The present paper reports an exact approach quantifying the electromagnetic contribution to the anomalous magnetic moment occurring in isolated system comprised of non-composite particle carrying elementary electric charge. Essential averaging procedure and regularization of the electromagnetic field potentials necessary when quantifying the electromagnetic self-interactions and when deriving equations of motion without singularities and obeying the conservation laws are thoroughly discussed. The study shows that the dynamics of the considered system is associated to unique classical transcendental equations of motion satisfied by the particle's velocity and the electromagnetic contribution to the anomalous $g$-factor known from the quantum electrodynamics. The equations of motion lead to an exact analytical expression for the anomalous $g$-factor that provides more accurate result than that calculated with the aid of quantum electrodynamics. It matches the experimentally measured value reported in the literature to a one part per trillion. We obtain a_e=0.00115965218000(65) thus reveling the potential of non-perturbative, non-probability methods in predicting the electron's anomalous g-factor.

Myocardial infarction is an uncommon manifestation in anomalous coronary artery (ACA). As usual, the electrocardiogram (ECG) was used to detect myocardial infarction. Unfortunately, the ECG’s pattern could not reveal the ACA’s condition. Some investigators tried to describe the pattern in ECG in ACA’s patients. Due to the rare patients of ACA, it was not yet found.

The electronic transport stability in nanodevices composed by metal/trans-polyacetylene /metal with different long length has contributed greatly for performance, homogeneity, stability, organization of the chains, reproducibility and higher conductivity. In this paper, we present an analytical study of the electronic transport characteristics from dimerized trans-polyacetylene (trans-PA) molecules containing an odd-even number of sites coupled to metal leads (left and right) in T-shaped geometry using the extended Su-Schrieffer-Heeger (SSH) model based on tight-binding Hamiltonian with the Non-Equilibrium Green´s Function (NEGF) via Heisenberg´s equation of motion and the Keldysh´s formalism. Due to the complexity of the T-shaped odd-even chain, our proposal was to test the effects on the finite-length network for three, four, five sites and furthermore foresee for 17-sites. We show how to tune dimerization strength () coupling to the parameters and T-shaped geometry of the device to which it affects the overlap integral localized at the three endpoints of the T-shaped system, making both the odd and even chains to undergo a metal-insulator transition in their electronic behavior. The results reached through control parity of the chain plane of the parameters governing () the electronic and experimental tunneling allow a better understanding of the subject.

Subwavelength hole array (HA) metasurfaces support the so-called extraordinary optical transmission (EOT) resonance that has already been exploited for sensing. In this work, we demonstrate the superior performance of a different resonant regime of HA metasurfaces called anomalous EOT, by doing a thorough numerical and experimental study of its ability as a thin-film label-free sensor in the terahertz (THz) band. A comprehensive analysis using both the regular and anomalous EOT resonances is done by depositing thin layers of a dielectric analyte of different thicknesses on the structures in different scenarios. We carry out a detailed comparison and demonstrate that the best sensing performance is achieved when the structure operates in the anomalous EOT resonance and the analyte is deposited on the non-patterned side, improving by a factor between 2 and 3 the results of the EOT resonance in any of the considered scenarios. This can be explained by the comparatively narrower linewidth of the anomalous EOT resonance. The results presented expand the reach of subwavelength hole arrays for sensing applications by considering the anomalous EOT regime that is usually overlooked in the literature.

Pulsed-field gradient (PFG) diffusion experiments can be used to measure anomalous diffusion in many polymer or biological systems. However, it is still complicated to analyze PFG anomalous diffusion, particularly the finite gradient pulse width (FGPW) effect. In practical applications, the FGPW effect may not be neglected such as in clinical diffusion magnetic resonance imaging (MRI). Here, two significantly different methods are proposed to analyze PFG anomalous diffusion: the effective phase shift diffusion equation (EPSDE) method and an observing the signal intensity at the origin method. The EPSDE method describes the phase evolution in virtual phase space, while the method to observe the signal intensity at the origin describes the magnetization evolution in real space. However, these two approaches give the same general PFG signal attenuation including FGPW effect, which can be numerically evaluated by a direct integration method. The direct integration method is fast and without overflow. It is a convenient numerical evaluation method for Mittag-Leffler function type PFG signal attenuation. The methods here provide a clear view of spin evolution under field gradient, and their results will help the analysis of PFG anomalous diffusion.

