Finite Kinetic Energy Research Articles

The structural, stability, electronic, optical and thermodynamic properties of MoX2 (X= S, Se, and Te) under hydrostatic pressures: a plasmon approach and first-principle study.

The new equations have been developed for the structural and electronic properties using the plasmon calculations for the first time for 2-D MoX2 structures. Literature shows still an extensive study is required on the stability and optical properties of MoX2 under different hydrostatic pressures and thermal properties under different temperatures using the first principles, for electronic industrial applications. The stability is analyzed using binding energy and phonon calculations. The phase transition of metallization of MoX2 is discussed using band structure calculations under different hydrostatic pressures. The calculated work function shows the photoemission starts from the threshold frequency of 4.189×104 cm-1, 3.184×104 cm-1, and 3.651×104 cm-1, respectively, for MoS2, MoSe2, and MoTe2 materials. The optical properties such as refractive index n(0), and static dielectric permittivity ε(0) for three successive materials are calculated under different hydrostatic pressures, applicable for optoelectronic applications. The calculated theoretical and computational values agree well with each other and also agree with reported and experimental values. Some of the values are calculated for the first time. The theoretical equations are derived using the molecular weight, effective valence electrons, and density of molecule of MoX2 structures. The simulation work is performed using GGA-PBE approximation in the CASTEP simulation package with DFT+D semi-empirical dispersion correction. An ultra-soft pseudopotential representation calculates the electronic and optical properties with a finite basis set kinetic energy cut-off of 381.0 eV. Each geometry has been optimized using Broyden, Fletcher, Goldfarb, and Shanno's (BFGS) algorithm for 100 iterations with a fixed basis quality variable cell method and finite electronic minimization parameters. The phonon calculations were performed using TDFT with a kinetic energy cut of 460 eV in a norm-conserving linear response method. The interpolation with a finite dispersion quality and q-vector grid spacing is performed.

Local existence of weak solutions to kinetic Cucker‐Smale‐Fokker‐Planck equation with singular commutation weights

In this paper, we investigate the Cauchy problem of the dimensional kinetic Cucker‐Smale‐Fokker‐Planck equation with singular communication weight behaving like as . First, local existence of weak solutions with finite kinetic energy is established for and . Second, for , we show that any initial datum with finite velocity moment of order launches a weak solution that propagates the initial velocity moment.

On the Regularity of Weak Solutions to Time-Periodic Navier–Stokes Equations in Exterior Domains

Consider the time-periodic viscous incompressible fluid flow past a body with non-zero velocity at infinity. This article gives sufficient conditions such that weak solutions to this problem are smooth. Since time-periodic solutions do not have finite kinetic energy in general, the well-known regularity results for weak solutions to the corresponding initial-value problem cannot be transferred directly. The established regularity criterion demands a certain integrability of the purely periodic part of the velocity field or its gradient, but it does not concern the time mean of these quantities.

Weak solutions of the three-dimensional hypoviscous elastodynamics with finite kinetic energy

We construct weak solutions to the 3D hypoviscous incompressible elastodynamics with finite kinetic energy which was unknown in literatures. Our result holds for fractional hypoviscosity (−Δ)θ, where 0≤θ<1. The proof consists of a convex integration scheme with new building blocks of 2D intermittency and suitable temporal correctors, which are motivated by the inherent geometric structure of the viscoelastic equations.

Ultrafast dissociation of ammonia: Auger Doppler effect and redistribution of the internal energy.

We study vibrationally-resolved resonant Auger (RAS) spectra of ammonia recorded in coincidence with the NH2+ fragment, which is produced in the course of dissociation either in the core-excited 1s-14a11 intermediate state or the first spectator 3a-24a11 final state. Correlation of the NH2+ ion flight times with electron kinetic energies allows directly observing the Auger-Doppler dispersion for each vibrational state of the fragment. The median distribution of the kinetic energy release EKER, derived from the coincidence data, shows three distinct branches as a function of Auger electron kinetic energy Ee: Ee + 1.75EKER = const for the molecular band; EKER = const for the fragment band; and Ee + EKER = const for the region preceding the fragment band. The deviation of the molecular band dispersion from Ee + EKER = const is attributed to the redistribution of the available energy to the dissociation energy and excitation of the internal degrees of freedom in the molecular fragment. We found that for each vibrational line the dispersive behavior of EKERvs. Ee is very sensitive to the instrumental uncertainty in the determination of EKER causing the competition between the Raman (EKER + Ee = const) and Auger (Ee = const) dispersions: increase in the broadening of the finite kinetic energy release resolution leads to a change of the dispersion from the Raman to the Auger one.

