Contact Transformations Research Articles

Dual Relativistic Quantum Mechanics I

In \cite{2} it was shown that Einstein's special theory of relativity and Maxwell's field theory have mathematically equivalent dual versions. The dual versions arise from an identity relating observer time to proper time as a contact transformation on configuration space, which leaves phase space invariant. The special theory has a dual version in the sense that, for any set of $n$ particles, every observer has two unique sets of global variables $({\bf{X}}, t)$ and $({\bf{X}}, \tau)$ to describe the dynamics, where ${\bf{X}}$ is the (unique) canonical center of mass. In the $({\bf{X}}, t)$ variables, time is relative and the speed of light is unique, while in the $({\bf{X}}, \tau)$ variables, time is unique and the speed of light is relative with no upper bound. In the Maxwell case, the two sets of particle wave equations are not equivalent. The dual version contains an additional longitudinal (dissipative) radiation term that appears instantaneously with acceleration, leading to the prediction that radiation from a betatron (of any frequency) will not produce photoelectrons. A major outcome is the dual unification of Newtonian mechanics and classical electrodynamics with Einstein's special theory of relativity, without a self-energy divergency, or need of the problematic Lorentz-Dirac equation or any assumptions about the size or structure of a particle. The purpose of this paper is to introduce and develop the dual theory of relativistic quantum mechanics. We obtain three distinct dual relativistic wave equations that reduce to the Schr{\"o}dinger equation when minimal coupling is turned off. We show that the dual Dirac equation provides a new formula for the anomalous magnetic moment of a charged particle. We can obtain the exact value for the electron g-factor and phenomenological values for the muon and proton g-factors.

High-order contact transformations of molecular Hamiltonians: general approach, fast computational algorithm and convergence of ro-vibrational polyad models

The paper describes methods and fast computational algorithm for building effective Hamiltonians in molecular physics using perturbative approach. Separations of fast and slow variables are considered in the framework of contact transformations (CT). The particular focus is on a systematic derivation of effective models for rovibrational spectroscopy from ab initio-based potential energy surfaces with an exhaustive review of previous studies in this field. We consider applications to several types of polyads coupled by Fermi, Coriolis, Darling-Dennison and other types of resonance interactions with examples for asymmetric top, symmetric top and spherical top molecules. A flexible choice of the modelling operator accounts for strong couplings of various types of nuclear motion in molecules among closely lying levels including vibrational resonance schemes (2:1:2 . ), (2:1:2:1), (4:2:6:3), (3:2:1:2:1:1), etc. that occur for C2v, C3v and Td molecules and their isotopic species. The method is implemented in the MOL_CT programme suite, which offers a complementary tool to variational methods in terms of convergence and computational time. The range of applications is also different. The goal of the CT method is providing mathematical models for analyses of molecular spectra with the high-resolution accuracy using physically meaningful parameters derived from ab initio functions.

Almost *-η-Ricci solitons on Kenmotsu pseudo-Riemannian manifolds

Abstract In this paper, we aim to study a special type of metric called almost * {*} -η-Ricci soliton on the special class of contact pseudo-Riemannian manifold. First, we prove that a Kenmotsu pseudo-Riemannian metric as an * {*} -η-Ricci soliton is Einstein if either it is η-Einstein or the potential vector field V is an infinitesimal contact transformation. Further, we prove that if a Kenmotsu pseudo-Riemannian manifold admits an almost * {*} -η-Ricci soliton with a Reeb vector field leaving the scalar curvature invariant, then it is an Einstein manifold. Finally, we present an example of * {*} -η-Ricci solitons which illustrate our results.

