Nonzero Potential Research Articles

Classification of the non-null electrovacuum solution of Einstein–Maxwell equations with three-parameter abelian group of motions

The classification of the Stackel spaces of the electrovacuum of the type (3.0) has been done. These spaces are invariant under the action of the three-parameter abelian group of motions and belong to the first type Bianchi spaces. In the case of a non-zero cosmological term, the metrics and potentials contain solutions of a nonlinear ordinary differential equation of the second order. When the cosmological term equals zero, the metrics and the components of the electromagnetic field tensor are expressed through elementary functions. Thus the classification of the electrovacuum stackel spaces of all types is completed and complete list of these spaces is constructed.

Electrokinetic properties of NaCl solution via molecular dynamics simulations with scaled-charge electrolytes.

Scaling ionic charges has become an alternative to polarizable force fields for representing indirect charge transfer effects in molecular simulations. In our work, we apply molecular dynamics simulations to investigate the properties of NaCl aqueous solutions in homogeneous and confined media. We compare classical integer- and scaled-charge force fields for the ions. In the bulk, we validate the force fields by computing equilibrium and transport properties and comparing them with experimental data. Integer-charge ions overestimate dielectric saturation and ionic association. Both force fields present an excess in ion-ion correlation, which leads to a deviation in the ionic conductivity at higher ionic strengths. Negatively charged quartz is used to simulate the confinement effect. Electrostatic interactions dominate counter-ion adsorption. Full-charge ions have stronger and more defined adsorption planes. We obtain the electroosmotic mobility of the solution by combining the shear plane location from non-equilibrium simulations with the ionic distribution from equilibrium simulations. From the Helmholtz-Smoluchowski equation, the zeta potential and the streaming potential coupling coefficient are computed. From an atomic-scale perspective, our molecular dynamics simulations corroborate the hypothesis of maximum packing of the Stern layer, which results in a stable and non-zero zeta potential at high salinity. The scaled-charge model representation of both properties is in excellent qualitative and quantitative agreement with experimental data. With our work, we demonstrate how useful and precise simple scaled-charge models for electrolytes can be to represent complex systems, such as the electrical double layer.

On K-contact metric manifolds satisfying an almost gradient Ricci–Bourguignon soliton

The main purpose of the paper is to study an almost gradient Ricci–Bourguignon soliton (RB soliton) within the framework of [Formula: see text]-contact manifolds and [Formula: see text]-contact manifolds. First, we prove that if complete [Formula: see text]-contact manifold endows a gradient RB soliton, then the manifold is compact Sasakian and isometric to unit sphere [Formula: see text]. Next, we show that if a complete contact metric satisfies an almost RB soliton with a non-zero potential vector field is collinear with the Reeb vector field [Formula: see text] and the Reeb vector field [Formula: see text] acting as an eigenvector of the Ricci operator, then it is compact Einstein Sasakian and the potential vector field is a constant multiple of the Reeb vector field [Formula: see text]. Lastly, we prove that if the metric of a non-Sasakian [Formula: see text]-contact manifold is an almost gradient RB soliton, then it is flat in dimension 3 and in higher dimensions it is locally isometric to [Formula: see text].

An exact new solution of the Schrödinger equation with a zero potential energy analogous to Fick’s equation of diffusion

This paper presents a novel and exact solution of the Schrödinger equation with zero potential energy, based on the analogy with Fick’s equation of diffusion. The author derived the wavefunction of a particle in a vacuum as an error function of the rotational phase angle, which corresponds to the geometry of a flat space. This solution reduces to the sinusoidal form of the wavefunction commonly used in quantum mechanics. The author also explored the implications of this solution for the connection between quantum physics and gas mechanics, and the possibility of using error functions and general transforms to model past, present, and future events in physics. The author used computer simulations to compare the error function solution and the sinusoidal solution in terms of response time, accuracy, and fit to the geometry of a flat space. The results showed that the error function solution was superior to the sinusoidal solution in all aspects, and that it had a stronger link to the gas mechanics, useful to Quantum ASTROPHYSICS. The results also suggested that the error function solution could be used to model past, present, and future events in physics, using error functions and general transforms. This paper is a preliminary analysis of the deeper physics underlying the error function solution of the Schrödinger equation, based on the author’s previous publications on point physics generalizing to Hod-PDP mechanism, field tensor modeling, string-metrics, and information-time event matrix formulations. The paper recommends that future research should extend the error function solution to space time geometry higher dimensions, non-zero potentials, and more diverse experiments. The paper also recommends that future research should explore the applications of error functions and general transforms within physics and other mathematical physical general related fields of sciences.