An analysis is presented of the possible existence of a second anomalous dipole moment of Dirac’s particle next to the one associated with the angular momentum. It includes a discussion why, in spite of his own derivation, Dirac has doubted about its relevancy. It is shown why since then it has been overlooked and why it has vanished from leading textbooks. A critical survey is given on the reasons of its reject, including the failure of attempts to measure and the perceived violations of time reversal symmetry and charge-parity symmetry. It is emphasized that the anomalous electric dipole moment of the pointlike electron (AEDM) is fundamentally different from the quantum field type electric dipole moment of an electron (eEDM) as defined in the standard model of particle physics. The analysis has resulted into the identification of a third type Dirac particle, next to the electron type and the Majorana particle. It is shown that, unlike as in the case of the electron type, its second anomalous dipole moment is real valued and is therefore subject to polarization in a vector field. Examples are given that it may have a possible impact in the nuclear domain and in the gravitational domain.

Innovative tissue engineering biomimetic hydrogels based on hydrophilic polymers have been investigated for their physical and mechanical properties. 5% to 25% by volume loading PHEMA-nanosilica glassy hybrid samples were equilibrated at 37°C in aqueous physiological isotonic and hypotonic saline solutions (0.15 and 0.05 M NaCl) simulating two limiting possible compositions of physiological extracellular fluids. The glassy and hydrated hybrid materials were characterized both for dynamo-mechanical properties and equilibrium absorptions in the two physiological-like aqueous solutions. Mechanical and the morphological modifications occurring in the samples have been described. The 5% volume nanosilica loading hybrid nanocomposite composition showed mechanical characteristics in the dry and hydrated states that were comparable to those of cortical bone and articular cartilage, respectively, and then chosen for further sorption kinetics characterization. Sorption and swelling kinetics were monitored up to equilibrium. Changes in water activities and osmotic pressures in the water-hybrid systems equilibrated at the two limiting solute molarities of the physiological solutions have been related to the observed anomalous sorption modes using the Flory-Huggins interaction parameter approach. The bulk modulus of the dry and glassy PHEMA-5% nanosilica hybrid at 37°C has been observed to be comparable with the values of the osmotic pressures generated from the sorption of isotonic and hypotonic solutions. The anomalous sorption modes and swelling rates are coherent with the difference between osmotic swelling pressures and hybrid glassy nano-composite bulk modulus: the lower the differences the higher the swelling rate and equilibrium solution uptakes. Bone tissue engineering benefits of use of tuneable biomimetic scaffold biomaterials that can be “designed” to act as biocompatible and biomechanically active hybrid interfaces are discussed.

Electricity price signal is a direct reflection of the attributes of electric power commodities, but due to the influence of market supply and demand, power producers' offer, line capacity and other factors, electricity price signals often show a variety of abnormal forms. The identification and traceability of abnormal tariff signals is an important daily work of power trading centers at all levels. However, at present, it is common to rely on manual experience to analyze the causes of abnormal tariffs, which is inefficient and difficult to ensure the objective and scientific traceability of abnormal tariff causes. Since different types of abnormal tariff signals are caused by different dominant factors, if the key features of abnormal tariffs can be classified and matched, the identification efficiency can be effectively improved. For this reason, this paper proposes a traceability method of abnormal tariffs based on the comparison analysis of key features. First of all, based on the characteristics of historical tariff data, this paper completes the classification of tariff spike magnitude anomaly and tariff mean value anomaly, further establishes the key features of each type of abnormal tariff signal based on principal component analysis, and finally calculates the influence degree of each element within the key features one by one based on alternative algorithms, and then realizes the screening and traceability of the causes of abnormal tariffs based on the importance of the degree of influence ordering. The effectiveness of the proposed method has been verified in a large number of examples constructed based on the actual data of the electricity market, and the average correctness rate of the proposed method for the traceability of the causes of the average value and spike anomalies of the electricity price reaches more than 85%, which can reduce the labor cost in the process of the traceability of the causes of the anomalous electricity price.

