Equations In Presence Research Articles

Large D gravity and charged membrane dynamics with nonzero cosmological constant

In this paper, we have found a class of dynamical charged ‘black-hole’ solutions to Einstein-Maxwell system with a non-zero cosmological constant in a large number of spacetime dimensions. We have solved up to the first sub-leading order using large D scheme where the inverse of the number of dimensions serves as the perturbation parameter. The system is dual to a dynamical membrane with a charge and a velocity field, living on it. The dual membrane has to be embedded in a background geometry that itself, satisfies the pure gravity equation in presence of a cosmological constant. Pure AdS / dS are particular examples of such background. We have also obtained the membrane equations governing the dynamics of charged membrane. The consistency of our membrane equations is checked by calculating the quasi-normal modes with different Einstein-Maxwell System in AdS/dS.

Black holes in presence of cosmological constant: second order in frac{1}{D}

We have extended the results of [1] upto second subleading order in an expansion around large dimension D. Unlike the previous case, there are non-trivial metric corrections at this order. Due to our ‘background-covariant’ formalism, the dependence on Ricci and the Riemann curvature tensor of the background is manifest here. The gravity system is dual to a dynamical membrane coupled with a velocity field. The dual membrane is embedded in some smooth background geometry that also satisfies the Einstein equation in presence of cosmological constant. We explicitly computed the corrections to the equation governing the membrane-dynamics. Our results match with earlier derivations in appropriate limits. We calculated the spectrum of QNM from our membrane equations and matched them against similar results derived from gravity.

New optical solitary wave solutions of Fokas-Lenells equation in presence of perturbation terms by a novel approach

A variety of new optical waves solutions of the Fokas-Lenells equation in presence of perturbation terms is investigated. A new approach is used, namely the generalized exponential function method. The physical meaning of the geometrical structures for some of these solutions is discussed for different choices of the free parameters present in the solutions. It is shown that the proposed methodology provides powerful mathematical tools for obtaining the exact traveling wave solutions of different nonlinear evolution equations.

Analytic and numeric computation of edge states and conductivity of a Kane-Mele nanoribbon

We compute analytic expressions for the edge states in a zigzag Kane-Mele nanoribbon (KMNR) by solving the eigenvalue equations in presence of intrinsic and Rashba spin-orbit couplings. Owing to the P-T symmetry of the Hamiltonian the edge states are protected by topological invariance and hence are found to be robust. This is not the case where either of the spin-orbit couplings in the Kane-Mele Hamiltonian is switched off. We have done a systematic study for each of the above cases, for example, a pristine graphene, graphene with an intrinsic spin-orbit coupling, graphene with a Rashba spin-orbit coupling, a Kane-Mele nanoribbon and supported our results on the robustness of the edge states by analytic computation of the electronic probability amplitudes, the local density of states (LDOS), band structures and the conductance spectra.

Dynamical survey of the dual power Zakharov–Kuznetsov–Burgers equation with external periodic perturbation

We investigate the dynamical behavior of the newly introduced dual power Zakharov–Kuznetsov–Burgers equation. Using bifurcation theory of planar dynamical systems, we study bifurcations of traveling wave solutions of the dual power Zakharov–Kuznetsov–Burgers equation in presence and absence of viscosity (μ) effect. In presence of an external periodic perturbation, we discuss the periodic and chaotic motions of the perturbed dual power Zakharov–Kuznetsov–Burgers equation by analyzing phase projection analysis, time series analysis, Poincaré section and sensitivity analysis. The effect of viscosity (μ) plays an important role in the transition from chaotic motion to periodic motion of the perturbed dual power Zakharov–Kuznetsov–Burgers equation.

Newton gauge cosmological perturbations for static spherically symmetric modifications of the de Sitter metric

Static coordinates can be convenient to solve the vacuum Einstein's equations in presence of spherical symmetry, but for cosmological applications comoving coordinates are more suitable to describe an expanding Universe, especially in the framework of cosmological perturbation theory (CPT). Using CPT we develop a method to transform static spherically symmetric (SSS) modifications of the de Sitter solution from static coordinates to the Newton gauge. We test the method with the Schwarzschild de Sitter (SDS) metric and then derive general expressions for the Bardeen's potentials for a class of SSS metrics obtained by adding to the de Sitter metric a term linear in the mass and proportional to a general function of the radius. Using the gauge invariance of the Bardeen's potentials we then obtain a gauge invariant definition of the turn around radius. We apply the method to an SSS solution of the Brans-Dicke theory, confirming the results obtained independently by solving the perturbation equations in the Newton gauge. The Bardeen's potentials are then derived for new SSS metrics involving logarithmic, power law and exponential modifications of the de Sitter metric. We also apply the method to SSS metrics which give flat rotation curves, computing the radial energy density profile in comoving coordinates in presence of a cosmological constant.