Conformal η-Ricci almost solitons of Kenmotsu manifolds

The aim of this paper is to find some important classes of Einstein manifolds using conformal [Formula: see text]-Ricci solitons and conformal [Formula: see text]-Ricci almost solitons. We prove that a Kenmotsu metric as conformal [Formula: see text]-Ricci soliton is Einstein if it is [Formula: see text]-Einstein or the potential vector field [Formula: see text] is infinitesimal contact transformation or collinear with the Reeb vector field [Formula: see text]. Next, we prove that a Kenmotsu metric as gradient conformal [Formula: see text]-Ricci almost soliton is Einstein if the Reeb vector field leaves the scalar curvature invariants. Finally, we construct some examples to illustrate the existence of conformal [Formula: see text]-Ricci soliton, gradient almost conformal [Formula: see text]-Ricci soliton on Kenmotsu manifold.

Theoretical insights into the uptake of sulfonamides onto phospholipid bilayers: Mechanisms, interaction and toxicity evaluation

Sulfonamides (SAs) are now recognized as the main emerging environmental pollutants in aquatic environments. Although the bioaccumulation capacities of SAs have been confirmed, the pathway for the penetration of the SAs into lipid bilayer has been not fully understood. In this study, the bioaccumulation mechanism of four typical SAs onto the dipalmitoyl phosphatidylcholine (DPPC) lipid bilayer and their effects on the properties of DPPC bilayer were employed and evaluated respectively by using molecular dynamics simulations. Results show that from the viewpoint of thermodynamics, it is favorable for these SAs partitioning to DPPC bilayer. The accommodation of four SAs onto the lipid membrane needs to undergo several processes, which include the contact stage, transformation stage, and absorption stage. Besides, the sulfamethoxazole (SMX) and sulfamethazine (SMZ) show a strong preference for the DPPC phase rather than the interface region while the sulfadiazine (SDZ) and sulfametoxydiazine (SMD) have similar tendencies in the interface region and DPPC phase. Furthermore, the cytotoxicity of SAs is reflected in their ability to affect the electrostatic potential of the membrane and to reduce the thickness of phospholipid bilayers. This molecular-level study provided an insightful understanding of the toxicity and bioaccumulation of SAs.

K-cosymplectic metric as an η-Ricci soliton

Let M be an almost cosymplectic manifold such that the Reeb vector field is Killing. In this paper, it is proved that if the metric of M satisfying the [Formula: see text]-Einstein condition is an [Formula: see text]-Ricci soliton, then either M is Ricci flat or the potential vector field is an infinitesimal contact transformation. Also, a concrete example of cosymplectic [Formula: see text]-manifold admitting non-trivial Ricci and [Formula: see text]-Ricci solitons is constructed.

Weak pion-production and the second resonance region

In this work we report the calculation of the total cross section for pion-production by the dispersion of neutrinos on nucleons. We use a consistent formalism for the intermediate resonance states of spin-$\frac{3}{2}$, taking care on the conditions imposed by the invariance on contact transformations and using the Sachs parametrization for the form factors. In addition, we incorporate states in the second resonance region up to 1.6 GeV and implement different approaches for all the dressed resonance propagators. In addition to the $\mathrm{\ensuremath{\Delta}}(1232)$, we include the ${N}^{*}(1440)$, ${N}^{*}(1535)$, and ${N}^{*}(1520)$ resonance contributions, and it is shown that this inclusion improves the description of the total cross section regarding a model where only the $\mathrm{\ensuremath{\Delta}}(1230)$ resonance is considered. Also, results for antineutrinos are properly described.

Some characterizations of -Einstein solitons on Sasakian manifolds

AbstractThe $\rho $ -Einstein soliton is a self-similar solution of the Ricci–Bourguignon flow, which includes or relates to some famous geometric solitons, for example, the Ricci soliton and the Yamabe soliton, and so on. This paper deals with the study of $\rho $ -Einstein solitons on Sasakian manifolds. First, we prove that if a Sasakian manifold M admits a nontrivial $\rho $ -Einstein soliton $(M,g,V,\lambda )$ , then M is $\mathcal {D}$ -homothetically fixed null $\eta $ -Einstein and the soliton vector field V is Jacobi field along trajectories of the Reeb vector field $\xi $ , nonstrict infinitesimal contact transformation and leaves $\varphi $ invariant. Next, we find two sufficient conditions for a compact $\rho $ -Einstein almost soliton to be trivial (Einstein) under the assumption that the soliton vector field is an infinitesimal contact transformation or is parallel to the Reeb vector field $\xi $ .