The present paper reports exact results for the muon self-energy and anomalous g-factor. A unique to the muon cut-off terms that remove the radial singularity in the system and regularize the corresponding electrodynamics are presented. Equations of motion and a transcendental equation satisfied by the muon anomalous g-factor are derived, with solution a_m=0.001165920162(198). The obtained value matches the latest experimental one found in the literature to about 0.43 ppb ruling out a possible tension between theory and experiment.

The physics of Hubble's law, motivated by the anomalous acceleration of Pioneer 10/11, suggests that the Hubble constant corresponds to a gravitational field of the Universe. The Hubble constant inferred from Pioneer 10/11 data is $\sim 69$ km/s/Mpc. The anomalous acceleration of Pioneer 10/11 can be interpreted as an observational evidence for Mach's principle. The redshift is an apparent value. Its intrinsic value has a limit resulting to $v

As a model for economic and ecological systems, replicator dynamics represents a basic form of agent competition for finite resources. Here, we investigate the effects of stochastic resetting in this kind of processes. Random reset events abruptly lead individual resources to a small value from which dynamics must start anew. Numerical results show that resource distribution over the population of competing agents develops highly nonuniform profiles, exhibiting clustering and fluctuations with anomalous dependence on the population size. This non-standard statistical behavior jeopardizes an analytical treatment based on mean-field assumptions. We propose alternative simplified analytical approaches which provide a stylized description of entropy evolution for the clustered distribution of resources and explain the unusually slow decrease of fluctuations.

An interesting anomaly of the diffusion process with an apparently negative diffusion coefficient defined through the mean-square displacement in a one-dimensional quantum molecular chain model is shown. Nevertheless, the system satisfies the H-theorem, so that the second law of thermodynamics is satisfied. The reason why the “diffusion constant” becomes negative is due to the effect of the phase mixing process, which is a characteristic result of the one-dimensionality of the system. We illustrate the situation where this negative “diffusion constant” appears.

FRAP technique have been used for decades to measure movements of molecules in 2D. Data obtained by FRAP experiments in cell plasma membranes are assumed to be described through means of two parameters, a diffusion coefficient D (as defined in a pure Brownian model) and a mobile fraction M. Nevertheless, it has also been shown that recoveries can be nicely fit using anomalous sub-diffusion. FRAP at variable radii has been developed using the Brownian diffusion model to access geometrical characteristics of the surrounding landscape of the molecule. Here we performed numerical simulations of continuous time random walk (CTRW) anomalous subdiffusion and interpreted them in the context of variable radii FRAP. These simulations were compared to experimental data obtained at variable radii on living cells using the PH domain of the membrane binding protein EFA6 (exchange factor for ARF6, a small G protein). This protein domain is an excellent candidate to explore the structure of the interface between cytosol and plasma membrane in cells. By direct comparison of our numerical simulations to the experiments, we show that this protein does not exhibit anomalous diffusion in BHK cells. The non Brownian PH-EFA6 dynamics observed here is more related to spatial heterogeneities such as cytoskeleton fences effects.

Two clear-air over-the-horizon propagation mechanisms affecting Automatic Identification System (AIS) detection range are considered. Comparison results are presented between the path loss due to tropospheric ducting and path loss due to tropospheric scattering (troposcatter) for the AIS frequencies. The calculations are based on the well-known parabolic equation approximation to the wave equation, in which a simple troposcatter formula is incorporated. In most studied cases the ducting assures significantly greater reduction of path loss than troposcatter even when the AIS frequencies are not well trapped in the duct. Emphasis is placed on elevated trapping layers and some features that may make ducting propagation less favorable in terms of increasing the AIS detection range are discussed.