Equilibrium states from gravitational collapse of a minimally coupled scalar field with a nonzero potential

Equilibrium states from gravitational collapse of a minimally coupled scalar field with a nonzero potential

Geometric classifications of k-almost Ricci solitons admitting paracontact metrices

Abstract The prime objective of the approach is to give geometric classifications of k k -almost Ricci solitons associated with paracontact manifolds. Let M 2 n + 1 ( φ , ξ , η , g ) {M}^{2n+1}\left(\varphi ,\xi ,\eta ,g) be a paracontact metric manifold, and if a K K -paracontact metric g g represents a k k -almost Ricci soliton ( g , V , k , λ ) \left(g,V,k,\lambda ) and the potential vector field V V is Jacobi field along the Reeb vector field ξ \xi , then either k = λ − 2 n k=\lambda -2n , or g g is a k k -Ricci soliton. Next, we consider K K -paracontact manifold as a k k -almost Ricci soliton with the potential vector field V V is infinitesimal paracontact transformation or collinear with ξ \xi . We have proved that if a paracontact metric as a k k -almost Ricci soliton associated with the non-zero potential vector field V V is collinear with ξ \xi and the Ricci operator Q Q commutes with paracontact structure φ \varphi , then it is Einstein of constant scalar curvature equals to − 2 n ( 2 n + 1 ) -2n\left(2n+1) . Finally, we have deduced that a para-Sasakian manifold admitting a gradient k k -almost Ricci soliton is Einstein of constant scalar curvature equals to − 2 n ( 2 n + 1 ) -2n\left(2n+1) .

Lee's transient protonic capacitor cannot explain the surface proton current observed in bacteriorhodopsin purple membranes

Recently in this Journal, James Lee employed his transmembrane electrostatically localized proton (TELP) hypothesis and the notion of a transient protonic capacitor to explain the force holding protons at the surface of bacteriorhodopsin purple membrane fragments. Here we show that purple membrane fragments cannot maintain the requisite transient non-zero transmembrane potential, and even if they could, it would not support the surface proton current moving from the P side to the N side that was reported by Heberle et al. (Nature, 1994). Currently accepted models explain the force keeping protons at the membrane surface by invoking the unusual structure of water at the interface which serves to stabilize the proton (energy well) and/or raise the activation ∆G‡ (energy barrier) for release to the bulk phase. Any future invocations of TELP should be required to include experimental measurements carried out at the surfaces of lipid bilayer membranes and/or biological membranes.

Generalized initial-boundary problem for the wave equation with mixed derivative

We study an initial-boundary problem for a second-order inhomogeneous hyperbolic equation in a half-strip of the plane containing a mixed derivative with constant coefficients and zero or nonzero potential. This equation is the equation of transverse oscillations of a moving finite string. The case of zero initial velocity and fixed ends (Dirichlet conditions) is considered. It is assumed that the roots of the characteristic equation are simple and lie on the real axis on opposite sides of the origin. The classical solution of the initial-boundary problem is determined. In the case of zero potential, a uniqueness theorem for the classical solution is formulated and a formula for the solution is given in the form of a series consisting of contour integrals containing the initial data of the problem. Based on this formula, the concepts of a generalized initial-boundary value problem and a generalized solution are introduced. The main theorems on finite formulas for the generalized solution in the case of homogeneous and inhomogeneous problems are formulated. To prove these theorems, we apply an approach that uses the theory of divergent series in the sense of Euler, proposed by A.P. Khromov (axiomatic approach). Using this approach, on the basis of formulas for solutions in the form of a series, the formulated main theorems are proved. Further, as an application of the main theorems obtained, we prove a theorem on the existence and uniqueness of a generalized solution of the initial-boundary problem in the presence of a nonzero summable potential and give a formula for the solution in the form of an exponentially convergent series.

