Nonconstant Potential Research Articles

Viscous effect in the late time evolution of phantom universe

We investigate the cosmological implications of a phantom dark energy model with bulk viscosity. We explore this model as a possible way to resolve the big rip singularity problem that plagues the phantom models. We use the latest type Ia supernova and Hubble parameter data to constrain the model parameters and find that the data favor a significant bulk viscosity over a non-constant potential term for the phantom field. We perform a dynamical analysis of the model and show that the only stable and physical attractor corresponds to a phantom-dominated era with a total equation of state that can be greater than -1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-1$$\\end{document} due to the viscosity. We also study the general effect of viscosity on the phantom field and the late time evolution of the universe. We apply the statefinder diagnostic to the model and find that it approaches a nearby fixed point asymptotically, indicating that the universe can escape the big rip singularity with the presence of bulk viscosity. We conclude that bulk viscosity can play an important role in affecting the late-time behavior as well as alleviating the singularity problem of the phantom universe.

Well-balanced kinetic schemes for two-phase flows

At equilibrium state of a two-phase fluid system, the chemical potential is constant and the velocity vanishes. However, such equilibrium state usually cannot be captured by numerical methods due to discretization errors. Consequently, inconsistent thermodynamic interfacial properties due to non-constant chemical potential, and spurious velocities due to discrete force imbalance, are frequently encountered in numerical simulations. Therefore, numerical schemes with well-balanced properties, which can capture the equilibrium state at discrete level, are preferred for simulating two-phase flows. In this paper, we report the progress of developing well-balanced mesoscopic numerical methods based on kinetic theory, focusing on the lattice Boltzmann equation (LBE) method and the discrete unified gas-kinetic scheme (DUGKS). First, the discrete balance property of a free-energy LBE for single-component two-phase flows is analyzed to identify the structure of force imbalance. Then, a well-balanced LBE (WB-LBE) model which has the same algorithm structure as the standard one is reviewed. The WB-LBE is theoretically shown to be able to achieve the discrete equilibrium state, and the well-balance properties are confirmed numerically. Some extensions to other two-phase LBE models are discussed with enhanced numerical stability. The well-balanced DUGKS, which can use non-uniform meshes and exhibits better numerical stability for large density ratio systems is also reported.

Diameter estimation of gradient ρ-Einstein solitons

The main aim of this article is to provide a lower bound of the diameter of a compact gradient ρ-Einstein soliton satisfying some given conditions. We have also deduced some conditions of the gradient ρ-Einstein soliton with bounded Ricci curvature to become non-shrinking and non-expanding. Further, we have proved that a complete non-compact gradient shrinking or expanding Schouten soliton with non-constant potential along with a condition for the boundedness of the scalar curvature must be non-parabolic.

New method of exponential potentials reconstruction based on given scale factor in phantonical two-field models

We investigate two-field cosmological model with phantom and canonical fields (phantonical model as a generalisation of the quintom model for global universe evolution, including early inflationary stage). The model is represented as the chiral cosmological model with the target space conformal to 2D pseudo-Euclidean space. We found three sorts of exact solutions for a constant potential by direct integration of dynamic equations and proposed new method of exact solution construction also extended for e-folds N-formalism for the case of non-constant exponential potential. We show that the exact solutions of cosmological dynamic equations can be obtained in explicit form for any type of scale factor evolution a(t) which implies the explicit inverse dependence t = t(a), considering the quasi de Sitter expansion of the universe with non-negligible kinetic energies of scalar fields and showing that the appeared effective cosmological constant can be considered as the source of second accelerated expansion of the universe. Further we analyze cosmological perturbations in the two-field model under consideration reducing it to the single field one. Such transition give us the way of cosmological parameters calculation and comparison them to observational data. We find that in proposed two-field cosmological model the isocurvature perturbations are negligible, and observable curvature perturbations are induced by adiabatic modes only. The series of phantonical models based on exact inflationary solutions are represented, and it is shown the correspondence to observational data for these models.