We develop a quantitative microscopic theory of decaying Turbulence by studying the dimensional reduction of the Navier-Stokes loop equation for the velocity circulation. We have found an infinite dimensional manifold of solutions of the Navier-Stokes loop equation\cite{M93, M23PR} for the Wilson loop in decaying Turbulence in arbitrary dimension $d >2$. This family of solutions corresponds to a fractal curve in complex space $\mathbb C^d$, described by an algebraic equation between consecutive positions plus a nonlinear periodicity condition. We derive the constrained SDE for the evolution of the fractal curve at a fixed moment of physical time as a function of an auxiliary stochastic time. We expect this stochastic process to cover our fixed manifold of the solutions of the decaying Turbulence. The energy density of the fluid decays as $\mathcal E_0/t$, where $\mathcal E_0$ is an initial dissipation rate. Presumably, we have found a new phase of extreme Turbulence yet to be observed in real or numerical experiments.

An analysis is presented of the possible existence of a second anomalous dipole moment of Dirac’s particle next to the angular one. It includes a discussion why, in spite of his own derivation, Dirac has doubted about its relevancy. It is shown why since then it has been overlooked and why it has vanished from leading textbooks. A critical survey is given on the reasons of its reject, including the failure of attempts to measure and the perceived violations of time reversal symmetry and chargeparity symmetry. It is emphasized that the anomalous electric dipole moment of the pointlike electron (AEDM) is fundamentally different from the quantum field type electric dipole moment of an electron (eEDM) as defined in the standard model of particle physics and that its measurement requires different instrumentation. A proposal has been described how to prove or disprove its existence by experiment. Moreover, by reference from literature, the possible impact is discussed in the nuclear domain and in the gravitational domain.

This paper presents a numerical method for solving a two-dimensional subdiffusion equation with a Caputo fractional derivative. The problem considered assumes symmetry in both the equation’s solution domain and the boundary conditions, allowing for a reduction of the two-dimensional equation to a one-dimensional one. The proposed method is an extension of the fractional Crank-Nicolson method, based on the discretization of the equivalent integral-differential equation. To validate the method, the obtained results were compared with a solution obtained through Laplace transform. The analytical solution in the image of the Laplace transform was inverted using the Gaver-Wynn-Rho algorithm implemented in the specialized mathematical computing environment, Wolfram Mathematica. The results clearly show the mutual convergence of the solutions obtained by the two methods.

The task of unsupervised anomalous sound detection (ASD) is challenging for detecting anomalous sounds from a large audio database without any annotated anomalous training data. Many unsupervised methods were proposed, but previous works have confirmed that the classification-based models far exceeds the unsupervised models in ASD. In this paper, we adopt two classification-based anomaly detection models: (1) Outlier classifier is to distinguish anomalous sounds or outliers from the normal; (2) ID classifier identifies anomalies using both the confidence of classification and the similarity of hidden embeddings. We conduct experiments in task 2 of DCASE 2020 challenge, and our ensemble method achieves an averaged area under the curve (AUC) of 95.82% and averaged partial AUC (pAUC) of 92.32%, which outperforms the state-of-the-art models.

The central limit theorem (CLT) and its generalization to stable distributions have been widely described in literature. However, many variations of the theorem have been defined and often their applicability in practical situations is not straightforward. In particular, the applicability of the CLT is essential for a derivation of heterogeneous ensemble of Brownian particles (HEBP). Here, we analyze the role of the CLT within the HEBP approach in more detail and derive the conditions under which the existing theorems are valid.