Boundary-obstructed topological superconductor in buckled honeycomb lattice under perpendicular electric field

In this work, we show that a buckled honeycomb lattice can host a boundary-obstructed topological superconductor (BOTS) in the presence of f-wave spin-triplet pairing (fSTP). The underlying buckled structure allows for the manipulation of both chemical potential and sublattice potential using a double gate setup. Although a finite sublattice potential can stabilize the fSTP with a possible higher-order band topology, because it also breaks the relevant symmetry, the stability of the corner modes is not guaranteed. Here we show that the fSTP on the honeycomb lattice gives BOTS under nonzero sublattice potential, thus the corner modes can survive as long as the boundary is gapped. Also, by examining the large sublattice potential limit where the honeycomb lattice can be decomposed into two triangular lattices, we show that the boundary modes in the normal state are the quintessential ingredient leading to the BOTS. Thus the effective boundary Hamiltonian becomes nothing but the Hamiltonian for Kitaev chains, which eventually gives the corner modes of the BOTS.

Approximate and Exact Solutions in the Sense of Conformable Derivatives of Quantum Mechanics Models Using a Novel Algorithm

The entirety of the information regarding a subatomic particle is encoded in a wave function. Solving quantum mechanical models (QMMs) means finding the quantum mechanical wave function. Therefore, great attention has been paid to finding solutions for QMMs. In this study, a novel algorithm that combines the conformable Shehu transform and the Adomian decomposition method is presented that establishes approximate and exact solutions to QMMs in the sense of conformable derivatives with zero and nonzero trapping potentials. This solution algorithm is known as the conformable Shehu transform decomposition method (CSTDM). To evaluate the efficiency of this algorithm, the numerical results in terms of absolute and relative errors were compared with the reduced differential transform and the two-dimensional differential transform methods. The comparison showed excellent agreement with these methods, which means that the CSTDM is a suitable alternative tool to the methods based on the Caputo derivative for the solutions of time-fractional QMMs. The advantage of employing this approach is that, due to the use of the conformable Shehu transform, the pattern between the coefficients of the series solutions makes it simple to obtain the exact solution of both linear and nonlinear problems. Consequently, our approach is quick, accurate, and easy to implement. The convergence, uniqueness, and error analysis of the solution were examined using Banach’s fixed point theory.

The membrane potential arising from the adsorption of ions at the biological interface.

Membrane theory makes it possible to compute the membrane potential of living cells accurately. The principle is that the plasma membrane is selectively permeable to ions and that its permeability to mobile ions determines the characteristics of the membrane potential. However, an artificial experimental cell system with an impermeable membrane can exhibit a nonzero membrane potential, and its characteristics are consistent with the prediction of the Goldman-Hodgkin-Katz eq., which is a noteworthy concept of membrane theory, despite the membrane's impermeability to mobile ions. We noticed this troublesome facet of the membrane theory. We measured the potentials through permeable and impermeable membranes where we used the broad varieties of membranes. Then we concluded that the membrane potential must be primarily, although not wholly, governed by the ion adsorption-desorption process rather than by the passage of ions across the cell membrane. A theory based on the Association-Induction Hypothesis seems to be a more plausible mechanism for the generation of the membrane potential and to explain this unexpected physiological fact. The Association-Induction Hypothesis states that selective ion permeability of the membrane is not a condition for the generation of the membrane potential in living cells, which contradicts the prediction of the membrane theory. Therefore, the Association-Induction Hypothesis is the actual cause of membrane potential. We continued the theoretical analysis by taking into account the Association-Induction Hypothesis and saw that its universality as a cause of potential generation mechanism. We then concluded that the interfacial charge distribution is one of the fundamental causes of the membrane potential.

Charge asymmetric electrolytes around a rigid cylindrical polyelectrolyte: A generalization of the capacitive compactness

The surface mean electrostatic potential and capacitive compactness of the electrical double layer surrounding an infinite rigid cylindrical polyelectrolyte are analysed for equally-sized -1:z+ aqueous electrolytes. Monte Carlo simulations, the non-linear Poisson–Boltzman equation, the modified Poisson–Boltzmann theory, and the hypernetted chain/mean spherical approximation integral equation are used to examine the role of multivalent cations (coions) when the properties of monovalent anions (counterions) are fixed. A non-zero mean electrostatic potential in the neighbourhood of an uncharged polyelectrolyte is predicted by the simulations and the modified Poisson–Boltzmann theory in the presence of multivalent cations. The concept of capacitive compactness is generalised to overcome the divergence found in the classical definition, when a non-zero potential at the point of zero charge is present. With a highly electrified colloidal surface an inversion is observed, as a function of colloidal charge, in the precedence of the mean electrostatic potential near the polyelectrolyte’s surface and of the capacitive compactness between -1:+1 and -1:z+ electrolytes.