Some quasilinear elliptic equations involving multiple $p$-Laplacians

This paper is devoted to the study, with variational technique, of (p,q)-Laplacian equations in presence of general nonlinearities. Especially we obtain the existence result for the zero mass case, which includes a large class of pure power nonlinearities. More general quasilinear problems of Born-Infeld type are also considered.

PREDICTION OF ELECTRON DRIFT VELOCITY IN HELICALLY COILED CARBON NANOTUBES

We studied electron transport in single wall carbon nanotubes placed in stationary homogeneous electric fields, oriented along tubes. Electron distributions for various electric fields are determined by solving stationary multi bands Boltzmann transport equation in presence of electron phonon scattering mechanisms. Contributions of all possible scattering channels, allowed by selection rules and energy conservation, are taken into account for finding scattering rate and collision integrals. As it is previously predicted, large electron drift velocities in straight single wall carbon nanotubes are obtained. Frequent electron scattering as well as low group velocity have strong impact on reduction of drift velocity in helically coiled carbon nanotubes.

Single-cone finite-difference schemes for the (2+1)-dimensional Dirac equation in general electromagnetic textures.

A single-cone finite-difference lattice scheme is developed for the (2+1)-dimensional Dirac equation in presence of general electromagnetic textures. The latter is represented on a (2+1)-dimensional staggered grid using a second-order-accurate finite difference scheme. A Peierls-Schwinger substitution to the wave function is used to introduce the electromagnetic (vector) potential into the Dirac equation. Thereby, the single-cone energy dispersion and gauge invariance are carried over from the continuum to the lattice formulation. Conservation laws and stability properties of the formal scheme are identified by comparison with the scheme for zero vector potential. The placement of magnetization terms is inferred from consistency with the one for the vector potential. Based on this formal scheme, several numerical schemes are proposed and tested. Elementary examples for single-fermion transport in the presence of in-plane magnetization are given, using material parameters typical for topological insulator surfaces.

Medium effects on the electrical conductivity of a hot pion gas

The electromagnetic response of an interacting system of pions has been studied at finite temperature. The corresponding transport parameter i.e. electrical conductivity has been estimated by solving the relativistic transport equation in presence of a finite electric field employing the Chapman–Enskog technique where the collision term has been treated in the relaxation time approximation. The scattering amplitudes of charged pions modeled by ρ and σ meson exchange using an effective Lagrangian have been obtained at finite temperature by introducing self-energy corrections in the thermal propagators in the real time formalism. The temperature behavior of electrical conductivity for a hot pion gas shows significant quantitative enhancement due to the inclusion of medium effects in scattering.

Effect of dust ion collision on dust ion acoustic waves in the framework of damped Zakharov-Kuznetsov equation in presence of external periodic force

The dynamics of dust ion acoustic waves (DIAWs) is investigated in a magnetized dusty plasma whose constituents are cold ions, superthermal electrons, and dust particles in the framework of a damped Zakharov-Kuznetsov (dZK) equation in the presence of externally applied periodic force. The dZK equation is derived employing the standard reductive perturbation technique. The effect of dust ion collision on the quasiperiodic and chaotic motion of dust ion acoustic waves is discussed. It is observed that the collision frequency νid0 plays the role of a switching parameter from the quasiperiodic route to chaos for the DIAWs.

On the comparison of two split-step methods for the numerical simulation of stochastic point kinetics equations in presence of Newtonian temperature feedback effects

In this article, a comparative study between two numerical approximation methods viz., split-step forward Euler-Maruyama method and derivative-free Milstein method have been established. The stochastic point reactor kinetics equations consist of a system of stiff nonlinear differential equations. This system has been solved for step and ramp external reactivity using split-step forward Euler-Maruyama method and derivative-free Milstein method. The obtained numerical results show that the split-step approximations are straightforward and effective methods in studying the behavior of neutron density of the stochastic point reactor kinetics equations which also have been represented graphically.

Non-minimally coupled dark fluid in Schwarzschild spacetime

If one assumes a particular form of non-minimal coupling, called the conformal coupling, of a perfect fluid with gravity in the fluid-gravity Lagrangian then one gets modified Einstein field equation. In the modified Einstein equation, the effect of the non-minimal coupling does not vanish if one works with spacetimes for which the Ricci scalar vanishes. In the present work we use the Schwarzschild metric in the modified Einstein equation, in presence of non-minimal coupling with a fluid, and find out the energy-density and pressure of the fluid. In the present case the perfect fluid is part of the solution of the modified Einstein equation. We also solve the modified Einstein equation, using the flat spacetime metric and show that in presence of non-minimal coupling one can accommodate a perfect fluid of uniform energy-density and pressure in the flat spacetime. In both the cases the fluid pressure turns out to be negative. Except these non-trivial solutions it must be noted that the vacuum solutions also remain as trivial valid solutions of the modified Einstein equation in presence of non-minimal coupling.

