Soliton Model Research Articles

Lack of a genuine time crystal in a chiral soliton model

In a recent publication [Phys. Rev. Lett. {\bf 124}, 178902] \"Ohberg and Wright claim that in a chiral soliton model it is possible to realize a genuine time crystal which corresponds to a periodic evolution of an inhomogeneous probability density in the lowest energy state. We show that this result is incorrect and present a solution which possesses lower energy with the corresponding probability density that does not reveal any motion. It implies that the authors' conclusion that a genuine time crystal can exist in the system they consider is not true.

The important consequences of the reversible heat production in nerves and the adiabaticity of the action potential

It has long been known that there is no measurable heat production associated with the nerve pulse. Rather, one finds that heat production is biphasic, and a heat release during the first phase of the action potential is followed by the reabsorption of a similar amount of heat during the second phase. We review the long history the measurement of heat production in nerves and provide a new analysis of these findings focusing on the thermodynamics of adiabatic and isentropic processes. We begin by considering adiabatic oscillations in gases, waves in layers, oscillations of springs and the reversible (or irreversible) charging and discharging of capacitors. We then apply these ideas to the heat signature of nerve pulses. Finally, we compare the temperature changes expected from the Hodgkin-Huxley model and the soliton theory for nerves. We demonstrate that heat production in nerves cannot be explained as an irreversible charging and discharging of a membrane capacitor as it is proposed in the Hodgkin-Huxley model. Instead, we conclude that it is consistent with an adiabatic pulse. However, if the nerve pulse is adiabatic, completely different physics is required to explain its features. Membrane processes must then be reversible and resemble the oscillation of springs more than resembling “a burning fuse of gunpowder” (quote A. L. Hodgkin). Theories acknowledging the adiabatic nature of the nerve pulse have recently been discussed by various authors. It forms the central core of the soliton model, which considers the nerve pulse as a localized sound pulse.

Nucleon quasi-parton distributions in the large Nc limit

In this letter, we investigate the nucleon quasi-parton distribution functions in the chiral quark soliton model. We derive a set of sum-rules depending on the velocity of the nucleon and on the Dirac matrix defining the distribution functions. We present numerical results for the isosinglet unpolarized distribution, in which we find that the anti-quark distribution breaks the positivity condition at nucleon velocities of v≈0.99(PN≈7.0MN) and smaller. We found that, for the isosinglet unpolarized case, a large nucleon momentum is required for the quasi-parton distribution to get close enough to the usual parton distribution function.

Magneto-Impedance in Co35Fe65/Cu/Co35Fe65 Single and Bi-layer Thin Films

The magneto-impedance response in Co35Fe65/Cu/Co35Fe65 thin film magneto-impedance cells deposited by the thermal evaporation method has been studied with single and bilayer structures at the substrate temperature 300 K and 150 K. While the thin film deposited at 300 K has BCC structure, the amorphous character is dominant for 150 K deposited ones. Entire films show soft magnetic behavior with high saturation magnetization (MS) and low coercive field (HC). Bilayer thin film structure reveals higher magneto-impedance values than single-layer thin films. The relation between the magneto-impedance effect and layered structure is discussed in terms of structural growing mechanism and scattering effect. The highest magneto-impedance sensitivity (η) 37%/Oe is observed for the Co35Fe65/Cu/Co35Fe65 bilayer thin film. The HC and remanence ratio (MR/MS) values for single layer at 300 K, single and bilayer cells at 150 K are measured as 51, 158 and 253 Oe—0.48, 0.78, and 0.80, respectively. When η with the Soliton wave model is compared with the sample at room temperature, an increase of over 1700% is observed. The difference between the classical growing method at 300 K and the Soliton wave model at 150 K is the evidence of the logic of the work performed and its accuracy. The relatively high sensitivity is connected with interlayer usage and low temperature-smaller particle size in Soliton model growth. The observed findings are of practical importance to develop future technological magnetic sensor applications with high sensitivity.