We study the Kelvinons: monopole ring solutions to the Euler equations, regularized as the Burgers vortex in the viscous core. There is finite anomalous dissipation in the inviscid limit. However, in the anomalous Hamiltonian, some terms are growing as logarithms of Reynolds number; these terms come from the core of the Burgers vortex. In our theory, the turbulent multifractal phenomenon is similar to asymptotic freedom in QCD, with these logarithmic terms summed up by an RG equation. The small effective coupling does not imply small velocity; on the contrary, velocity is large compared to its fluctuations, which opens the way for a quantitative theory. In the leading order in the perturbation theory in this effective coupling constant, we compute running multifractal dimensions for high moments of velocity circulation, in good agreement with the data for quantum Turbulence and available data for classical Turbulence. The logarithmic dependence of fractal dimensions on the loop size comes from the running coupling in anomalous dimensions. This slow logarithmic drift of fractal dimensions would be barely observable at Reynolds numbers achievable at modern DNS.

Natural circulation loop (NCL) systems are buoyancy-driven heat exchangers that are used in various industrial applications. The concept of passive heat exchange in NCL systems is attractive, because there is no need for an externally driven equipment (e.g., a pump) to maintain the fluid circulation. However, relying on buoyancy as the sole driving force may lead to several potential difficulties, one of which is generation of (possibly) time-varying nonlinearities in the dynamical system, where a difference in the time scales of heat transfer and fluid flow causes the flow to change from a steady-state regime to either an oscillatory regime or a flow-reversal regime, both of which are undesirable. In this paper, tools of symbolic time series analysis (e.g., probabilistic finite state automata (PFSA)) are proposed to identify selected regimes of operation in NCL systems, where the underlying principle is built upon the concept of pattern classification from measurements of fluid-flow dynamics. The proposed method is shown to be capable of identifying the current regime of operation from the initial time response under a given set of operational parameters. The efficacy of regime classification is demonstrated by testing on two data sets, generated from numerical simulation of a MATLAB SimuLink model that has previously been validated with experimental data. The results of the proposed PFSA-based classification are compared with those of a hidden Markov model (HMM) that serves as the baseline.

This is the second paper in a cycle investigating the exact solution of loop equations in decaying turbulence. We perform numerical simulations of the Euler ensemble, suggested in the previous work, as a solution to the loop equations. We designed novel algorithms for simulation, which take a small amount of computer RAM so that only the CPU time grows linearly with the size of the system and its statistics. This algorithm allows us to simulate systems with billions of discontinuity points on our fractal curve, dual to the decaying turbulence. For the vorticity correlation function, we obtain \textbf{quantum fractal laws} with regime changes between universal discrete values of indexes. The traditional description of turbulence with fractal or multifractal scaling laws does not apply here. The measured conditional probabilities of fluctuating variables are smooth functions of the logarithm of scale, with statistical errors being negligible at our large number of random samples $T = 167,772,160$ with $N = 200,000,000$ points on a fractal curve. The quantum jumps arise from the analytical distribution of scaling variable $X = \frac{\cot^2(\pi p/q)}{q^2}$ where $\frac{p}{q}$ is a random fraction. This distribution is related to the totient summatory function and is a discontinuous function of $X$. In particular, the energy spectrum is a devil's staircase with tilted uneven steps with slopes between $-1$ and $-2.03$. The logarithmic derivative of energy decay $n(t)$ as a function of time is jumping down the stairs of universal levels between $1.50$ and $1.53$. The quantitative verification of this quantization would require more precise experimental data.

This paper brings to fruition recently found \cite{migdal2023exact} exact reduction of decaying turbulence in the Navier-Stokes equation in $3 + 1$ dimensions to a Number Theory problem of finding the statistical limit of the Euler ensemble. We reformulate the Euler ensemble as a Markov chain and show the equivalence of this formulation to the \textbf{quantum} statistical theory of $N$ fermions on a ring, with an external field related to the random fractions of $\pi$. We find the solution of this system in the turbulent limit $N\to \infty, \nu \to 0$ in terms of a complex trajectory (instanton) providing a saddle point to the path integral over the density of these fermions. This results in an analytic formula for the observable correlation function of vorticity in wavevector space. This is a full solution of decaying turbulence from the first principle without approximations or fitted parameters. The energy spectrum decays as $k^{-\frac{7}{2}}$. We compute resulting integrals in \Mathematica{} and present effective index $n(t) = -t\partial_t \log E $ for the energy decay as a function of time Fig.\ref{fig::NPlot}. The asymptotic value of the effective index in energy decay $n(\infty) = \frac{5}{4}$, but the universal function $n(t)$ is neither constant nor linear.

