Velocity-dependent Potential Research Articles

Comparison of energy-dependent and independent interactions-a case study

In the present text we construct velocity-dependent or equivalently energy-dependent potential (EDP) to an energy-independent nonlocal potential (EIP) of rank-1 by Taylor series method. The phase shifts for the nucleon-nucleon and alpha-nucleon systems are computed for these two potentials by exploiting the variable phase method and the Fredholm determinant, respectively. The velocity-dependent potential is found to be superior to central nonlocal interaction in generating the scattering phase shifts up to high energy region.

Velocity-Dependent Potential for nn-αn-αα Scattering

An energy momentum-dependent potential is considered to study nucleon-nucleon, nucleon-nucleus and nucleus-nucleus elastic scattering by exploiting the variable phase method to potential scattering. The velocity dependent potential, equivalent to Graz separable potential, has the ability to reproduce the correct nature and numerical values of the NN phase parameters up to 400 MeV. Also it works equally well for alpha-nucleon and alpha-alpha systems up to few higher partial waves. Our results are in close conformity with the previous theoretical and experimental data. For alpha-alpha scattering we have treated only s-wave case.

Solutions of the Schrödinger equation with velocity-dependent potentials:a study on Kratzer, Mie and Hulthen potentials

The effect of isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Kratzer, Mie and Hulthen potentials is obtained for any quantum states in the presence of constant form factor εr=γρ0. The corresponding energy eigenvalues and eigenfunctions are determined and tabulated for a set of finite quantum numbers n and l in the framework of the well-known Nikiforov-Uvarov method.

Density and energy dependent semi-microscopic optical potential of nucleon–nucleus elastic scattering

A nonlocal velocity-dependent optical potential was used to study the angular distribution of the differential cross section of nucleon–nucleus elastic scattering. The potential parameters were calculated by fitting elastic angular distributions over a wide range of energy (10-65 MeV) and mass (12-208). The real part of the local optical potential was calculated using the CDM3Y6-Paris interaction, whereas the imaginary part was a Woods-Saxon form factor and its derivative.

New classes of quadratically integrable systems with velocity dependent potentials: non-subgroup type cases

New classes of quadratically integrable systems with velocity dependent potentials: non-subgroup type cases

Velocity dependent potential for alpha 40Ca-elastic scattering

Angular distribution of the differential cross section of α40Ca elastic scattering has been investigated in the anomalous large angle scattering (ALAS) region by a nonlocal velocity dependent optical potential with surface term. The geometrical potential parameters were fixed and the depths of the potential were determined by fitting elastic angular distribution over the energy range (23–53.9 MeV). The real and the imaginary parts of the optical potential used here are of Woods–Saxon form factors. An energy dependence of the potential depths has been investigated at fixed geometrical potential parameters.

Suppression of extreme events and chaos in a velocity-dependent potential system with time-delay feedback

The foremost aim of this study is to investigate the influence of time-delayed feedback on extreme events in a non-polynomial system with velocity dependent potential. To begin, we investigate the effect of this feedback on extreme events for four different values of the external forcing parameter. Among these four values, in the absence of time-delayed feedback, for two values, the system does not exhibit extreme events and for the other two values, the system exhibits extreme events. On the introduction of time-delayed feedback and varying the feedback strength, we found that extreme events get suppressed as well as get induced. When the feedback is positive, suppression occurs for a larger parameter region whereas in the case of negative feedback it is restricted to the limited parameter region. We confirm our results through Lyapunov exponents, probability density function of peaks, dmax plot and two parameter probability plot. Finally, we analyse the changes in the overall dynamics of this system under the influence of time-delayed feedback. We notice that complete suppression of chaos occurs in the considered system for higher values of the time-delayed feedback.

Comparing the effects of nonlocal sources on the neutron-nucleus elastic scattering process

The wave function of a nonlocal potential is reduced or enhanced in the nuclear interior where the potential acts. This is known as the Perey effect. We use the Perey damping factor to demonstrate that the phenomenological Perey-Buck and the velocity-dependent nonlocal potentials simulate sources of nonlocality. We compare their effectiveness in simulating nonlocal effects by comparing their corresponding Perey damping factors. The importance of the nonlocality arising from the dynamic polarization potential is also estimated by determining the corresponding damping factors. To calculate the needed wave functions corresponding to the local and nonlocal potentials, we determine the parameters of each considered potential by fitting the experimental angular distributions for neutron scattering off nuclei from 6Li to 208Pb for various energies in the range 9 - 35 MeV. Our results show that the nonlocality simulated by each of the three potentials is energy and angular momentum dependent. The effect of the nonlocality simulated by the velocity-dependent potential increases with increasing mass number and, for a given target, becomes more important for higher partial waves. The Perey-Buck potential simulates a nonlocality that is more important for light nuclei. Finally, the nonlocality arising from the dynamic polarization potential increases when more inelastic channels are coupled to the ground state, and becomes more important with increasing energy.

Altered Gastrocnemius Contractile Behavior in Former Achilles Tendon Rupture Patients During Walking.

