In this paper we give approximations to the Mittag-Leffler functions in terms of elementary functions using different methods. This allowed us to establish a practical method we called integerization principle. This principle states that many fractional nonlinear oscillators may be solved by means of the solution to some integer-order Duffing oscillator equation. The accuracy of the obtained results is illsutrated in concrete examples. Formulas for estimating the errors in the approximations are also provided.

The paper is dedicated to the numerical and experimental study of nonlinear oscillations exhibited by the Vilnius chaotic generator. The need for practical applicability of the mentioned generator in chaotic communication systems defined the necessity to study the operation of the circuit in a wide parameter range. The bifurcation maps and corresponding one-parameter diagrams, obtained and analysed utilising the Method of Complete Bifurcation Groups, reveal the complex nonlinear dynamics and regions of robust chaotic oscillations. Laboratory experiments allow the verification of the numerical results and identification of the most practically relevant phenomena.

As known all physical properties of solids are described well by the system of quantum linear harmonic oscillators. It is shown in the present paper that the system consisting of classical linear harmonic oscillators having temperature dependent masses or (and) frequencies has the same partition function as the system consisting of quantum linear harmonic oscillators having temperature independent masses and frequencies while the means of the square displacements of the positions of the oscillators from their mean positions for the system consisting of classical linear harmonic oscillators having: the temperature dependent masses; temperature dependent frequencies; and temperature dependent masses and frequencies differ from each other and from that of the system consisting of quantum linear harmonic oscillators, and hence, the system consisting of classical linear harmonic oscillators describes well the thermodynamic properties of the system consisting of quantum linear harmonic oscillators and solids.

Sixty years ago in the lab adjacent to Fred Sanger (1958 Nobel Prize for protein chemistry), I discovered the cell surface hydroxyproline-rich glycoproteins. Nature keeps some of her secrets longer than others. It has taken many years to dissect the molecular function and biological role of extensins and arabinogalactan proteins (AGPs). Extensins template the formation of new cell walls. AGPs remained baffling and enigmatic until a Eureka moment when computer prediction of AGP calcium binding depicted paired glucuronic acid residues and thus the likely role of a cell surface AGP-Ca²⁺capacitor: In conjunction with the auxin-activated proton pump that releases bound Ca²⁺ it led us to formulate the Hechtian Growth Oscillator as A Global Paradigm with a pivotal role in Ca²⁺ homeostasis. The ramifications are profound. They cannot be shrugged off with sceptical disdain but demand critical reappraisal of current dogma. Phyllotaxis is an ancient problem; it involves an essential role for auxin and the auxin efflux “PIN” proteins together with mechanotransduction of stress-strain as phyllotactic determinants. However, a general explanation remains elusive despite much effort, particularly by mathematicians. Here we propose a novel biochemical algorithm: Hechtian oscillator transduction of cell wall stress generates phyllotactic patterns quite independent of a mathematical approach. Plants simply use different rules and follow a different route.

The physics of the human brain has two components – basic physics common to all mammals and the physics of thinking inherent only in man. The development of the mental component of the structural and functional organization of the brain in phylogeny was associated with the chiral factor of the external environment, and in ontogenesis - with the social factor. The sensitivity of the brain to these factors was based on the single-connected nature of its aqueous basis, the mechanism of electromagnetic induction, and the features of the thermodynamics of the brain in a state of night sleep. In order to unify the description of the mechanism of electromagnetic processes in the brain, the concept of a quasiphoton has been introduced, combining all forms of excitation of electronic and molecular-cellular structures of the brain. Equivalent schemes of vibrational contours of neural network elements and macrostructures of the brain are proposed. Estimates of the kinetic parameters (activation energy, velocity) of the physical processes underlying the energy-information exchange of the brain with the external environment are made. Mechanisms of operative (physical) and permanent (chemical) memory of the brain, including a model of nonlocal quantum correlations, are discussed.