Complex waves and their collisions of the breaking soliton model describing hydrodynamics

As one of the important physical models, the variable-coefficient breaking soliton model describes the dynamics of solitary waves and Riemann waves in hydrodynamics. Applying the two function approach into the variable-coefficient breaking soliton model, we find an exponential-form variable separation solution with two arbitrary functions, which covers many hyperbolic and trigonometric function solutions. Based on this solution and choosing suitably two arbitrary functions, complex waves including dromion pair and single dromion superposed on a line soliton background and their collisions between complex waves and between dromion and periodic wave are discussed. For the complex waves such as the dromion pair and single dromion superposed on a line soliton background and their collisions between complex waves, two components of this model possess both striking physical meanings. However, for the collision between dromion and periodic wave, one component of this model has unique physical meaning, yet the other component of the same model appears the singularity structure. Therefore, when one discusses complex waves and their collisions for one component of the model, one must take care of non-physical structures for another component of the same model lest one arbitrarily claims that he finds the so-called novel localized structures, which are actually false non-physical structures.

Bifurcations of a soliton model of dark matter towards natural inflation

Axion-like scalar fields with a periodic potential provide a solitonic model of dark matter halos of galaxies. Here we point out that their stability analysis bridges over, via bifurcations, to natural inflation. Then the (pseudo-) scalar part of the Lagrangian can be mapped into a gravity model mildly nonlinear in the scalar curvature. In the case of an axionic periodic potential, the equivalent Lagrangian L(R) exhibits a combination of swallow tail cusps with transitions of stability, well-known from catastrophe theory. The resulting almost Einsteinian branches indicate a ‘unification’ of dark matter, dark energy and inflation.

Soliton modeling of public key algorithm security

Quantum key distribution protocols and problems of their protection were studied with the soliton model of entangled photons. There were estimated mutual influences between legitimate users and for any types of cracker attack. For example, BB84 protocol is shown to be unconditional security protocols using photon polarization between outlying channels. Secret keys share quantum state between spatially separated (removed or remote) legitimate users. A simple method of generating a dichotomy signal has also been accomplished. In fact, this method can open the way of probabilistic quantum states. We argue that quantum cryptographic systems can be partially simulated on a classical computer with entangled soliton model. The quantum entanglement is a basic tool of communication and processing of the information.

Unstable cardiac multi-spiral waves in a FitzHugh–Nagumo soliton model under magnetic flow effect

This work deals with the stimulation of cardiac spiral waves in a two-dimensional FitzHugh–Nagumo model through modulational instability phenomenon in the presence of intracellular magnetic flux. The nonlinear generic model is firstly transformed into a two-dimensional complex Ginzburg–Landau equation with a small real damping term. Then, the latter is explored to perform the linear stability analysis and some modulational instability properties are derived and found to be modified with the change of either the magnetic coupling strength or the diffusion coefficient which are set as the control parameters. The bifurcation theory analysis is numerically performed, and the range of values of the stimulation parameter for which firing patterns emerge in cardiac media is well estimated. The recording of membrane potential as well as the magnetic flux as functions of time or spatial coordinates allows to picture some features such as time series, phase portraits and spatial patterns of membrane potential. As a result, diamond-shaped, squared-shaped and spiral-shaped waves are obtained. An elimination process of multi-spiral waves is proposed by exposing such patterns to an external magnetic flux. Thus, for suited values of parameters, the cardiac spiral waves are transmuted into target waves which obviously protect heart against harmful attacks such as ventricular tachycardia and fibrillation. Our results suggest that uncontrolled electromagnetic induction within cardiac tissue may be considered as the principal source of many heart injuries which are the first cause of mortality in the industrial world.

