greatly simplify the study of areas of science where three-dimensional space is involved.

Preprint ARTICLE | doi:10.20944/preprints202212.0045.v15

The Imaginary Universe

Szymon Łukaszyk

Subject: Physical Sciences, Mathematical Physics Keywords: emergent dimensionality; imaginary dimensions; natural units; fine-structure constant; black holes; neutron stars; white dwarfs; patternless binary messages; complex energy; complex force; Hawking radiation; extended periodic table; general relativity; entropic gravity; holographic principle; mathematical physics

Online: 21 August 2023 (11:39:16 CEST)

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Maxwell’s equations in vacuum provide the negative speed of light $-c$, which leads to imaginary Planck units. However, the second, negative fine-structure constant $\alpha_2^{-1} \approx -140.178$, present in the Fresnel coefficients for the normal incidence of electromagnetic radiation on monolayer graphene, establishes the different, negative speed of light in vacuum $c_2 \approx -3.06 \times 10^8~\text{[m/s]}$, which introduces imaginary Planck units different in magnitude from those parametrized with $c$. It follows that electric charges are the same in real and imaginary dimensions. We model neutron stars and white dwarfs, emitting perfect black-body radiation, as \textit{objects} having energy exceeding their mass-energy equivalence ratios. We define complex energies in terms of real and imaginary natural units. Their imaginary parts, inaccessible for direct observation, store the excess of these energies. It follows that black holes are fundamentally uncharged, masses of charged neutron stars and white dwarfs satisfy $M \lesssim 5.7275 \times 10^{-10}~[\text{kg}]$, and the radii of white dwarfs' cores are limited to $R_{\text{WD}} \lesssim 3.3967~R_{\text{BH}}$, where $R_{\text{BH}}$ is the Schwarzschild radius of a white dwarf mass. It is conjectured that the maximum atomic number $Z=238$. A black-body \textit{object} is in the equilibrium of complex energies if its radius $R_\text{eq} \approx 1.3833~R_{\text{BH}}$, which is close to the photon sphere radius $R_{\text{ps}}=1.5~R_{\text{BH}}$, and marginally greater than a locally negative energy density bound of $4/3~R_{\text{BH}}$. Complex Newton’s law of universal gravitation, based on complex energies, leads to the black-body object's surface gravity and the generalized Hawking radiation temperature, which includes its charge. The proposed model takes into account the value(s) of the fine-structure constant(s), which is/are otherwise neglected in general relativity, and explains the registered (GWOSC) high masses of neutron stars' mergers and the associated fast radio bursts (CHIME) without resorting to any hypothetical types of exotic stellar \textit{objects}.

Preprint ARTICLE | doi:10.20944/preprints202308.0515.v1

Induced Electrostatic Fields in the Presence of Conductors and Dielectrics: A Purely Laplace Equation-Based Treatment

George Bjornsen

Subject: Physical Sciences, Mathematical Physics Keywords: potential; field; uniqueness; Legendre polynomial

Online: 8 August 2023 (07:34:45 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202308.0608.v1

Seismological Problem, Seismic Waves and the Seismic Mainshock

Bogdan Felix Apostol

Subject: Physical Sciences, Mathematical Physics Keywords: primary seismic waves; seismic mainshock; elastic wave equation; seismic tensorial force; regularization

Online: 8 August 2023 (07:17:12 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202308.0432.v1

Perturbation-Based Non-Perturbative Method

Wu-Sheng Dai

Subject: Physical Sciences, Mathematical Physics Keywords: Non-perturbative Method; Eigenproblem; Analytic continuation; Rational approximation

Online: 7 August 2023 (03:04:12 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202308.0205.v1

Modeling the Complexity of Elliptic Black Hole Solution In 4D Using Hamiltonian Monte Carlo with Stacked Neural Networks

Ehsan Hatefi, Armin Hatefi, Roberto Javier Lopez-Sastre

Subject: Physical Sciences, Mathematical Physics Keywords: mathematical physics; black holes; statistical analysis; computational physics

Online: 2 August 2023 (13:16:28 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202307.1764.v1

On a Model of Propagation of Two Component Nonlinear OpticalWaves

Aleksandr Smirnov, Eugeni Frolov

Subject: Physical Sciences, Mathematical Physics Keywords: spectral curve; derivative NLS equation; lax pair; vector NLS equation; monodromy matrix

Online: 26 July 2023 (08:42:05 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202307.1491.v1

Symmetries of the Energy-Momentum Tensor for Static Plane Symmetric Spacetimes

Fawad Khan, Wajid Ullah, Tahir Hussain, Wojciech Sumelka

Subject: Physical Sciences, Mathematical Physics Keywords: Matter collineations; Static Plane-Symmetric Spacetimes; Contravariant and Mixed Energy-Momentum Tensor

Online: 21 July 2023 (09:34:39 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202307.0515.v1

Quantum Purity as an Information Measure and Nernst law

F. Pennini, A. Plastino

Subject: Physical Sciences, Mathematical Physics Keywords: Nernst law, statistical mechanics, purity

Online: 7 July 2023 (18:58:07 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202307.0480.v1

Magic Numbers and Mixing Degree in Many-Fermion Systems

Angelo Plastino, Angel Ricardo Plastino, Diana Monteoliva

Subject: Physical Sciences, Mathematical Physics Keywords: Tsallis entropy; Many fermion systems; Mixture-degree; Finite temperature; Magic numbers

Online: 7 July 2023 (10:51:53 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202307.0458.v1

Numerical Investigation of a Combustible Polymer in a Rectangular Stockpile: A Spectral Approach

Adeshina T Adeosun, Juel C. Ukaegbu, Ramoshweu S. Lebelo

Subject: Physical Sciences, Mathematical Physics Keywords: Combustible polymer; Carreau fluid; BSLLS; Thermal stability

Online: 7 July 2023 (10:11:28 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202307.0404.v1

Dynamical Behaviours of Matter Wave Positons in Bose-Einstein Condensates

K. Manikandan, N. Serikbayev, S.P. Vijayasree, D. Aravinthan

Subject: Physical Sciences, Mathematical Physics Keywords: Matter waves; Positons; Bose-Einstein condensates; Gross-Pitaevskii equation; Similarity transformation

Online: 6 July 2023 (08:55:56 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202306.1967.v1

SU(3) Brachistochrone and the Isotropic Oscillator

Peter Morrison

Subject: Physical Sciences, Mathematical Physics Keywords: gell-mann; calculus; quantum; control; brachistochrone; optimal; time; operator; eigenstate; eigenmatrix

Online: 28 June 2023 (09:43:37 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202306.1433.v1

Dynamics of Non-autonomous Stochastic Semi-linear Degenerate Parabolic Equations with Nonlinear Noise

Xin Liu, Yan jiao Li

Subject: Physical Sciences, Mathematical Physics Keywords: Stochastic degenerate parabolic equation; Nonlinear noise; Pullback random attractor; Wong-Zakai approximation; Upper semicontinuity

Online: 20 June 2023 (11:02:50 CEST)

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