Data on the atmospheric gas concentrations can be received with high efficiency and on a large spatial scale only from remote laser sounding instruments. The remote laser techniques with the use of lidars are widely used in the study of the atmosphere and control of its state. The aims of this work are the design and test in numerical and field experiments of a DIAL OPO lidar system based on KTA and KTP crystals for gas analysis of the atmosphere. Lidar measurements of atmospheric gases in the near/mid infrared region have been numerically simulated. The differential absorption lidar system based on optical parametric oscillators with nonlinear KTA and KTP crystals which allow laser radiation tuning both in the near and in the middle IR spectral region is described; it allows tuning laser radiation in the near/mid-IR wavelength regions. Lidar echo signals have been experimentally recorded in the 1.8–2.5 and 3–4 m wavelength ranges. The results of H2O and CO2 profile measurements along the surface sounding path are presented.

We compare the well known Rayleigh-Ritz variational method (RRVM) with a recently proposed approach based on supersymmetric quantum mechanics and the Gram-Schmidt orthogonalization method (SSQMGS). We apply both procedures to a particular class of double-well harmonic oscillators that had been conveniently chosen for the application of the latter approach. The RRVM eigenvalues converge smoothly from above providing much more accurate results with less computational effort. Present results show that the unproved SSQMGS upper bounds do not hold.

To build a stable power factor and high output accuracy, it should use balanced active and reactive power, also used ultrasonic PWM was used with the frequencies (20–500 kHz). I also used a three-phase dynamic load at the output system and was connected to the compound splicing (CS) system this is a novelty. An oscillator circuit with 4Ghz as a microcontroller is a novelty, and designing ADC is utilized to increase accuracy, as well as contribute to the reduction of loss brought on by the characteristics of voltage source inverters (VSI), such as dead time determined by the excess voltage or voltage drop in the inverter, circumstances abnormal to the load current, such as short circuit current in the production phase, and so forth. The innovation relates to the inverter's load sensing circuit, current smoothing during operation, reaction, spontaneous power factor enhancement of the inverter, and correction of reactive power of passive devices. This invention contributes to the advancement of D.C to A.C power converter by the achievement of extremely low losses, excellent precision, and lightweight construction. Additionally, the accuracy ranges from 99%, and the total harmonic distortion (THD) of the voltage and current is (0.1%-0.8%). We Power MOSFET are used, along with FPGA to improve control over the creation of ultrasonic PWM signals, the programmable peripheral interface (PPI) 8255A for regulatory work. The marks serve as proof of this.

The oscillation of an elastically mounted rigid cylinder excited by steady fluid flow is investigated. Regarding the nonlinearity of real practical structures like marine risers and the stay cable of a long-span bridge, the dynamic behavior of the circular cylinder is described by double Duffing equations and the aerodynamic force performance of the wake flow is expressed by wake oscillator equation. Unlike previous studies, in the present investigation, attention is focused on coupling the wake oscillator equations, taking into account quadratic terms. Following this approach, the cylinder's combined cross-flow and in-line Vortex-Induced Vibrations (VIV) are modeled more accurately. Empirical coefficients are adjusted through comparison with previous credible experimental studies and the effects of changing coefficients of the quadratic terms on major VIV parameters are investigated. The oscillating amplitude calculated by the present model is close to that of the experiment. The relative error of results obtained by the present coupled model is lower than the previous model. Moreover, the present model successfully predicts the moving trajectories of a circular cylinder under VIV in a figure-of-eight shape.

Current sources play an essential role in tissue excitation used in bioelectrical impedance spectroscopy. Most investigations use Howland current sources that, despite their practicality and simplified implementation, have operating frequency limitations and dependence on the load impedance due to theirs narrow output impedance, specially at higher frequencies. The objective of this work is to propose model for a robust current-controlled sinusoidal oscillator. The oscillator is based on fully analog electronics, which enables controlling oscillation phase and amplitude by using a voltage reference. The mathematical model is based on Pyragas control application to the classical harmonic oscillator. From the modelling process, it was build an oscillator topology based on second-generation current carriers and on transconductance amplifiers. The reference signal (Fsync) was a sinusoidal voltage source having a frequency of 1MHz and an amplitude of 1Vpp. The oscillator output current synchronized the oscillations’ phase and amplitude with Fsync, regardless of their magnitude before the control signal acted in the circuit at t≈13.5μs. SPICE simulations using ideal components have confirmed the successful operation of the proposed oscillator. This type of oscillator can be implemented in SOIC, then allowing oscillation control interface with logic circuits.