Equivalence Conditions and Invariants for the General Form of Burgers\u2019 Equations

Equivalence of differential equations is one of the most important concepts in the theory of differential equations. In this paper, the moving coframe method is applied to solve the local equivalence problem for the general form of Burgers’ equation, which has two independent variables under action of a pseudo-group of contact transformations. Using this method, we found the structure equations and invariants of these equations, as a result some conditions for equivalence of them will be given.

Conformal vector fields on almost co-Kähler manifolds

Abstract In this paper, we characterize almost co-Kähler manifolds with a conformal vector field. It is proven that if an almost co-Kähler manifold has a conformal vector field that is collinear with the Reeb vector field, then the manifold is a K-almost co-Kähler manifold. It is also shown that if a (κ, μ)-almost co-Kähler manifold admits a Killing vector field V, then either the manifold is K-almost co-Kähler or the vector field V is an infinitesimal strict contact transformation, provided that the (1,1) tensor h remains invariant under the Killing vector field.

Second-Order PDEs in 3D with Einstein–Weyl Conformal Structure

Einstein–Weyl geometry is a triple ({mathbb {D}},g,omega ) where {mathbb {D}} is a symmetric connection, [g] is a conformal structure and omega is a covector such that bullet connection {mathbb {D}} preserves the conformal class [g], that is, {mathbb {D}}g=omega g; bullet trace-free part of the symmetrised Ricci tensor of {mathbb {D}} vanishes. Three-dimensional Einstein–Weyl structures naturally arise on solutions of second-order dispersionless integrable PDEs in 3D. In this context, [g] coincides with the characteristic conformal structure and is therefore uniquely determined by the equation. On the contrary, covector omega is a somewhat more mysterious object, recovered from the Einstein–Weyl conditions. We demonstrate that, for generic second-order PDEs (for instance, for all equations not of Monge–Ampère type), the covector omega is also expressible in terms of the equation, thus providing an efficient ‘dispersionless integrability test’. The knowledge of g and omega provides a dispersionless Lax pair by an explicit formula which is apparently new. Some partial classification results of PDEs with Einstein–Weyl characteristic conformal structure are obtained. A rigidity conjecture is proposed according to which for any generic second-order PDE with Einstein–Weyl property, all dependence on the 1-jet variables can be eliminated via a suitable contact transformation.

Almost Cosymplectic (k,mu )-metrics as eta-Ricci Solitons

In this paper, we study eta-Ricci solitons on almost cosymplectic (k,mu )-manifolds. As an application, it is proved that if an almost cosymplectic (k,mu )-metric with k<0 represents a Ricci soliton, then the potential vector field of the Ricci soliton is a strict infinitesimal contact transformation, and the corresponding almost cosymplectic manifold is locally isometric to a Lie group whose local structure is determined completely by k<0. In addition, a concrete example is constructed to illustrate the above result.

Tunable properties of ZnSe/graphene heterostructure as a promising candidate for photo/electro-catalyst applications