Achilles tendon rupture (ATR) remains associated with functional limitations years after injury. Architectural remodeling of the gastrocnemius medialis (GM) muscle is typically observed in the affected leg and may compensate force deficits caused by a longer tendon. Yet patients seem to retain functional limitations during—low-force—walking gait. To explore the potential limits imposed by the remodeled GM muscle-tendon unit (MTU) on walking gait, we examined the contractile behavior of muscle fascicles during the stance phase. In a cross-sectional design, we studied nine former patients (males; age: 45 ± 9 years; height: 180 ± 7 cm; weight: 83 ± 6 kg) with a history of complete unilateral ATR, approximately 4 years post-surgery. Using ultrasonography, GM tendon morphology, muscle architecture at rest, and fascicular behavior were assessed during walking at 1.5 m⋅s–1 on a treadmill. Walking patterns were recorded with a motion capture system. The unaffected leg served as control. Lower limbs kinematics were largely similar between legs during walking. Typical features of ATR-related MTU remodeling were observed during the stance sub-phases corresponding to series elastic element (SEE) lengthening (energy storage) and SEE shortening (energy release), with shorter GM fascicles (36 and 36%, respectively) and greater pennation angles (8° and 12°, respectively). However, relative to the optimal fascicle length for force production, fascicles operated at comparable length in both legs. Similarly, when expressed relative to optimal fascicle length, fascicle contraction velocity was not different between sides, except at the time-point of peak series elastic element (SEE) length, where it was 39 ± 49% lower in the affected leg. Concomitantly, fascicles rotation during contraction was greater in the affected leg during the whole stance-phase, and architectural gear ratios (AGR) was larger during SEE lengthening. Under the present testing conditions, former ATR patients had recovered a relatively symmetrical walking gait pattern. Differences in seen AGR seem to accommodate the profound changes in MTU architecture, limiting the required fascicle shortening velocity. Overall, the contractile behavior of the GM fascicles does not restrict length- or velocity-dependent force potentials during this locomotor task.

Maxwell-Chern-Simons-Higgs theory

We consider the three dimensional electrodynamics described by a complex scalar field coupled with the U(1) gauge field in the presence of a Maxwell term, a Chern-Simons term and the Higgs potential. The Chern-Simons term provides a velocity dependent gauge potential and the presence of the Maxwell term makes the U(1) gauge field dynamical. We study the Hamiltonian formulation of this Maxwell-Chern-Simons-Higgs theory under the appropriate gauge fixing conditions.

Nucleon-nucleus velocity-dependent optical model: revisited

In this work we study nucleon-nucleus elastic scattering using a nonlocal, velocity-dependent optical potential. The potential parameters are determined by fitting elastic angular distributions and polarization data for nucleon scattering off a wide range of nuclei falling in the mass range 12 ⩽ A ⩽ 208 and over the energy range 10–60 MeV. Our potential parameters lead to smoothly varying local equivalent potentials and, unlike previous works, the potential depths corresponding to the real volume, imaginary surface, and imaginary volume terms show systematic linear dependences on energy. In addition, for each nuclear target, we determined constant sets of geometric parameters. Including the polarization data in the fitting procedure helped in reducing the large variations in the depths of the spin–orbit term. Our best-fit angular distributions and polarization data are in very good agreement with measured data, and are either as good as the cross sections obtained with widely-used systematics or better.

Constant bias and weak second periodic forcing : tools to mitigate extreme events

We propose two potentially viable non-feedback methods, namely (i) constant bias and (ii) weak second periodic forcing as tools to mitigate extreme events. We demonstrate the effectiveness of these two tools in suppressing extreme events in two well-known nonlinear dynamical systems, namely (i) Liénard system and (ii) a non-polynomial mechanical system with velocity-dependent potential. As far as the constant bias is concerned, in the Liénard system, the suppression occurs due to the decrease in large amplitude oscillations and in the non-polynomial mechanical system the suppression occurs due to the destruction of chaos into a periodic orbit. As far as the second periodic forcing is concerned, in both the examples, extreme events get suppressed due to the increase in large amplitude oscillations. We also demonstrate that by introducing a phase in the second periodic forcing one can decrease the probability of occurrence of extreme events even further in the non-polynomial system. To provide a support to the complete suppression of extreme events, we present the two parameter probability plot for all the cases. In addition to the above, we examine the feasibility of the aforementioned tools in a parametrically driven version of the non-polynomial mechanical system. Finally, we investigate how these two methods influence the multistability nature in the Liénard system.

Velocity-dependent potential effects on two interacting electrons in Cornell quantum dot planted in plasma medium

In this study, the energy levels of two-electron Cornell quantum dot (TECQD) immersed in Debye and quantum plasma mediums are probed. To model plasma mediums, the more general exponential cosine screened Coulomb (MGECSC) is suggested. The presence of TECQD in plasma environment and velocity-dependent potential (VDP) effect in the system render very difficult to solve the relevant wave equation. Since the analytical solution of the relevant wave equation is very difficult, the numerical asymptotic iteration method (AIM) is used. As well as the effects of the encompassing parameters on the energy levels and possible radiations of TECQD, the effects of VDP and quantum (and Debye) plasma medium are also presented in detail. In addition, the alternativeness of VDP, quantum (and Debye) plasma and encompassing parameters to each other on these effects are also discussed.