Life evolved in an euxinic world with subsequent oxic 'invasion' leading to two parallel but interconnected biospheres, hydrogen sulphide (H₂S) and hydrogen peroxide (H₂O₂) exemplify these worlds respectively. Their concentration gradients have informational value in meromictic lakes. Similarly, it is posited, there exists a whole body chemocline in humans in which the two molecules form an inversely coupled oxic/sulphidic oscillator (OSO). The OSO is hormetic and characterised by a range of amplitudes and frequencies in health. Deviations from its baseline profile heralds the onset of SIRS before the appearance of clinical signs. Loss of oscillator status and transition to a steady state causes widespread intercellular and inter-organ communication failure presaging multi-organ dysfunction. The salient clinico-pathophysiological features of SIRS of any aetiology are emergent phenomena related to the OSO profile. Extent of recovery of organ function will mirror the recovery of the OSO profile thereby providing a tool to predict outcomes in SIRS.

Morphogenesis remains a riddle, wrapped in a mystery, inside an enigma. It remains a formidable problem viewed from many different perspectives of morphology, genetics, and computational modelling. We propose a biochemical reductionist approach that shows how both internal and external physical forces contribute to plant morphogenesis via mechanical stress-strain transduction from the primary cell wall tethered to the plasma membrane by a specific arabinogalactan protein (AGP). The resulting stress vector with direction defined by Hechtian adhesion sites, has a magnitude of a few picoNewtons amplified by a hypothetical Hechtian growth oscillator. This paradigm shift involves stress activated plasma membrane Ca2+channels and auxin-activated H+-ATPase. The proton pump dissociates periplasmic AGP-glycomodules that bind Ca2+. Thus, as the immediate source of cytosolic Ca2+ an AGP-Ca2+ capacitor directs vectorial exocytosis of cell wall precursors and auxin efflux (PIN) proteins. In toto these components comprise the Hechtian Oscillator and also the gravisensor. Thus interdependent auxin and Ca2+ morphogen gradients account for the predominance of AGPs. The size and location of a cell surface AGP-Ca2+ capacitor is essential to differentiation and explains AGP correlation with all stages of morphogenetic patterning from embryogenesis to root and shoot. Finally, evolutionary origins of the Hechtian Oscillator in the unicellular Chlorophycean algae reflect the ubiquitous role of chemiosmotic proton pumps that preceded DNA at the dawn of life.

In this paper, a low-power Injection-Locked Clock and Data Recovery (ILCDR) using 28nm FDSOI technology is presented. The back-gate auto-biasing of UTBB-FDSOI transistors allows us to create a QRO (Quadrature Ring Oscillator) reducing both size and power consumption. By injecting a digital signal into this circuit, we realize an Injection-Locked Oscillator (ILO) with low jitter. Thanks to the good performance of this oscillator, we propose a low power ILCDR with fast locking time and low jitter for burst-mode applications. The main novelty consists in the implementation of a complementary QRO based on back-gate control using FDSOI technology to realize a simple and efficient ILCDR circuit. With a Pseudo-Random Binary Sequence (PRBS7) at 868Mbps, the recovered clock jitter is 26.7ps (2.3%UIp-p) and the recovered data jitter is 11.9ps (1%UIp-p). With a 0.6V power supply, the power consumption is 318μW. The estimated Chip area is around 6600μm².

We use a recently proposed formulation of quantum mechanics based, not on potential functions but rather, on orthogonal energy polynomials. In this context, the most important building block of a quantum mechanical system, which is the wavefunction at a given energy, is expressed as pointwise convergent series of square integrable functions in configuration space. The expansion coefficients of the series are orthogonal polynomials in the energy; they contain all physical information about the system. No reference is made at all to the usual potential function. We consider, in this new formulation, few representative problems at the level of undergraduate students who took at least two courses in quantum mechanics and are familiar with the basics of orthogonal polynomials. The objective is to demonstrate the viability of this formulation of quantum mechanics and its power in generating rich energy spectra illustrating the physical significance of these energy polynomials in the description of a quantum system. To assist students, partial solutions are given in an appendix as tables and figures.