The graphene-based Van der Waals (vdW) heterostructures show great potential for the next generation of photoelectronic nanodevices. Here, we constructed the ZnSe/graphene vdW heterojunction and investigated its structural, electronic, optical, transportable, and catalytic properties by using density functional theory (DFT). The results show that ZnSe is a direct semiconductor with a bandgap of 3.24 eV. The electron mobility of ZnSe is seven times higher than that of the hole, which is beneficial for the photogenerated hole-electron separation. Besides, the n-type Schottky to Ohmic contact transformation can be realized by applying an external electric field of 0.2 V/Å, and the underlying mechanism is discussed. Finally, the potential ability of photo/electrocatalysis for graphene/ZnSe heterostructure and electrocatalysis for ZnSe monolayer is also explored. The hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) can spontaneously activate in acid (PH = 1,2) and alkaline (PH > 9) media under light irradiation. The overpotential of oxygen reduction reaction reaches 0.42 eV, which indicates graphene/ZnSe heterostructure would be a potential electrocatalyst. For the HER process of ZnSe monolayer, the overpotential is significantly decreased to 0.23 eV by doping 3d transition metal atom. Consequently, we hope our work can provide useful guidance for designing practical ZnSe-based applications.

Almost $$\eta $$-Ricci solitons on Kenmotsu manifolds

We characterize the Einstein metrics in such broad classes of metrics as almost \(\eta \)-Ricci solitons and \(\eta \)-Ricci solitons on Kenmotsu manifolds, and generalize some known results. First, we prove that a Kenmotsu metric as an \(\eta \)-Ricci soliton is Einstein metric if either it is \(\eta \)-Einstein or the potential vector field V is an infinitesimal contact transformation or V is collinear to the Reeb vector field. Further, we prove that if a Kenmotsu manifold admits a gradient almost \(\eta \)-Ricci soliton with a Reeb vector field leaving the scalar curvature invariant, then it is an Einstein manifold. Finally, we present new examples of \(\eta \)-Ricci solitons and gradient \(\eta \)-Ricci solitons, which illustrate our results.

Sasakian 3-metric as a generalized Ricci-Yamabe soliton

In the present paper, we first investigate a Sasakian 3-metric as a quasi-Yamabe gradient soliton. In the sequel, extending the notions of quasi-Yamabe soliton and Ricci-Yamabe soliton, the notion of generalized Ricci-Yamabe soliton is introduced. It is shown that if (g, V, λ, α, β, γ) is a generalized gradient Ricci-Yamabe soliton on a complete Sasakian 3-manifold M with potential function f , then M is compact Einstein and locally isometric to a unit sphere. Moreover, the potential vector field V is an infinitesimal contact transformation and pointwise collinear with the characteristic vector field ξ. Further, if h is the Hodge-de Rham potential for V, then, upto a constant, f = h.

Glycosaminoglycans role in hippocampal neural networks interneuronal communications

In the development of neurotechnologies, the search for applications for invasive neuroelectronic devices is relevant. One of the promising areas can be the development of ways of influencing intercellular communication, that is, not by acting on pre-, post- and extrasynaptic receptors, but on the extracellular matrix surrounding neurons and glia. For the development of bioelectronic pharmaceuticals, it is important to search for stimulation parameters at which a controlled change in the structural and functional parameters of the nervous tissue is possible. We considered one of the actual mechanisms of the molecular pathogenesis of SARS-CoV-2 infection - the induction of glycosaminoglycan metabolism. It is assumed that, getting into the olfactory epithelium and the olfactory bulbs of the brain, the virus is able to reach the structures of the central nervous system. When modeling changes in the enzymatic activity of hyaluronidase (0.1; 1.0; 10.0 U/ml) for 5 minutes in one of the key structures of the limbic system - the hippocampus (3-4-week-old ratpups, n = 64), the conditions for the transformation of intercellular contacts were revealed and evoked electrical activity of populations of CA1 region. The recorded development of synaptic plasticity processes has an adaptive potential at hyaluronidase concentrations not exceeding 1.0 U/ml.The in vitro method proposed in this work and a reasonable target for exposure - elements of the extracellular matrix, make it possible to simulate one of the mechanisms of the development of viral infection, optimize the process of preliminary screening of new medicinal substances that can minimize the risk of developing neuroinflammatory processes, and also substantiate the conditions for safe and/or therapeutic effects and electrical impulses on the elements of the nervous tissue.