Numerical approximation of the scattering amplitude in elasticity

We propose a numerical method to approximate the scattering amplitudes for the elasticity system with a non-constant matrix potential in dimensions d=2 and 3. This requires to approximate first the scattering field, for some incident waves, which can be written as the solution of a suitable Lippmann-Schwinger equation. In this work we adapt the method introduced by Vainikko (Res Rep A 387:3–18, 1997) to solve such equations when considering the Lamé operator. Convergence is proved for sufficiently smooth potentials. Implementation details and numerical examples are also given.

A diffusion Monte Carlo method for charge density on a conducting surface at non-constant potentials

Abstract We develop a last-passage Monte Carlo algorithm on a conducting surface at non-constant potentials. In the previous researches, last-passage Monte Carlo algorithms on conducting surfaces with a constant potential have been developed for charge density at a specific point or on a finite region and a hybrid BIE-WOS algorithm for charge density on a conducting surface at non-constant potentials. In the hybrid BIE-WOS algorithm, they used a deterministic method for the contribution from the lower non-constant potential surface. In this paper, we modify the hybrid BIE-WOS algorithm to a last-passage Monte Carlo algorithm on a conducting surface at non-constant potentials, where we can avoid the singularities on the non-constant potential surface very naturally. We demonstrate the last-passage Monte Carlo algorithm for charge densities on a circular disk and the four rectangle plates with a simple voltage distribution, and update the corner singularities on the unit square plate and cube.

Towards constant potential modeling of CO-CO coupling at liquid water-Cu(1 0 0) interfaces

We use density functional theory, molecular dynamics, and metadynamics to study electrochemical *CO–*CO coupling in explicit electrolyte. We consider both the *CO–*CO coupling reaction and the charging process required to keep the potential constant. The charging process consists of transferring explicit cations from the electrolyte and electrons from the potentiostat to the interface. Under constant charge conditions (non-constant electrostatic potential), the *CO–*CO coupling reaction energies are relative insensitive to the charge state at the interface and the electrolyte composition and the reaction occurs with co-adsorption of water. Under constant potential conditions, the *CO–*CO coupling reaction is stabilized at lower potentials because of charging, the reaction is influenced by the electrolyte composition, and water-coadsorption is reduced. The *CO–*CO coupling reaction changes the electrosorption valency by around 0.4–0.5. We propose a simple approach to convert energetics from constant charge to estimates at constant potential. The approach is generally applicable to electrochemical processes.

Least energy solutions for a class of fractional Schrödinger-Poisson systems

In this paper, the existence of a nontrivial least energy solution is considered for the nonlinear fractional Schrödinger-Poisson systems (−Δ)su + V(x)u + ϕu = |u|p−1u and (−Δ)tϕ = u2 in R3, where (−Δ)α is the fractional Laplacian for α = s, t ∈ (0, 1) with s < t and 2s + 2t > 3. Under some appropriate assumptions on the non-constant potential V(x), we prove the existence of a nontrivial least energy solution when 2<p<2s*−1=(3+2s)/(3−2s) by using some new analytical skills and the Nehari-Pohožaev type manifold.

Reflectionless Discrete Schrödinger Operators are Spectrally Atypical

We prove that, if an isospectral torus contains a discrete Schr\"odinger operator with nonconstant potential, the shift dynamics on that torus cannot be minimal. Consequently, we specify a generic sense in which finite unions of nondegenerate closed intervals having capacity one are not the spectrum of any reflectionless discrete Schr\"odinger operator. We also show that the only reflectionless discrete Schr\"odinger operators having zero, one, or two spectral gaps are periodic.