A lightweight image encryption algorithm based on chaos induction via a 5-dimensional hyperjerk oscillator (5DHO) is presented. First, the dynamics of our 5DHO network is investigated and shown to exhibit up to five coexisting hidden attractors in the state space that depend exclusively on the system’s initial values. Further, a simple implementation of the circuit was used to validate its ability to exhibit chaotic dynamical properties. Second, an Arduino UNO platform is used to confirm the usability of our oscillator in digital implementation of the system. Finally, an efficient image encryption application is executed using the proposed chaotic networks based on the use of permutation-substitution sequences. The superior qualities of the proposed strategy are traced to the dynamic set of keys used in the substitution process which heralds the generation of the final ciphered image. Based on the results obtained from the entropy analysis (7.9976), NPCR values (99.62), UACI tests (33.69) and encryption execution time for 512x512 images (0.1179 sec), the proposed algorithm is adjudged to be fast and robust to differential and statistical attacks relative to similar approaches.

Chaotic systems are systems whose results are sensitive to the initial conditions. Chaotic systems generally have nonlinearities that can be difficult to model. One example of a chaotic system with nonlinearities is the Lorenz system. The Lorenz system can be used to model weather, wind disturbances, and electronic circuit design, among other applications. In this manuscript, the Lorenz system is modeled and various control methods are applied in an effort to dictate the system’s state and rate trajectories. The combination of the linear feedback and nonlinear feedforward controllers can show over an 80% improvement in state trajectory errors when compared to the baseline run. However, the improved state trajectory performance comes at a cost of as much as 1800% error in the rate trajectories.

Novel molecular pinball machines of the plasma membrane control cytosolic Ca²⁺ levels that regulate plant metabolism. [https://youtu.be/zABg7LiBk88] Essential components involve: 1. an auxin-activated proton pump; 2. arabinogalactan glycoproteins (AGPs); 3. Ca²⁺ channels; 4. auxin-efflux “PIN” proteins. Typical pinball machines release pinballs that trigger various sound and visual effects. However, in plants “proton pinballs” eject Ca²⁺ bound by paired glucuronic acid residues of numerous glycomodules in periplasmic AGP-Ca²⁺. Freed Ca²⁺ ions flow down the electrostatic gradient through open Ca²⁺ channels into the cytosol thus activating numerous Ca²⁺-dependent activities.Clearly cytosolic Ca²⁺ levels depend on activity of the proton pump, the state of Ca²⁺ channels and size of the periplasmic AGP-Ca²⁺ capacitor: Proton pump activation is a major regulatory focal point tightly controlled by the supply of auxin: auxin efflux carriers conveniently known as “PIN” proteins [null mutants are pin-shaped!] pump auxin from cell to cell. Mechanosensitive Ca²⁺ channels and their activation by reactive oxygen species (ROS) are yet another factor regulating cytosolic Ca²⁺.Cell expansion also triggers proton pump/pinball activity by mechanotransduction of wall stress via Hechtian adhesion thus forming a Hechtian oscillator that underlies cycles of wall plasticity and oscillatory growth.Finally, Ca²⁺ homeostasis of plants depends on cell surface external storage as source of dynamic Ca²⁺, unlike the internal ER storage source of animals where the added regulatory complexities ranging from vitamin D to parathormone contrast with the elegant simplicity of plant life. This paper summarises a sixty year Odyssey.

In this paper, we address the energy eigenvalues of two-dimensional Dirac oscillator perturbed by dynamical noncommutative space. We derived the relativistic Hamiltonian of Dirac oscillator in dynamical noncommutative space ($\tau$-space), in which the space-space Heisenberg–like commutation relations and noncommutative parameter are position-dependent. Then used this Hamiltonian to calculate the first-order correction to the eigenvalues and eigenvectors, based on the second quantization and using the perturbation theory. It is shown that the energy shift depends on the dynamical noncommutative parameter $\tau$. Knowing that with a set of two-dimensional Bopp-shift transformation, we mapped the noncommutative problem to the standard commutative one.