Construction and evolution of knotted vortex tubes in incompressible Schrödinger flow

We propose a theoretical method for constructing an initial two-component wave function that can be transformed into a knotted velocity field with finite kinetic energy and enstrophy. The wave function is constructed using two complex-valued polynomials, with one determining the desired shape of the knotted central axis and the other encoding the twisting nature of vortex lines, which facilitates the study of helicity conversions. We construct six knotted vortex fields with various centerline and twist helicity as initial conditions for direct numerical simulation of incompressible Schrödinger flow (ISF) in a periodic box. Although the evolution of morphological structure is similar for ISF and classical viscous flow, with all the knots becoming untied after a short time to form one or more separate vortex rings, their statistics are quite different. During the critical period of vortex reconnection, the increase in enstrophy is much more moderate in ISF than in viscous flow, indicating that the Landau–Lifshitz term in ISF inhibits the energy cascade from large to small scales. We also find that the centerline helicity changes dramatically during reconnection, which is consistent with the evolution of the geometrical shape of vortex lines.

Local existence and blowup criterion for the Euler equations in a function space with nondecaying derivatives

We consider the Cauchy problem for the incompressible Euler equations on Rd for d≥3. Then we demonstrate the local-in-time solvability of classical solutions with the nondecaying derivatives and finite kinetic energy. Moreover, we establish the blowup criterion of such solutions in terms of the vorticity.

Staggered superfluid phases of dipolar bosons in two-dimensional square lattices

We study the quantum ground state of ultracold bosons in a two-dimensional square lattice. The bosons interact via the repulsive dipolar interactions and s-wave scattering. The dynamics is described by the extended Bose-Hubbard model including correlated hopping due to the dipolar interactions, the coefficients are found from the second quantized Hamiltonian using the Wannier expansion with realistic parameters. We determine the phase diagram using the Gutzwiller ansatz in the regime where the coefficients of the correlated hopping terms are negative and can interfere with the tunneling due to single-particle effects. We show that this interference gives rise to staggered superfluid and supersolid phases at vanishing kinetic energy, while we identify parameter regions at finite kinetic energy where the phases are incompressible. We compare the results with the phase diagram obtained with the cluster Gutzwiller approach and with the results found in one dimension using DMRG.

Global Regularity of the 2D HVBK Equations

The Hall-Vinen-Bekharevich-Khalatnikov (HVBK) equations are a macroscopic model of superfluidity at non-zero temperatures. For smooth, compactly supported data, we prove the global well-posedness of strong solutions to these equations in $\mathbb{R}^2$, in the incompressible and isothermal case. The proof utilises a contraction mapping argument to establish local well-posedness for high-regularity data, following which we demonstrate global regularity using an analogue of the Beale-Kato-Majda criterion in this context. In the appendix, we address the sufficient conditions on a 2D vorticity field, in order to have a finite kinetic energy.

Convergence of filtered weak solutions to the 2D Euler equations with measure-valued vorticity

We study weak solutions of the two-dimensional (2D) filtered Euler equations whose vorticity is a finite Radon measure and velocity has locally finite kinetic energy, which is called the vortex sheet solution. The filtered Euler equations are a regularized model based on a spatial filtering to the Euler equations. The 2D filtered Euler equations have a unique global weak solution for measure valued initial vorticity, while the 2D Euler equations require initial vorticity to be in the vortex sheet class with a distinguished sign for the existence of global solutions. In this paper, we prove that vortex sheet solutions of the 2D filtered Euler equations converge to those of the 2D Euler equations in the limit of the filtering parameter provided that initial vortex sheet has a distinguished sign. We also show that a simple application of our proof yields the convergence of the vortex blob method for vortex sheet solutions. Moreover, we make it clear what kind of condition should be imposed on the spatial filter to show the convergence results and, according to the condition, these results are applicable to well-known regularized models like the Euler-$\alpha$ model and the vortex blob model.