In the last ten years, plasma waste treatment has gained increasing prominence as a technology in response to growing challenges in waste disposal and the recognition of opportunities for generating valuable by-products. The efficiency and outcomes of this process are intricately linked to the characteristics of the plasma involved, such as plasma enthalpy and heat flux. We employed an experimental radio frequency inductively coupled plasma (RF-ICP) torch operating at atmospheric pressure to generate plasma. Utilizing optical emission spectroscopy (OES), we measured plasma parameters, specifically the effective electron temperature (Teff) and plasma density (ne), while varying argon gas flow rates and RF powers. Our investigations revealed that both flow rate and RF power exert significant control over plasma parameters, and we observed an unusual phenomenon within this range of discharge pressures. Consequently, both the plasma's enthalpy and the heat flux it generates are influenced by variations in both flow rate and RF power.

We have found an infinite dimensional manifold of exact solutions of the Navier-Stokes loop equation for the Wilson loop in decaying Turbulence in arbitrary dimension $d >2$. This solution family is equivalent to a fractal curve in complex space $\mathbb C^d$ with random steps parametrized by $N$ Ising variables $\sigma_i=\pm 1$, in addition to a rational number $\frac{p}{q}$ and an integer winding number $r$, related by $\sum \sigma_i = q r$. This equivalence provides a \textbf{dual} theory describing a strong turbulent phase of the Navier-Stokes flow in $\mathbb R_d$ space as a random geometry in a different space, like ADS/CFT correspondence in gauge theory. From a mathematical point of view, this theory implements a stochastic solution of the unforced Navier-Stokes equations. For a theoretical physicist, this is a \textbf{quantum} statistical system with integer-valued parameters, satisfying some number theory constraints. Its long-range interaction leads to critical phenomena when its size $N \rightarrow \infty$ or its chemical potential $\mu \rightarrow 0$. The system with fixed $N$ has different asymptotics at odd and even $N\rightarrow \infty$, but the limit $\mu \rightarrow 0$ is well defined. The energy dissipation rate is analytically calculated as a function of $\mu$ using methods of number theory. It grows as $\nu/\mu^2$ in the continuum limit $\mu \rightarrow 0$, leading to anomalous dissipation at $\mu \propto \sqrt{\nu} \to 0$. The same method is used to compute all the local vorticity distribution, which has no continuum limit but is renormalizable in the sense that infinities can be absorbed into the redefinition of the parameters. The small perturbation of the fixed manifold satisfies the linear equation we solved in a general form. This perturbation decays as $t^{-\lambda}$, where the anomalous dimensions $\lambda$ satisfy the spectral equation \eqref{spectralEq}. The spectrum becomes a continuum in the statistical limit $N \to \infty$, presumably leading to multifractal phenomena.

Fractional differential equations have become a fundamental modelling approach for understanding and simulating the many aspects of nonlocality and spatial heterogeneity of complex materials and systems. Yet, while real-order fractional operators are nowadays widely adopted, little progress has been made in extending such operators to complex-order counterparts. In this work, we introduce new definitions for the complex-order fractional Laplacian, fully consistent with the theory of averaging of smooth functions over fractal sets, and present tailored spectral methods for their numerical treatment. The proposed complex-order operators exhibit a dual particle-wave behaviour, with solutions manifesting wave-like features depending on the magnitude of the imaginary part of the fractional order. Reaction-diffusion systems driven by the complex-order fractional Laplacian exhibit unique spatio-temporal dynamics, such as equilibrium of diffusion in random materials by interference of scattered waves, conduction block and highly fractionated propagation, or the generation of completely novel Turing patterns. Taken together, our results support that the proposed complex-order operators hold unparalleled capabilities to advance the description of multiscale transport phenomena in physical and biological processes highly influenced by the heterogeneity of complex media.