Topological solitons in chain molecular crystals with stoichiometric obstacles and hydrogen bonds

The present paper examines molecular motion mechanisms in lamellar molecular crystals of undecylenic acid. Thermophysical, dielectric, and infrared spectroscopy methods were used to demonstrate the presence of a relaxation process in crystals of undecylenic acid in the temperature range of −60°С to −10°С. The process is thought to be due to the free rotation of carboxylic groups after dissociation of dimeric rings (which the undecylenic acid forms via hydrogen bonds) and the nucleation of topological solitons. Topological solitons originate once the carboxylic groups begin to rotate freely.This hypothesis does not contradict the calculations of the dielectric permittivity increment performed in accordance with the model of a system of identical relaxators, each of which has two non-equivalent positions separated by a potential barrier. For this model, the change in dipole moment per unit volume due to carboxylic group free rotation and the propagation of topological solitons along carbon chains was calculated. The dielectric permittivity calculations for the model of several solitons nucleating simultaneously matched the experimentally obtained values. The topological soliton hypothesis was also confirmed by comparing the experimentally obtained activation energy value (101 kJ mol−1) with the hydrogen bonds energy (29 kJ mol−1 each) and the nucleation of a topological soliton energy (40 kJ mol−1).

On biological signaling

Abstract Presently, nerve pulse propagation is understood to take place by electric action pulses. The theoretical description is given by the Hodgkin-Huxley model. Recently, an alternative model was proclaimed, where signaling is carried out by acoustic solitons. The solitons are built by a local phase transition in the lyotropic liquid crystal (LLC) of a biologic membrane. We argue that the crystal structure arranging hydrogen bonds at the membrane surface do not allow such an acoustic soliton model. The bound water is a component of the LLC and the assumed phase transition represents a negative entropy step.

Analytical modeling of electrical solitons in a nonlinear transmission line using Schamel–Korteweg deVries equation

Abstract Nonlinear transmission lines (NLTLs) provide an effective means of experimental investigation of nonlinear dispersive media paving the way for accurate modeling of electrical solitons. In this work, an appropriate analytical model is proposed to analyze and predict electrical solitons in an NLTL. The model is based on a new form of nonlinearity which utilizes fractional powers to render an accurate representation of the Capacitance-Voltage (C-V) curve, even for relatively higher voltages. A complete analytical procedure is adopted to obtain the soliton solution in an NLTL. Nonlinear analysis results in a Schamel type Korteweg deVries (S-KdV) equation, instead of a conventional KdV equation. An extended version of the Tanh method is employed to find the solution of S-KdV which yields narrower solitons of Sech4 shape. The proposed model is validated experimentally by using a specially designed NLTL (100 sections) comprising of linear inductors and nonlinear capacitances. Square pulses with a repetition rate of 100 kHz are used to generate the solitons. The comparative analysis shows excellent profile matching between theoretically predicted and experimentally obtained solitons. Furthermore, in consistence with the prediction of the proposed model, the product of the Amplitude and fourth power of the Width (A × W4) is found to be constant in experimental results. This model proposed in the present work can be of help in understanding and predicting the behavior of electrical solitons in NLTLs.

On a semiclassical model for damped dust ion-acoustic solitons with analysis of quantum electron exchange-correlation potential

The semiclassical hydrodynamic model is used to study the effect of electron exchange-correlation potential, quantum Bohm term, and degenerate pressure on the dynamics of dust ion acoustic waves by following the two-fluid theory in collisional, unmagnetized dusty plasma. For linear analysis, the dispersion relation modified by the exchange-correlation coefficient is derived. For nonlinear analysis, the standard perturbative approach is used to derive a deformed Korteweg–deVries equation with a linear damping term for finite amplitude waves. The analytical and numerical investigations in the presence of low collisional frequencies reveal the existence of compressive dissipative solitons. Considering the dense astrophysical objects, the dissipative compressive solitons are numerically investigated with the effect of different plasma parameters including collisions and exchange-correlation potential.

Novel Localized Excitations Structures with Fusion and Fission Properties to a (2 + 1)-Dimensional Breaking Soliton Equation

Using suitable transformations of dependent variables, a separable of variables solution of the (2 + 1)-dimensional breaking soliton model has developed with two arbitrary functions. We determine lump solutions by picking trustworthy arbitrary functions from the separable of variables solution. Also, critical points of the lump solution have evaluated. We determine the non-elastic interaction of two solitons evolves that the offers interface subsequently collision moderates into a breather wave regiment. We regulate the most important phenomena of soliton solutions as ring type exciting solitons, soliton fission, fusion and annihilation phenomena from our achieved variables separable solution selecting appropriate functions. Likewise, profiles of achieved solutions are presented to visualize the properties of the solutions. These properties of the breaking soliton model are associated to physical phenomena: inner waves in a gyrating ocean and thoughtful of the influencing machinery twisted by the interface of Riemann waves.