On the relation between very weak and Leray–Hopf solutions to Navier–Stokes equations

We prove a general result that implies that very weak solutions to the Cauchy problem for the Navier–Stokes equations must be, in fact, Leray–Hopf solutions if only their initial data are (solenoidal) with finite kinetic energy.

Kinetic Energy Represented in Terms of Moments of Vorticity and Applications

We study 2d vortex sheets with unbounded support. First we show a version of the Biot–Savart law related to a class of objects including such vortex sheets. Next, we give a formula associating the kinetic energy of a very general class of flows with certain moments of their vorticities. It allows us to identify a class of vortex sheets of unbounded support being only sigma -finite measures (in particular including measures omega such that omega (mathbb {R}^2)=infty ), but with locally finite kinetic energy. One of such examples are celebrated Kaden approximations. We study them in details. In particular our estimates allow us to show that the kinetic energy of Kaden approximations in the neighbourhood of an origin is dissipated, actually we show that the energy is pushed out of any ball centered in the origin of the Kaden spiral. The latter result can be interpreted as an artificial viscosity in the center of a spiral.

Finite energy weak solutions of 2d Boussinesq equations with diffusive temperature

We show the existence of finite kinetic energy solution with prescribed kinetic energy to the 2d Boussinesq equations with diffusive temperature on torus.

On two-dimensional self-similar axisymmetric vortices

Superpositions of Lamb-Oseen axisymmetric vortices with Gaussian vorticity having zero net circulation and finite kinetic energy in unbounded domain are considered. Their evolution is described by self-similar solutions depending on a certain combination of space, time, and viscous diffusion. It is shown that the structure of a popular self-similar solution for a shielded vortex with Gaussian fluid rotation rate corresponds to two Lamb-Oseen vortices with opposite sign and nearly the same spatial scale. The radial structure of a combined vortex with different spatial scales is well suited for characterization of realistic vortical structures like atmospheric hurricanes. The linear stability of the combined vortex is investigated. The results have important implications for better understanding of vortex structures in two-dimensional flow.

Geometric classification of warped product submanifolds of nearly Kaehler manifolds with a slant fiber

There are two types of warped product pseudo-slant submanifolds, [Formula: see text] and [Formula: see text], in a nearly Kaehler manifold. We derive an optimization for an extrinsic invariant, the squared norm of second fundamental form, on a nontrivial warped product pseudo-slant submanifold [Formula: see text] in a nearly Kaehler manifold in terms of a warping function and a slant angle when the fiber [Formula: see text] is a slant submanifold. Moreover, the equality is verified for depending on what [Formula: see text] and [Formula: see text] are, and also we show that if the equality holds, then [Formula: see text] is a simply Riemannian product. As applications, we prove that the warped product pseudo-slant submanifold has the finite Kinetic energy if and only if [Formula: see text] is a totally real warped product submanifold.

Nonuniqueness of weak solutions to the Navier-Stokes equation

For initial datum of finite kinetic energy, Leray has proven in 1934 that there exists at least one global in time finite energy weak solution of the 3D Navier-Stokes equations. In this paper we prove that weak solutions of the 3D Navier-Stokes equations are not unique in the class of weak solutions with finite kinetic energy. Moreover, we prove that Holder continuous dissipative weak solutions of the 3D Euler equations may be obtained as a strong vanishing viscosity limit of a sequence of finite energy weak solutions of the 3D Navier-Stokes equations.

On the width of the Δ(1232) in NΔ and ΔΔ states

Due to the finite kinetic energy in the intermediate NΔ state the (internal) energy available for mesonic decay is decreased and consequently the effective NΔ width is suppressed in NN scattering. The same can happen also in ΔΔ case. Also the NΔ angular momentum suppresses the width as well, while the effect of the initial NN angular momentum is more subtle. The state dependence affects e.g. pion production observables and can also be seen as the origin of T = 1 “dibaryons”.