This paper introduces the complex Rayleigh-van der Pol-Duffing oscillators (RVDOs), which are hyperchaotic and can be either autonomous or non-autonomous. The fundamental dynamics of the autonomous and nonautonomous complex RVDOs including dissipation, symmetry, fixed points and their stability are studied. These oscillators are found in various important fields of physics and engineering. The paper proposes a scheme to achieve phase synchronization (PS) and antiphase synchronization (APS) for different dimensional models. These kinds of synchronization are considered as generalization of several other types of synchronization. For this scheme we use the active control method based on Lyapunov stability theory. By analytically determining the control functions, the scheme achieved PS and APS. Our scheme is applied to study PS of hyperchaotic behaviours for two distinct hyperchaotic non-autonomous and autonomous complex RVDOs. Additionally, the scheme is employed to achieve APS of chaotic real non-autonomous RVDO and hyperchaotic complex autonomous RVDO, including those with different dimensions. Our work presents numerical results that plot the amplitudes and phases of these hyperchaotic behaviours, demonstrating the successful achievement of PS and APS.

Photoacoustic spectroscopy allows the identification of specific molecules in gases. We evaluate the spectral resolution and detection limits for a PAS system in the broadband infrared wavelength region 3270 nm ≲ λ ≲ 3530 nm driven by a continuous wave optical parametric oscillator with P ≈ 1.26 W by measuring the absorption of diluted propane, ethane and methane test gases at low concentrations c ~ 100 ppm for ~1350 discrete wavelengths λ_i. The resulting spectra I_PAS(λ_i) were compared to the high resolution cross section data σ_FTIR obtained by Fourier Transform Infrared Spectroscopy from the HITRAN database. Deviations as little as 7.1(6)% for propane, 8.7(11)% for ethane and 15.0(14)% for methane with regard to the average uncertainty between I_PAS(λ_i) and the expected reference values based on σ_FTIR were recorded. The wavelengths λ_res of the characteristic absorption lines can be pinpointed with a high relative accuracy <5 × 10⁻⁵ corresponding to a resolution of λ_res ~ 0.16 nm. Detection limits range between 7.1 ppb (ethane) to 13.6 ppb (methane) coinciding with high experimental signal-to-noise ratios. Moreover, using EUREQA, an artificial intelligence program, simulated mixed gas samples at low limits of detection could be deconvoluted. These results justify a further development of PAS technology to support, e.g., biomedical research.

This paper demonstrates an on-off keying (OOK) super-regenerative quenching transmitter operating in 402- 405MHz MICs band applications. To reduce power consumption, the transmitter is controlled by a novel digital quenching signal controller that generates a digital control signal to start transmitter operation when a baseband signal is input to the transmitter. The digital signal controller consists of an envelope detector, a comparator, and a quench timer designed using a state machine to synchronize the operation between the digital controller and the input baseband signal. The transmitter consists of a Colpitts oscillator operating in double operating frequency followed by a frequency divider by 2, this configuration reduces system area and improves phase noise and signal spectrum. The proposed transmitter is implemented using UMC 130nm CMOS technology, and a 1.2V supply. Simulation shows that the proposed transmitter can meet MICS band mask specifications with data rates up to 1Mbps and total power dissipation of 537uW.

The response of the Cold-Electron Bolometers (CEBs), integrated into a 2-D array of dipole antennas, has been measured by irradiation from YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) 50 $\mu$m long Josephson junction into the THz region at frequencies from 0.1 to 0.8 THz. The possibility of controlling the amplitude-frequency characteristic is demonstrated by the external magnetic field in the traveling wave regime of a long Josephson junction. YBCO junction has been formed on the bicrystal Zr$_{1-x}$Y$_x$O$_2$ (YSZ) substrate by magnetron sputtering and etching of the film. CEBs have been fabricated using an Al multilayer structure by a self-aligned shadow evaporation technique on Si substrate. Both receiver and oscillator have been located inside the same cryostat at 0.3K and 2.7K plates, respectively.