We show that the compound samarium hexaboride is a strong topological insulator using the eigenvalues of the space inversion operator in the low-energy limit of the periodic Anderson model. Additionally, we assume the presence of the ferromagnetic exchange interaction (M). A Dirac cone like feature in the surface state energy spectra is observed for M equals zero in a certain parameter range. For M not equal to zero, there is no Kramers degeneracy. We have been able to show that this phase corresponds to the quantum anomalous Hall state by calculating Berry curvature and the Chern number. Using Floquet theory, we further show that the access to a novel state with broken time reversal symmetry is possible due to the normal incidence of circularly polarized optical field on the surface of the compound despite M being absent.

In this paper, we revisit a modified version of the classical Whitehead's theory of gravity in which all possible bilinear forms are considered to define the corresponding metric. Although, this is a linear theory that fails to give accurate results for the most sophisticated predictions of general relativity, such as gravity waves, it can still provide a convenient framework to analyze some new phenomena in the Solar System. In particular, recent development in the accurate tracking of spacecraft and the ephemerides of planetary positions have revealed certain anomalies in relation with our standard paradigm for celestial mechanics. Among them the so-called flyby anomaly and the anomalous increase of the astronomical unit play a prominent role. In the first case the total energy of the spacecraft changes during the flyby and a secular variation of the semi-major axis of the planetary orbits is found in the second anomaly. For this to happen it seems that a net energy and angular momentum transfer is taken place among the orbiting and the central body. We evaluate the total transfer per revolution for a planet orbiting the Sun in order to predict the astronomical unit anomaly in the context of Whitehead's theory. This could lead to a more deeply founded hypothesis for an extended gravity model.

Master equations define the dynamics that govern the time evolution of various physical processes on lattices. In the continuum limit, master equations lead to Fokker-Planck partial differential equations that represent the dynamics of physical systems in continuous spaces. Over the last few decades, nonlinear Fokker-Planck equations have become very popular in condensed matter physics and in statistical physics. Numerical solutions of these equations require the use of discretization schemes. However, the discrete evolution equation obtained by the discretization of a Fokker-Planck partial differential equation depends on the specific discretization scheme. In general, the discretized form is different from the master equation that has generated the respective Fokker-Planck equation in the continuum limit. Therefore, the knowledge of the master equation associated with a given Fokker-Planck equation is extremely important for the correct numerical integration of the latter, since it provides a unique, physically motivated discretization scheme. This paper shows that the Kinetic Interaction Principle (KIP) that governs the particle kinetics of many body systems, introduced in [G. Kaniadakis, Physica A 296, 405 (2001)], univocally defines a very simple master equation that in the continuum limit yields the nonlinear Fokker-Planck equation in its most general form.

In this paper we present the measurement of charged pion two-particle femtoscopic correlation functions in $\sqrt{S_{NN}}$= 200 GeV Au+Au collisions, in 31 average transverse mass bins, separately for positive and negative pion pairs. Lévy-shaped source distributions yield a statistically acceptable description of the measured correlation functions, with three physical parameters: correlation strength parameter λ , Lévy index α and Lévy scale parameter R. The transverse mass dependence of these Lévy parameters is then investigated. Their physical interpretation is also discussed, and the appearance of a new scaling variable is observed.

Magnetic nanoparticles are met across many biological species ranging from magnetosensitive bacteria, fishes, bees, bats, rats, birds, to humans. They can be both of biogenetic origin and due to environmental contamination, being either in paramagnetic or ferromagnetic state. The energy of such naturally occurring single-domain magnetic nanoparticles can reach up to 10-20 room k_BT in the magnetic field of the Earth, which naturally led to supposition that they can serve as sensory elements in various animals. This work explores within a stochastic modeling framework a fascinating hypothesis of magnetosensitive ion channels with magnetic nanoparticles serving as sensory elements, especially, how realistic it is given a highly dissipative viscoelastic interior of living cells and typical sizes of nanoparticles possibly involved.