Lump Soliton Model on Chinese Microblog Public Opinion

There has been a tremendous rise in the growth of Chinese Microblog--- Sina Weibo in the past few years. Sina Weibo contains many interesting hot issues. In particular, the trend of some hot topics can be described by the soliton wave model based on some hypothesis and parameter settings. The theoretical strategies to control the trend of hot topics are stated by employing the lump soliton solution theory of the KdV equation and KP equation.

Role of low substrate temperature deposition on Co–Fe thin films

This paper presents the role of the conventional and Soliton wave model deposition at low substrate temperature (300–100 K) on the structural, electric and magnetic properties of Co35Fe65 thin films deposited by thermal evaporation using bulk polycrystalline Co35Fe65 alloy. On account of obtaining superior quality magnetic thin films without any high temperature growth processes or heat treatment, the Soliton wave growth model at suitable low temperature range is used. X-ray diffraction (XRD) and scanning electron microscopy (SEM) techniques are employed to investigate the various structural properties. Morphological and structural analyses of entire 30 nm Co35Fe65 thin films deposited on Si (100) substrate reveal that the stoichiometry is preserved over the whole temperature deposition and BCC crystalline formed with (110) texture. To attain the electrical and magnetic properties, resistivity and vibrating-sample magnetometer (VSM) measurements are evaluated. Soliton wave model deposition significantly increased magnetic anisotropy constant K1 = 0.105 Merg/cm3, MR/MS = 0.83 and coercivity HC = 272 Oe at 300 K when the compared to conventional deposition range in this work (K1 = 0.014 Merg/cm3, MR/MS = 0.6 and HC = 50 Oe). Growth with novel approach of Co35Fe65 thin films highlights the reasonable low coercivity, the high saturation magnetization, the high magnetic anisotropy and the low electrical resistivity values, with tailored grain size, make them feasible to use in magnetic sensor technology in the near future.

Uniting the wave and the particle in quantum mechanics

We present a unified field theory of wave and particle in quantum mechanics. This emerges from an investigation of three weaknesses in the de Broglie–Bohm theory: its reliance on the quantum probability formula to justify the particle-guidance equation; its insouciance regarding the absence of reciprocal action of the particle on the guiding wavefunction; and its lack of a unified model to represent its inseparable components. Following the author’s previous work, these problems are examined within an analytical framework by requiring that the wave–particle composite exhibits no observable differences with a quantum system. This scheme is implemented by appealing to symmetries (global gauge and spacetime translations) and imposing equality of the corresponding conserved Noether densities (matter, energy, and momentum) with their Schrödinger counterparts. In conjunction with the condition of time-reversal covariance, this implies the de Broglie–Bohm law for the particle where the quantum potential mediates the wave–particle interaction (we also show how the time-reversal assumption may be replaced by a statistical condition). The method clarifies the nature of the composite’s mass, and its energy and momentum conservation laws. Our principal result is the unification of the Schrödinger equation and the de Broglie–Bohm law in a single inhomogeneous equation whose solution amalgamates the wavefunction and a singular soliton model of the particle in a unified spacetime field. The wavefunction suffers no reaction from the particle since it is the homogeneous part of the unified field to whose source the particle contributes via the quantum potential. The theory is extended to many-body systems. We review de Broglie’s objections to the pilot-wave theory and suggest that our field-theoretic description provides a realization of his hitherto unfulfilled ‘double solution’ programme. A revised set of postulates for the de Broglie–Bohm theory is proposed in which the unified field is taken as the basic descriptive element of a physical system.