Odd-frequency superconducting pairing and subgap density of states at the edge of a two-dimensional topological insulator without magnetism

We investigate the emergence and consequences of odd-frequency spin-triplet s-wave pairing in superconducting hybrid junctions at the edge of a two-dimensional topological insulator without any magnetism. More specifically, we consider several different normal-superconductor hybrid systems at the topological insulator edge, where spin-singlet s-wave superconducting pairing is proximity-induced from an external conventional superconductor. We perform fully analytical calculations and show that odd-frequency mixed spin-triplet s-wave pairing arises due to the unique spin-momentum locking in the topological insulator edge state and the naturally non-constant pairing potential profile in hybrid systems. Importantly, we establish a one-to-one correspondence between the local density of states (LDOS) at low energies and the odd-frequency spin-triplet pairing in NS, NSN and SNS junctions along the topological insulator edge; at interfaces the enhancement in the LDOS can directly be attributed to the contribution of odd-frequency pairing. Furthermore, in SNS junctions we show that the emergence of the zero-energy LDOS peak at the superconducting phase $\phi=\pi$ is associated purely with odd-frequency pairing in the middle of the junction.

Dynamical system approach to scalar–vector–tensor cosmology

Using scalar-vector-tensor Brans Dicke (VBD) gravity [3] in presence of self interaction BD potential $V(\phi)$ and perfect fluid matter field action we solve corresponding field equations via dynamical system approach for flat Friedmann Robertson Walker metric (FRW). We obtained 3 type critical points for $\Lambda CDM$ vacuum de Sitter era where stability of our solutions are depended to choose particular values of BD parameter $\omega.$ One of these fixed points is supported by a constant potential which is stable for $\omega<0$ and behaves as saddle (quasi stable) for $\omega\geq0.$ Two other ones are supported by a linear potential $V(\phi)\sim\phi$ which one of them is stable for $\omega=0.27647.$ For a fixed value of $\omega$ there is at least 2 out of 3 critical points reaching to a unique critical point. Namely for $\omega=-0.16856(-0.56038)$ the second (third) critical point become unique with the first critical point. In dust and radiation eras we obtained 1 critical point which never become unique fixed point. In the latter case coordinates of fixed points are also depended to $\omega.$ To determine stability of our solutions we calculate eigenvalues of Jacobi matrix of 4D phase space dynamical field equations for de Sitter, dust and radiation eras. We should be point also potentials which support dust and radiation eras must be similar to $V(\phi)\sim\phi^{-\frac{1}{2}}$ and $V(\phi)\sim\phi^{-1}$ respectively. In short our study predicts that radiation and dust eras of our VBD-FRW cosmology transmit to stable de Sitter state via non-constant potential (effective variable cosmological parameter) by choosing $\omega=0.27647$.

Treatment of hydrochloric acid using Mg–Al layered double hydroxide intercalated with carbonate

Mg–Al layered double hydroxide intercalated with CO32− (CO3·Mg–Al LDH) was found to take up only low amounts of Cl− during the treatment of hydrochloric acid. Low pH promotes the removal of Cl−. HCl is considered to react with CO32− in the interlayers of Mg–Al LDH as a result of which Cl− is probably intercalated in the interlayers. High pH of the Mg–Al LDH suspension leads to a lower extent of reaction between HCl and Mg–Al LDH, owing to the neutralization of the acid. We can state that the adsorption of Cl− on Mg–Al LDH is best described by the Dubinin–Radushkevich adsorption isotherm. The maximum adsorption amounts were calculated to be 1.4 and 0.6mmol/g for CO3·Mg–Al LDH with Mg/Al molar ratios of 2 and 4, respectively, whereas the adsorption energies were calculated to be 82 and 124kJ/mol, respectively. In summary, the removal of Cl− is caused by both the reaction between hydrochloric acid and CO32− in the interlayers of Mg–Al LDH as well as anion exchange between the HCO3− produced and a different Cl− ion in hydrochloric acid. This explains why the adsorption is best expressed by the D–R adsorption isotherm, which assumes a heterogeneous surface and non-constant adsorption potential.

An asymptotic eigenvalue problem for a Schrödinger type equation on domains with boundaries

The first eigenvalue and corresponding eigenfunction of a certain Schro dinger type problem with a nonconstant potential is asymptotically determined by the behaviour of this potential near its minimum. If the domain is the whole space or when the potential does not assume its minimum at the boundary, the problem has been extensively studied by Simon, Helffer and Sjostrand, respectively by Dancer and Lopez-Gomez. We consider the problem on bounded domains in the case that the potential assumes its minimum at several places, which may include a boundary point.