Linearized boundary control method for an acoustic inverse boundary value problem

We develop a linearized boundary control method for the inverse boundary value problem of determining a potential in the acoustic wave equation from the Neumann-to-Dirichlet map. When the linearization is at the zero potential, we derive a reconstruction formula based on the boundary control method and prove that it is of Lipschitz-type stability. When the linearization is at a nonzero potential, we prove that the problem is of Hölder-type stability in two and higher dimensions. The proposed reconstruction formula is implemented and evaluated using several numerical experiments to validate its feasibility.

Black bounces, wormholes, and partly phantom scalar fields

Simpson and Visser recently proposed a phenomenological way to avoid some kinds of space-time singularities by replacing a parameter whose zero value corresponds to a singularity (say, $r$) with the manifestly nonzero expression $r(u) = \sqrt{u^2 + b^2}$, where $u$ is a new coordinate, and $b =$ \const $>0$. This trick, generically leading to a regular minimum of $r$ beyond a black hole horizon (called a "black bounce"), may hopefully mimic some expected results of quantum gravity, and was previously applied to regularize the Schwarzschild, Reissner-Nordstr\"om, Kerr and some other metrics. In this paper it is applied to regularize the Fisher solution with a massless canonical scalar field in general relativity (resulting in a traversable wormhole) and a family of static, spherically symmetric dilatonic black holes (resulting in regular black holes and wormholes). These new regular metrics represent exact solutions of general relativity with a sum of stress-energy tensors of a scalar field with a nonzero self-interaction potential and a magnetic field in the framework of nonlinear electrodynamics with a Lagrangian function $L(F)$, $F = F_{\mu\nu} F^{\mu\nu}$. A novel feature in the present study is that the scalar fields involved have "trapped ghost" properties, that is, are phantom in a strong-field region and canonical outside it, with a smooth transition between the regions. It is also shown that any static, spherically symmetric metric can be obtained as an exact solution to the Einstein equations with the stress-energy tensor of the above field combination.

Positively charged mineral surfaces promoted the accumulation of organic intermediates at the origin of metabolism.

Identifying plausible mechanisms for compartmentalization and accumulation of the organic intermediates of early metabolic cycles in primitive cells has been a major challenge in theories of life's origins. Here, we propose a mechanism, where positive membrane potentials elevate the concentration of the organic intermediates. Positive membrane potentials are generated by positively charged surfaces of protocell membranes due to accumulation of transition metals. We find that (i) positive membrane potentials comparable in magnitude to those of modern cells can increase the concentration of the organic intermediates by several orders of magnitude; (ii) generation of large membrane potentials destabilize ion distributions; (iii) violation of electroneutrality is necessary to induce nonzero membrane potentials; and (iv) violation of electroneutrality enhances osmotic pressure and diminishes reaction efficiency, resulting in an evolutionary driving force for the formation of lipid membranes, specialized ion channels, and active transport systems.

A novel approach for solving linear and nonlinear time-fractional Schrödinger equations

There is significant literature on Schrödinger differential equation (SDE) solutions, where the fractional derivatives are stated in terms of Caputo derivative (CD). There is hardly any work on analytical and numerical SDE solutions involving conformable fractional derivative (CFD). For the reasons stated above, we are required to solve the SDE in the form of CFD. The main goal of this research is to offer a novel combined computational approach by using conformable natural transform (CNT) and the homotopy perturbation method (HPM) for extracting analytical and numerical solutions of the time-fractional conformable Schrödinger equation (TFCSE) with zero and nonzero trapping potential. We call it the conformable natural transform homotopy perturbation method (CNTHPM). The relative, recurrence, and absolute errors of the problems are analyzed to evaluate the efficiency and consistency of the CNTHPM. The error analysis has confirmed the higher degree of accuracy and convergence rates, which indicates the effectiveness and reliability of the suggested method. Furthermore, 2D and 3D graphs compare the exact and approximate solutions. The procedure is quick, precise, and easy to implement, and it yields outstanding results. In addition, numerical results are also compared with other methods such as the differential transform method (DTM), split-step finite difference method (SSFDM), homotopy analysis method (HAM), homotopy perturbation method (HPM), Adomian decomposition method (ADM), and two-dimensional differential transform method (TDDTM). The comparison shows excellent agreement with these methods, which means that CNTHPM is a suitable alternative tool to the methods based on CD for the solutions of the time-fractional SDE. Moreover, we can conclude that the CFD is a suitable alternative to the CD in the modeling of time-fractional SDE. The Banach fixed point theory was also used to test the uniqueness of the solution, convergence, and error analysis.