New narrow nucleon resonances $N^{\ast}(1685)$ and $N^{\ast}(1726)$ within the chiral quark–soliton model

AbstractWe investigate the strong and radiative decay widths of the narrow nucleon resonances $N^*(1685)$ and $N^{\ast}(1726)$ within the framework of the SU(3) chiral quark–soliton model. All the relevant parameters are taken from those used to describe the properties of the baryon octet and decuplet in previous works. The masses of the antidecuplet nucleon and the eikosiheptaplet (27-plet) nucleon with spin 3/2 are determined respectively to be $(1690.2\pm 10.5)\, \mathrm{MeV}$ and $(1719.6\pm7.4)\,\mathrm{MeV}$. The decay width for $N^{\ast}(1685)\to \eta + N$ is found to be approximately three times larger than that for $N^{\ast}(1685)\to \pi + N$. The width of the decay $N^{\ast}\left(1726\right)3/2^+\to \eta + N$ is about 31 times larger than that of $N^{\ast}\left(1726\right)3/2^+\to \pi + N$. The ratio of the radiative decays for $N^*(1685)$ is obtained to be $\Gamma_{nn^*(1685)}/\Gamma_{pp^*(1685)}=8.62\pm3.45$, which explains very well the neutron anomaly. In contrast, we find $\Gamma_{pp^*(1726)}/\Gamma_{nn^*(1726)}=3.72\pm0.64$, which indicates that the production of $N^*(1726)$ is more likely to be observed in the proton channel. We also examine the decay modes of these narrow nucleon resonances with the strangeness hadrons involved.

Galaxy rotation curves using a non-parametric regression method: core, cuspy and fuzzy scalar field dark matter models

ABSTRACT We present a non-parametric reconstruction of the rotation curves (RCs) for 88 spiral galaxies using the LOESS (locally weighted scatterplot smoothing) + SIMEX (simulation and extrapolation) technique. In order to compare methods, we also use a parametric approach, assuming core and cuspy dark matter (DM) profiles: pseudo-isothermal (PISO), Navarro−Frenk–White (NFW), Burkert, Spano, the soliton, and two fuzzy soliton + NFW. As a result of these two approaches, a comparison of the RCs obtained is carried out by computing the distance between the central curves and the distance between the 1σ error bands. Furthermore, we perform a model selection according to two statistical criteria, the Bayesian information criterion and the value of $\chi ^2_{\rm red}$. We work with two groups. The first is a comparison between PISO, NFW, Spano and Burkert, showing that Spano is the most favoured model satisfying our selection criteria. For the second group, we select the soliton, NFW and fuzzy models, resulting in soliton as the best model. Moreover, according to the statistical tools and non-parametric reconstruction, we are able to classify galaxies as core or cuspy. Finally, using a Markov chain Monte Carlo method, for each of the DM models we compute the characteristic surface density, μDM = ρsrs, and the mass within 300 pc. We find that there is a common mass for spiral galaxies of the order of 107 M⊙, which is in agreement with results for dSph Milky Way satellites, independent of the model. This result is also consistent with our finding that there is a constant characteristic volume density of haloes. Finally, we also find that μDM is not constant, which is in tension with the literature.

Nucleon structure functions from the NJL-model chiral soliton

We present numerical simulations for unpolarized and polarized structure functions in a chiral soliton model. The soliton is constructed self-consistently from quark fields from which the structure functions are extracted. Central to the project is regularizing the Dirac sea (or vacuum) contribution to structure functions directly from the regularized action functional that defines the model. In turn, the structure functions are obtained from matrix elements of symmetry currents without assumptions on the nature of quark bilocal and bilinear operators. We discuss in detail how sum rules are realized at the level of the quark wave-functions in momentum space. The comparison with experimental data is convincing for the polarized structure functions but exhibits some discrepancies in the unpolarized case. The vacuum contribution to the polarized structure functions is particularly small.

Nonlinear interaction of domain walls and breathers with a spin-wave field

Abstract We present the analytical solutions of the sine–Gordon model for magnetic solitons in a field of nonlocalized spin waves. We show, that nonlinear interference of solitons and waves leads to oscillations of solitons, relaxing with time in a power-law fashion. We study an interaction of the solitons with the running spin waves of the system: we find the expressions for the velocities and frequencies of the kinks and the breathers in the field of radiation.