Almost Kenmotsu $$(k,\mu )'$$-manifolds with Yamabe solitons

Let $$(M^{2n+1},\phi ,\xi ,\eta ,g)$$ be a non-Kenmotsu almost Kenmotsu $$(k,\mu )'$$ -manifold. If the metric g represents a Yamabe soliton, then either $$M^{2n+1}$$ is locally isometric to the product space $$\mathbb {H}^{n+1}(-4)\times \mathbb {R}^n$$ or $$\eta $$ is a strict infinitesimal contact transformation. The later case can not occur if a Yamabe soliton is replaced by a gradient Yamabe soliton. Some corollaries of this theorem are given and an example illustrating this theorem is constructed.

Few-Layered MoS2 Field-Effect Transistors with a Vertical Channel of Sub-10 nm.

Few-layered molybdenum disulfide (MoS2) has demonstrated promising advantages for the integration of next-generation electronic devices. A vertical short-channel MoS2 transistor with a channel length of sub-10 nm can be realized using mica as the insulated mesa and MoS2 flake dry-transferred onto the mica as the channel. A near-perfect symmetrical and fully saturated output characteristic can be obtained for the positive or negative drain-source voltage. This result is attributed to an effective transformation of the drain-source electrode contact from Schottky contact to Ohmic contact via forming gas annealing. The vertical-channel MoS2 transistor with a channel length of 8.7 nm exhibits excellent electrical characteristics, for example, a negligible hysteresis voltage of 60 mV, an extraordinarily small subthreshold swing of 73 mV/dec, a considerably weakened drain-induced barrier-lowering effect (100 mV/V), and the first-reported intrinsic delay time of 2.85 ps. Moreover, a logic inverter can be realized using the two vertical-channel MoS2 transistors, with a high voltage gain of 33. Experimental results indicate that the developed method is a potential approach for fabricating MoS2 transistors with an ultrashort channel and high performance, and consequently, manufacturing MoS2-based integrated circuits.

Numerical simulation of friction stir-assisted incremental forming with synchronous bonding of heterogeneous sheet metals

Friction stir-assisted incremental sheet forming with synchronous bonding is developed as a novel variant of incremental sheet forming, by which the two sheet metals form incrementally and get bonded simultaneously. Numerical simulation of this process is crucial in revealing the forming mechanism and optimizing the process compared with expensive physical tryouts. A coupled thermo-mechanical finite element model was established to take the contact and heat transformation in every interface into consideration, and VUINTER contact subroutine which can express the heat partition coefficient and coefficient of friction was complied, validated and revised by groove tests. The effectiveness of the numerical simulation was verified by experiments. Furthermore, a comparative study based on numerical simulation is conducted to analyze the effects of process variables including feed rate, spindle speed, wall angle and vertical step size on temperature, thickness, and central bulge.

Conservation laws of the equation of one-dimensional shallow water over uneven bottom in Lagrange’s variables

The systems of equations of one-dimensional shallow water over uneven bottom in Euler’s and Lagrange’s variables are considered. The intermediate system of equations is introduced. Hydrodynamic conservation laws of intermediate system of equations are used to find all first order conservation laws of shallow water equations in Lagrange’s variables for all bottom profiles. The obtained conservation laws are compared with the hydrodynamic conservation laws of the system of equations of one-dimensional shallow water over uneven bottom in Euler’s variables. Bottom profiles, providing additional conservation laws, are given. The problem of group classification of contact transformations of the shallow water equation in Lagrange’s variables is solved. First order conservation laws of the shallow water equation in Lagrange’s variables are obtained using Noether’s theorem. In the considered cases, the correspondence between non-divergence symmetries and the original Lagrangian is shown. A similar correspondence is valid for an arbitrary ordinary differential equation of the second order. It is shown that the application of Lagrange’s identity did not find all first order conservation laws of the shallow water equation in Lagrange’s variables.