Entire Solutions of Superlinear Problems with Indefinite Weights and Hardy Potentials

We provide the structure of regular/singular fast/slow decay radially symmetric solutions for a class of superlinear elliptic equations with an in- definite weight on the nonlinearity f (u, r). In particular we are interested in the case where f is positive in a ball and negative outside, or in the re- versed situation. We extend the approach to elliptic equations in presence of Hardy potentials. By the use of Fowler transformation we study the corresponding dynamical systems, presenting the construction of invariant manifolds when the global existence of solutions is not ensured.

Investigation of Conformable Fractional Schrödinger Equation in Presence of Killingbeck and Hyperbolic Potentials**Supported by the National Research Foundation of Korea Grant Funded by the Korean Government under Grant No. NRF-2015R1D1A1A01057792

In this article, conformable fractional form of Schrödinger equation has been presented. Then in this formalism two different and well-known potential have been come in. Wave function of these potential are obtained in terms of Heun function and energy eigen values of each case is determined as well.

A Landau‐Lifshitz‐Gilbert‐Type equation and torsion effects on the dynamics of magnetization

Based on the non‐relativistic regime of electrons described by a Dirac equation coupled to a torsion pseudo‐vector, we study the dynamics of magnetization and how it may be affected by the presence of this (background) torsion field. The latter describes some anisotropy of the bulk and it may be accounted for in two ways: by means of a minimal coupling in a covariant derivative endowed with spin connection and a gauge magnetic field; in addition, through a non‐minimal interaction term with the spin density. We show, within this framework, that it is possible to attain a version of the Landau‐Lifshitz equation in presence of the torsion background where its effects are included, re‐enforcing that torsion corresponds to a geometric anisotropy with relevant unfolds on the spin coupling mechanism. We also conclude that the torsion terms can open up two important landscapes in the magnetization dynamics: one of them, related with a damping effect; the other, related with the screw dislocation that gives us a global effect like a sharped‐helix damping. The whole effort here is then to pursue an investigation of torsion in connection with the precession dynamics of the magnetization. image

Existence and stability of dispersive solutions to the Kadomtsev–Petviashvili equation in the presence of dispersion effect

The paper deals with Kadomtsev–Petviashvili (KP) equation in presence of a small dispersion effect. The nature of solutions are examined under the dispersion effect by using Lyapunov function and dynamical system theory. We prove that when dispersion is added to the KP equation, in certain regions, yet there exist bounded traveling wave solutions in the form of solitary waves, periodic and elliptic functions. The general solution of the equation with or without the dispersion effect are obtained in terms of Weirstrass ℘ functions and Jacobi elliptic functions. New form of kink-type solutions are established by exploring a new technique based on factorization method, use of functional transformation and the Abel’s first order nonlinear equation. Furthermore, the stability analysis of the dispersive solutions are examined which shows that the traveling wave velocity is a bifurcation parameter which governs between different classes of waves. We use the phase plane analysis and show that at a critical velocity, the solution has a transcritical bifurcation.

Dirac equation in presence of the Hartmann and Higgs oscillator superintegrable potentials with the spin and pseudospin symmetries

The spin and pseudospin symmetries in the Dirac Hamiltonian are investigated in the presence of the Hartmann and the Higgs oscillator superintegrable potentials. The Pauli-Dirac representation is used in the Dirac equation with scalar and vector potentials of equal magnitude. Then, the Dirac equation is reduced to a Schrödinger-like equation. The symmetry algebras of the Schrödinger-like equation corresponding to the superintegrable potentials are represented. Also, the associated irreducible representations are shown by means of the quadratic algebras. Finally, the relativistic energy spectra of the Hartmann and the Higgs oscillator superintegrable potentials are calculated.

3D controlling the bead linking to DNA molecule in a single-beam nonlinear optical tweezers

The approximate expressions describing the redistribution of laser beam and optical forces in Kerr fluid, and the ratio of refractive indexes basing on the optical Kerr effect in fluid are derived. Basing on them, the dynamic of nonlinear bead in the nonlinear fluid is simulated by the finite different Langevin equation in presence of the optical Kerr and self-focused effects. The radial and axial control processes of bead linking to λ-phage WLC DNA molecule in fluid space are numerically observed by calibration of the laser power under and upper the critical value, respectively. The stable position-laser power characteristics are numerically found out. Based on the results, a sample of single-beam optical tweezers for 3D (axial and radial) control of bead is proposed and discussed.

PREDICTION OF ELECTRON DRIFT VELOCITY IN HELICALLY COILED CARBON NANOTUBES

We studied electron transport in single wall carbon nanotubes placed in stationary homogeneous electric fields, oriented along tubes. Electron distributions for various electric fields are determined by solving stationary multi bands Boltzmann transport equation in presence of electron phonon scattering mechanisms. Contributions of all possible scattering channels, allowed by selection rules and energy conservation, are taken into account for finding scattering rate and collision integrals. As it is previously predicted, large electron drift velocities in straight single wall carbon nanotubes are obtained. Frequent electron scattering as well as low group velocity have strong impact on reduction of drift velocity in helically coiled carbon nanotubes.