The spin magnetic moments and spin g factors (g_s = -2) of electron, muon and tau are explained based on the electric charges (EC) and lepton charges (LC) in terms of the three-dimensional quantized space model. The spin g factors of electron, muon and tau are g_s = -2 which is the sum of the EC g factor (g_EC = -1) and the LC g factor (g_LC = -1). The spin g factor (g_s = -2) of the electron is predicted by the Dirac’s equation. The orbit g factors of electron, muon and tau are g_L = g_EC = -1 from the EC g factor (g_EC = -1) without the contribution of the LC g factor (g_LC = -1). The spin g factors of the elementary fermions are calculated from the equation of g_s = g_EC + g_LC + g_CC where g_EC = EC/|EC|, g_LC = LC/|LC| and g_CC = CC/|CC|. For example, the spin g factors of the neutrinos and dark matters are g_s = -1. The spin g factors of the u and d quarks are g_s = 0 and g_s = -2, respectively. The g factor problem of neutrinos with the non-zero LC charges are solved by the LC Coulomb force of F_c(LC) ≈0. It is, for the first time, proposed that the binary motion (fluctuations) of the m_EC and m_LC masses for the electron, muon and tau leptons make the anomalous g factor. This binary motion could be originated from the virtual particle processes including the photons. Also, the weak force (beta) decay is closely related to the binary motion of the m_EC and m_LC for the electron, muon and tau leptons.

Experiments to measure a single molecule/particle, i.e. an individual molecule/particle, at room temperature or under physiological conditions without immobilization, for example on a surface, or without significant hydrodynamic flow have so far failed. This failure has given impetus to the underlying theory of Brownian molecular motion towards its stochastics due to diffusion. Quantifying the thermodynamic jitter of molecules/particles inspires many and forms the theoretical basis of single-molecule/single-particle biophysics and biochemistry. For the first time, our simulation results for a live cell (cytoplasm) show that the tracks of individual single molecules are localized in Brownian motion, while there is fanning out in fractal diffusion (anomalous diffusion).

In this paper, we review a new treatment of classical radiation damping, which resolves a well-known contradiction in the Abraham-Lorentz equation that has long been a concern. This radiation damping problem has already been solved in quantum mechanics by the method introduced by Friedrichs. Based on Friedrichs’ treatment, we solved this long-standing problem by classicizing quantum mechanics by replacing the canonical commutation relation in quantum mechanics with the Poisson bracket relation in classical mechanics. As an application of our new approach, we will analyze the anomalous damping experienced by electrons undergoing cyclotron motion inside a waveguide near the cut-off frequency. This anomalous damping cannot be described using the existing Abraham-Lorentz equation.

Experiments to measure a single molecule/particle, i.e. an individual molecule/particle, at room temperature or under physiological conditions without immobilization, for example on a surface, or without significant hydrodynamic flow have so far failed. This failure has given impetus to the underlying theory of Brownian molecular motion towards its stochastics due to diffusion. Quantifying the thermodynamic jitter of molecules/particles inspires many and forms the theoretical basis of single-molecule/single-particle biophysics and biochemistry. For the first time, our simulation results for a live cell (cytoplasm) show that the tracks of individual single molecules are localized in Brownian motion, while there is fanning out in fractal diffusion (anomalous diffusion).

In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long–range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long–range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations and agent–based models. Reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first–passage time distributions. Research has lead us to question whether the observed long–range memory is a result of actual long–range memory process or just a consequence of non–linearity of Markov processes. As our most recent result we discuss the long–range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the ARFIMA sample series. Our newly obtained results seem indicate that new estimators of self–similarity and long–range memory for analyzing systems with non–Gaussian distributions have to be developed.