In this article, we report the generation of alternating current by application of constant and ramping DC voltages across oil-water interfaces. The work reported here can be broadly divided into two parts depending on the shapes of oil-water interfaces i.e. flattened and curved. In the first part, an alternating current of ~100 nA (amplitude)was generated by applying a constant DC voltage of -3V& above across a free standing and flattened oil-water interface.In another part, an alternating current of ~150 nA (amplitude) was generated by applying a ramping up DC voltage starting from -5V to 5V, then again ramping back down to -5V for the free standing and curved interface. The suggested qualitative mechanism that engenders such a phenomenon includes the oil-water interface acting like a membrane. This membrane oscillates due to the electrophoretic movement of ions present in aqueous phase by application of a DC voltage across the interface.This electrophoretic movement of ions across oil-water interfaces causes the Faraday instabilities leading to oscillations of the said interface.This method could also be used to study the stress levels in the interfacial films between two immiscible liquids. It explores more-than-Moore’s paradigm by finding a substitute to a conventional alternator/inverter that generates alternating current upon applying DC voltage input. This work would be of substantial interest to researchers exploring alternatives to conventional AC generators that can be used in liquid environments and in the design of novel integrated circuits that could be used for unconventional computing applications.

The refractive index of solids guages their transparency to incident light, while the energy gap determines the threshold for light absorption. This paper provides a mathematical formulation for the relationship between refractive index and energy gap. It is also established that this formulation aided in the unification of the Moss, Ravindra, and Herve-Vandamme relationships.

We think of time as one of four dimensions appearing in the equations of motion of Newtonian and quantum physics, but participating independently of space. In these pages we explore the way the time variable affects how space is perceived. We show first that non-commutation may be interpreted as the difference between electron and photon cycling during radiation processes. For every electron cycle of a quantum oscillator there are two photon cycles. Secondly, the difference between relativistic and non-relativistic quantum mechanics is shown to be related to time evolution. Only relativistic models evolve continuously. The reasoning of Einstein is implicit to an understanding of both physical models. Previously obtained derivations of relativistic quantum mechanics are reaffirmed by following the ideas of Dirac.

In this article we study the presence of chaos in supersymmetric(SUSY) quantum mechanics. For that purpose we present a form of 4-point out of time order correlator(OTOC) for SUSY quantum mechanical systems using tensor product formalism. We calculate the 4-point OTOC for SUSY 1D harmonic oscillator and find that the OTOC is exactly equal to that of 1D bosonic harmonic oscillator system. In similar manner using the eigenstate representation of supersymmetric systems we calculate the generalized higher order out of time order correlator. The higher order OTOC is a more sensitive measure of chaos than the usual 4-point correlator used in literature. Finally, we calculate the generalized 2N-point OTOC for SUSY 1D harmonic oscillator.

Orthogonal operators can successfully be used to calculate eigenvalues and eigenvector compositions in complex spectra. Orthogonality ensures least correlation between the operators and thereby more stability in the fit, even for small interactions. The resulting eigenvectors are used to transform the pure transition matrix into realistic intermediate coupling transition probabilities. Calculated transition probabilities for close lying levels illustrate the power of the complete orthogonal operator approach.

The goal of this paper is to present a low-cost, low-power prototype of a pulsed Ultra Wide Band UWB) oscillator and an UWB elliptical dipole antenna integrated on the same Radio Frequency (RF) Printed Circuit Board (PCB) and its digital control board for Real Time Locating System (RTLS) applications. The design is compatible with IEEE 802.15.4 high rate pulse repetition UWB standard being able to work between 6 GHz and 8.5 GHz with 500 MHz bandwidth and with a pulse duration of 2 ns. The UWB system has been designed using the CST Microwave Studio transient Electro-Magnetic (EM) circuit co-simulation method. This method integrates the functional circuit simulation together with the full wave (EM) simulation of the PCB’s 3D model allowing fast parameter tuning. The PCB has been manufactured and the entire system has been assembled and measured. Simulated and measured results are in excellent agreement with respect to the radiation performances as well as the power consumptions.