Magnetic proximity induced valley-contrasting quantum anomalous Hall effect in a graphene- CrBr3 van der Waals heterostructure

The magnetic proximity effect is an imperative tool to comprehend the valley contrasting quantum anomalous Hall (QAH) effect in van der Waals (vdW) heterostructure. The introduction of magnetic exchange and spin orbit interaction together enables to realize topological phases, with a particular emphasis on an interface can be envisioned towards dissipationless electronics. Herein, the proximity coupled valley contrasting QAH effect is predicted in vdW heterostructure consisting of graphene and a ferromagnetic (FM) semiconductor ${\mathrm{CrBr}}_{3}$ with the implication of relativistic effect, from the ab initio density functional theory (DFT) simulation. The valley contrasting QAH effect is observed with a nonzero Chern number at a high-symmetry point stemming from Berry curvature and Wannier charge center (WCC), leading to a topologically nontrivial state. The occurrence of strong magnetic proximity coupling between graphene and ${\mathrm{CrBr}}_{3}$ monolayer is realized intrinsically, from shifting of Hall coefficient value near Fermi level. The opening of the global band gap (178 meV) is observed with the inclusion of spin orbit coupling (SOC). The anomalous Hall conductivity (AHC) demonstrates the presence of two maxima peaked at valley ${K}^{\ensuremath{'}}$ and $K$. The observation of AHC is mainly dominated by nonzero surface charge and localized potential at the heterointerface due to proximity interaction. The Fermi level is found to be located exactly inside the nontrivial global band gap, which can be tuned effectively by applying the external electric field or by introducing a staggered sublattice potential. This robustness makes experimental fabrication highly favorable for developing a valley contrasting QAH device prototype.

Nonlinear adiabatic electron plasma waves: I. General theory and nonlinear frequency shift

This paper provides a complete self-consistent nonlinear theory for electron plasma waves, within the framework of the adiabatic approximation. The theory applies whatever the variations of the wave amplitude provided that they are slow enough, and it is also valid when the plasma is inhomogeneous and non-stationary. Moreover, it accounts for: (i) the geometrical jump in action resulting from separatrix crossing; (ii) the continuous change in phase velocity making the wave frame non-inertial; (iii) the harmonic content of the scalar potential; (iv) a non-zero vector potential; (v) the transition probabilities from one region of phase space to the other when an orbit crosses the separatrix; and (vi) the possible change in direction of the wavenumber. The relative importance of each of the aforementioned effects is discussed in detail, based on the derivation of the nonlinear frequency shift. This allows us to specify how the general formalism may be simplified, depending on the value of the wavenumber normalized to the Debye length. Specific applications of our theory are reported in Paper II.

Singularity resolution in gravitational collapse

We investigate the unhindered gravitational collapse of a homogeneous scalar field with nonzero potential, a two-dimensional analog of the Mexican hat-shaped Higgs field potential. The collapsing scalar field is surrounded by an exterior retarded (outgoing) generalized Vaidya spacetime. We prove that the density dependence on the scale factor cannot be expressed as an algebraic function in such a scenario. For a certain transcendental expression of the density of such a field as a function of scale factor, we then show that the collapse evolves to a singularity at an infinite comoving time, which is equivalent to saying that the singularity is avoided altogether. An ultra high density region of the order of Planck length can, however, be reached in a finite comoving time. The absence of the formation of trapped surfaces makes this ultra high density region globally visible.

Axial perturbations of hairy Gauss-Bonnet black holes with a massive self-interacting scalar field

We study the axial quasinormal modes of hairy black holes in Gauss-Bonnet gravity with a massive self-interacting scalar field. Two coupling functions of the scalar field to the Gauss-Bonnet invariant are adopted with one of them leading to black hole scalarization. The axial perturbations are studied via time evolution of the perturbation equation, and the effect of the scalar field mass and the self-interaction constant on the oscillation frequency and damping time is examined. We study as well the effect of nonzero scalar field potential on the critical point at which the perturbation equation loses hyperbolicity in the case of black hole scalarization. The results show that the nonzero scalar field potential extends the range of parameters where such a loss of hyperbolicity is observed thus shrinking the region of stable black hole existence. This will have an important effect on the nonlinear dynamical simulation studies in massive scalar Gauss-Bonnet gravity.