Optimal mixing in two-dimensional stratified plane Poiseuille flow at finite Péclet and Richardson numbers

We consider the nonlinear optimisation of irreversible mixing induced by an initial finite amplitude perturbation of a statically stable density-stratified fluid with kinematic viscosity $\unicode[STIX]{x1D708}$ and density diffusivity $\unicode[STIX]{x1D705}$. The initial diffusive error function density distribution varies continuously so that $\unicode[STIX]{x1D70C}\in [\bar{\unicode[STIX]{x1D70C}}-\unicode[STIX]{x1D70C}_{0}/2,\bar{\unicode[STIX]{x1D70C}}+\unicode[STIX]{x1D70C}_{0}/2]$. A constant pressure gradient is imposed in a plane two-dimensional channel of depth $2h$. We consider flows with a finite Péclet number $Pe=U_{m}h/\unicode[STIX]{x1D705}=500$ and Prandtl number $Pr=\unicode[STIX]{x1D708}/\unicode[STIX]{x1D705}=1$, and a range of bulk Richardson numbers $Ri_{b}=g\unicode[STIX]{x1D70C}_{0}h/(\bar{\unicode[STIX]{x1D70C}}U^{2})\in [0,1]$ where $U_{m}$ is the maximum flow speed of the laminar parallel flow, and $g$ is the gravitational acceleration. We use the constrained variational direct-adjoint-looping (DAL) method to solve two optimisation problems, extending the optimal mixing results of Foures et al. (J. Fluid Mech., vol. 748, 2014, pp. 241–277) to stratified flows, where the irreversible mixing of the active scalar density leads to a conversion of kinetic energy into potential energy. We identify initial perturbations of fixed finite kinetic energy which maximise the time-averaged perturbation kinetic energy developed over a finite time interval, and initial perturbations that minimise the value (at a target time, chosen to be $T=10$) of a ‘mix-norm’ as first introduced by Mathew et al. (Physica D, vol. 211, 2005, pp. 23–46), further discussed by Thiffeault (Nonlinearity, vol. 25, 2012, pp. 1–44) and shown by Foures et al. (2014) to be a computationally efficient and robust proxy for identifying perturbations that minimise the long-time variance of a scalar distribution. We demonstrate, for all bulk Richardson numbers considered, that the time-averaged kinetic-energy maximising perturbations are significantly suboptimal at mixing compared to the mix-norm minimising perturbations, and also that minimising the mix-norm remains (for density-stratified flows) a good proxy for identifying perturbations which minimise the variance at long times. Although increasing stratification reduces the mixing in general, mix-norm minimising optimal perturbations can still trigger substantial mixing for $Ri_{b}\lesssim 0.3$. By considering the time evolution of the kinetic energy and potential energy reservoirs, we find that such perturbations lead to a flow which, through Taylor dispersion, very effectively converts perturbation kinetic energy into ‘available potential energy’, which in turn leads rapidly and irreversibly to thorough and efficient mixing, with little energy returned to the kinetic-energy reservoirs.

On global solutions to the Vlasov-Poisson system with radiation damping

In this paper, the dynamics of three dimensional Vlasov-Poisson system with radiation damping is investigated. We prove global existence of a classical as well as weak solution that propagates boundedness of velocity-space support or velocity-space moment of order two respectively. This kind of solutions possess finite mass but need not necessarily have finite kinetic energy. Moreover, uniqueness of the classical solution is also shown.

Global m-Equivariant Solutions of Nematic Liquid Crystal Flows in Dimension Two

In this article we construct a global solution of the simplified Ericksen-Leslie system. We show that the velocity of the solution can be decomposed into the sum of three parts. The main flow is governed by the Oseen vortex with the same circulation Reynolds number as the initial fluid. The secondary flow has finite kinetic energy and decay in the speed (1 + t)−2 as $${t \rightarrow \infty}$$ . The third part is a minor flow whose kinetic energy decays faster than the secondary flow. As for the orientation variable, our solution has a phase function which diverges logarithmically to $${\infty}$$ as $${t \rightarrow \infty}$$ . This indicates that the orientation variable will keep rotating around the z-axis while $${t \rightarrow \infty}$$ . This phenomenon results from a non-trivial coupling between the orientation variable and a fluid with a non-zero circulation Reynolds number.