Emergence and mitigation of extreme events in a parametrically driven system with velocity-dependent potential

In this paper, we discuss the emergence of extreme events in a parametrically driven non-polynomial mechanical system with a velocity-dependent potential. We confirm the occurrence of extreme events from the probability distribution function of the peaks, which exhibits a long-tail. We also present the mechanism for the occurrence of extreme events. We found that the probability of occurrence of extreme events alternatively increase and decrease with a brief region where the probability is zero. At the point of highest probability of extreme events, when the system is driven externally, we find that the probability decreases to zero. Our investigation confirms that the external drive can be used as an useful tool to mitigate extreme events in this nonlinear dynamical system. Through two parameter diagrams, we also demonstrate the regions where extreme events gets suppressed. In addition to the above, we show that extreme events persits when the sytem is influenced by noise and even gets transformed to super-extreme events when the state variable is influenced by noise.

Optical analysis of quantum dot with velocity‐dependent potential

AbstractIn this study, for the first time, the velocity‐dependent potential (VDP) effects on the total refractive index changes (TRICs) and the total absorption coefficients (TACs) of the parabolic quantum dot with spherical confinement, generated by GaAs/GaAlAs heterostructure, are comprehensively investigated. In order to obtain the subband energy spectra and the electronic wave function of the quantum dot system, the wave equation is numerically solved due to the VDP's complexity by using Runge‐Kutta‐Fehlberg method within the effective mass approximation. The nonlinear optical specifications of the quantum dot with velocity‐dependent potential (QDVDP) are analyzed using the compact density matrix formalism within the framework of the iterative method. To investigate the optical specifications of QDVDP, the isotropic form factor of VDP is taken into consideration as the harmonic oscillator type, F(r) = γρ0r2 (being γ and ρ0 are constants). Optical analysis is also executed for parabolic encompassing under the influence of VDP, as well as VDP, analyzing for TRICs and TACs of QDVDP, for which the result is quite a change compared to cases without VDP due to the symmetry‐breaking repercussion on system confinement of VDP. The main motivation of the present study is to clearly distinguish VDP effects on optical properties of the quantum dot, carrying out an analysis on optimal range and alternative parameter for optical properties.

Generating velocity-dependent potential in all partial waves

Velocity/energy-dependent potential to a parent nonlocal interaction is constructed for all partial waves by Taylor series expansion method and the related s and p-wave phase shifts for N-N and α-N systems are computed by application of modified phase equation. Our phase shifts are in good agreement with standard data.

Accelerating imperfect fluid

An inhomogeneous fluid in accelerated motion is investigated. When the velocity field v(x) is not constant, the geometry viewed by a static observer is curved, as if the observer were immersed in a gravitational field. A velocity-dependent semiclassical gravitational potential is introduced, which obeys an Yukawa-type equation, written in Cartesian coordinates. The timelike and null geodesic equations are investigated. One finds that the fluid has zero energy density corresponding to the perfect fluid part but nonzero anisotropic energy density. The pressures will no longer depend on ħ for time intervals t>>1/m, where m is the field mass.

Damping Potential, Generalized Potential, and D’Alembert’s Principle

An alternative form of Lagrange’s equations is used to introduce a new equation for deriving a monogenic force from a velocity-dependent potential. Based on this and corresponding to a linear damping force, a bilinear potential function is introduced, which obviates the need for a dissipation function to represent a damping force. This idea is then generalized by introducing a generalized potential function which allows D’Alembert’s principle, Lagrange’s equations, and Hamilton’s principle to be represented solely in terms of potential functions. The introduced potential functions and equations are used to derive motion equations of a floating body.

On the canonical distributions of a thermal particle in a generalized velocity-dependent potential

We consider a thermal particle diffusing in velocity-space under a generalized velocity-dependent potential characterized by the inverse hyperbolic sine function of the particle velocity v and the control parameter vc. This velocity-dependent potential can be considered as a deformation of Rayleigh’s dissipation function. The stationary state of the corresponding Fokker–Planck equation is shown to be a canonical probability distribution. Furthermore an appropriate re-parameterization relates this stationary state with the κ-deformed Gaussian. A possible interpretation of the deformation parameter κ is proposed.

Analytical solution of the Schrödinger equation for isotropic velocity-dependent potentials

The energy spectrum of the velocity-dependent potentials with respect to the harmonic oscillator potential and Coulomb potential are obtained for any and quantum states using the Nikiforov–Uvarov method for different cases of velocity-dependent terms. The effects of isotropic velocity-dependent potentials on the bound state energy eigenvalues are examined in analytic form when the form factor is considered as and As an application to a physical system, we evaluated the vibrational partition function and other thermodynamic properties for the isotropic velocity-dependent potential harmonic oscillator.