We try to solve three decades-old physics challenges. List all elementary particles. Describe dark matter. Describe mechanisms that govern the rate of expansion of the universe. We propose new modeling. The modeling uses extensions to harmonic oscillator mathematics. The modeling points to all known elementary particles. The modeling suggests new particles. Based on those results, we do the following. We explain observed ratios of dark matter amounts to ordinary matter amounts. We suggest details about galaxy formation. We suggest details about inflation. We suggest aspects regarding changes in the rate of expansion of the universe. We interrelate the masses of some elementary particles. We interrelate the strengths of electromagnetism and gravity. Our work seems to offer new insight regarding applications of harmonic oscillator mathematics. Our work seems to offer new insight regarding three branches of physics. The branches are elementary particles, astrophysics, and cosmology.

We develop and apply new physics theory. The theory suggests specific unfound elementary particles. The theory suggests specific constituents of dark matter. We apply those results. We explain ratios of dark matter amounts to ordinary matter amounts. We suggest details about galaxy formation. We suggest details about inflation. We suggest aspects regarding changes in the rate of expansion of the universe. The theory points to relationships between masses of elementary particles. We show a relationship between the strength of electromagnetism and the strength of gravity. The mathematics basis for matching known and suggesting new elementary particles extends mathematics for harmonic oscillators.

Motivated by assumptions that Quantum Mechanics (QM) is not the basement of reality and that additional dimensionality (XD) is required to complete and extend the Standard Models (SM) of Particle Physics and Cosmology, experimental protocols utilizing putative properties of Kaluza-Klein-like (KK) cyclicality embedded within Dirac’s electron hypertube model in conjunction with a Dirac covariant polarized vacuum is developed to produce a new type of low-energy tabletop cross section based on topological phase transitions rather than high energy collision sprays as in the LHC. The model is presented in a highly theoretical axiomatic manner utilizing off-the-shelf parameters generally marginalized by the mainstream physics community. When successful the protocol leads to obsolescence of the highly efficacious 100-year supercollider run producing a paradigm shift with an inherent new set of Unified Field (UF) transformations beyond the Galilean Lorentz-Poincaré transformations of the SM to 3rd regime natural science: Classical – Quantum - UF.

Physics theory has yet to settle on specific descriptions for new elementary particles, for dark matter, and for dark energy forces. Our work extrapolates from the known elementary particles. The work suggests well-specified candidate descriptions for new elementary particles, dark matter, and dark energy forces. This part of the work does not depend on theories of motion. This work embraces symmetries that correlate with motion-centric conservation laws. The candidate descriptions seem to explain data that prior physics theory seems not to explain. Some of that data pertains to elementary particles. Our theory suggests relationships between masses of elementary particles. Our theory suggests a relationship between the strengths of electromagnetism and gravity. Some of that data pertains to astrophysics. Our theory seems to explain ratios of dark matter effects to ordinary matter effects. Our theory seems to explain aspects of galaxy formation. Some of that data pertains to cosmology. Our theory suggests bases for inflation and for changes in the rate of expansion of the universe. Generally, our work proposes extensions to theory in three fields. The fields are elementary particles, astrophysics, and cosmology. Our work suggests new elementary particles and seems to explain otherwise unexplained data.

The Van der Pol oscillator is a chaotic non-linear system. Small perturbations in initial conditions may result in wildly different trajectories. Because of its chaotic nature, controlling, or forcing, the behavior of a Van der Pol oscillator is difficult to achieve through traditional adaptive control methods. Connecting two Van der Pol oscillators together where the output of one oscillator, the driver, drives the behavior of its partner, the responder, is a proven technique for controlling the Van der Pol oscillator. Deterministic AI (DAI) is an adaptive feedback control method that leverages the known physics of the Van der Pol system to learn optimal system parameters for the forcing function. We assessed the performance of DAI employing three different online parameter estimation algorithms. Our evaluation criteria include mean absolute error (MAE) between the target trajectory and the response oscillator trajectory over time. RLS with exponential forgetting (RLS-EF) had the lowest MAE overall, with a 2.46% reduction in error. However, another method was notable. Least Mean Squares with normalized gradient adaptation (LMS-NG) had worse initial error in the first 10% of the simulation, but after that point had consistently better performance. We found that over the last 90% of the simulation, DAI with LMS-NG had a 48.7% reduction in MAE compared to feedforward alone.