On the Bulk Velocity of Brownian Ratchets

In this paper we study the unidirectional transport effect for Brownian ratchets modeled by Fokker--Planck-type equations. In particular, we consider the adiabatic and semiadiabatic limits for tilting ratchets, generic ratchets with small diffusion, and the multistate chemical ratchets. Having established a linear relation between the bulk transport velocity and the biperiodic solution, and using relative entropy estimates and new functional inequalities, we obtain explicit asymptotic formulas for the transport velocity and qualitative results concerning the direction of transport. In particular, we prove the conjecture by Blanchet, Dolbeault, and Kowalczyk that the bulk velocity of the stochastic Stokes' drift is nonzero for every nonconstant potential.

Two electrically-conducting stamps on the surface of piezoelectric materials

A model of two electrically-conducting stamps acting on the surface of piezoelectric materials is developed by using the generalized Almansi’s theorem. General solutions for distinctive or repeated eigenvalues are given. A system of singular integral equations is obtained and solved analytically. Explicit expressions for two flat, electrically conducting stamps with constant electric potential and non-constant electric potential are presented, which are valid for general cases since the present method is feasible for general cases. Numerical analyses were performed to reveal the effect of the distance between the two flat stamps on the contact behavior and to show the validity of the present derivation. The present work is very promising for FEM or BEM simulation of piezoelectric materials.

Fluctuation with dust of de Sitter ground state of scalar-tensor gravity

An exact de Sitter solution of scalar-tensor gravity is found in our recent work, in which the non-minimal coupling scalar is rolling along a non-constant potential. Based on this solution, a dust-filled FRW universe is explored in frame of scalar-tensor gravity in this article. The effective dark energy induced by the sole non-minimal scalar can be quintessence-like, phantom-like, and more significantly, can cross the phantom divide. The rich and varied properties of scalar-tensor gravity even with only one scalar is shown.

Soliton dynamics for CNLS systems with potentials

The semiclassical limit of a weakly coupled nonlinear focusing Schrodinger system in presence of a nonconstant potential is studied. The initial data is of the form (u1,u2) with ui = ri( x−x e )e (i/e)x·ξ , where (r1, r2) is a real ground state solution, belonging to a suitable class, of an associated autonomous elliptic system. For e sufficiently small, the solution (φ1,φ2) will been shown to have, locally in time, the form (r1( x−x(t) e )e (i/e)x·ξ(t), r2( x−x(t) e )e (i/e)x·ξ(t)), where (x(t), ξ(t)) is the solution of the Hamiltonian system ẋ(t) = ξ(t), ξ(t) = −∇V (x(t)) with x(0) = x and ξ(0) = ξ.

Experimental verification of nonconstant potential and density on magnetic surfaces of helical nonneutral plasmas

For the first time, nonconstant space potential ϕs and electron density ne on magnetic surfaces of helical nonneutral plasmas are observed experimentally. The variation of ϕs grows with increasing electron injection energy, implying that thermal effects are important when considering the force balance along magnetic field lines. These observations confirm the existence of plasma equilibrium having nonconstant ϕs and ne on magnetic surfaces of helical nonneutral plasmas.

Fractional Fokker-Planck dynamics: Stochastic representation and computer simulation

A computer algorithm for the visualization of sample paths of anomalous diffusion processes is developed. It is based on the stochastic representation of the fractional Fokker-Planck equation describing anomalous diffusion in a nonconstant potential. Monte Carlo methods employing the introduced algorithm will surely provide tools for studying many relevant statistical characteristics of the fractional Fokker-Planck dynamics.

Uniqueness and stability of ground states for some nonlinear Schrödinger equations

We discuss the orbital stability of standing waves of a class of nonlinear Schrödinger equations in one space dimension. The crucial feature for our treatment is the presence of a non-constant linear potential that is even and decreasing away from the origin in space. This enables us to establish the orbital stability of all ground states over the whole range of frequencies for which such solutions exist.