Initial Total Energy Research Articles

Kinetic energy estimates for the accuracy of the time-dependent Hartree–Fock approximation with Coulomb interaction

We study the time evolution of a system of N spinless fermions in R3 which interact through a pair potential, e.g., the Coulomb potential. We compare the dynamics given by the solution to Schrödinger's equation with the time-dependent Hartree–Fock approximation, and we give an estimate for the accuracy of this approximation in terms of the kinetic energy of the system. This leads, in turn, to bounds in terms of the initial total energy of the system.

State to State Photodissociation Dynamics of Vibrationally Excited D2O in B Band

The state-to-state photodissociassion dynamics for the B band of D2O have been explored from quantum dynamical calculations including the electronic ̃X and ̃B states. The calculations were carried out using a Chebyshev real wave packet method. The calculated absorption spectra, product state distributions, and branching ratios from different initial vibrational states show different dynamic features, due to the different shapes of the vibrational wavefunctions. The initial bending mode (0,1,0) generates two lobes with a shallow minimum on the absorption spectrum and a slight inverted vibrational population of OD(̃X) product at high total energies. The rotational state distributions of OD(̃X, v=0) product are highly inverted and depend weakly on the initial state and total energy. On the other hand, the ro-vibrational distributions of OD(̃A) product strongly oscillate with the total energy, which are dominated by the long-living resonances and depend sensitively on the potential surfaces. The antisymmetric stretching mode (0,0,1) has large OD(̃A)/OD(̃X) branching ratios at high total energies, which indicates that the B band dissociation proceeds mainly via the adiabatic pathway in some cases.

Weak solutions and blow-up for wave equations of p-Laplacian type with supercritical sources

This paper investigates a quasilinear wave equation with Kelvin-Voigt damping, utt − Δpu − Δut = f(u), in a bounded domain Ω ⊂ ℝ3 and subject to Dirichlét boundary conditions. The operator Δp, 2 < p < 3, denotes the classical p-Laplacian. The nonlinear term f(u) is a source feedback that is allowed to have a supercritical exponent, in the sense that the associated Nemytskii operator is not locally Lipschitz from W01,p(Ω) into L2(Ω). Under suitable assumptions on the parameters, we prove existence of local weak solutions, which can be extended globally provided the damping term dominates the source in an appropriate sense. Moreover, a blow-up result is proved for solutions with negative initial total energy.

The energetics of relativistic magnetic reconnection: ion-electron repartition and particle distribution hardness

Collisionless magnetic reconnection is a prime candidate to account for flare-like or steady emission, outflow launching, or plasma heating, in a variety of high-energy astrophysical objects, including ones with relativistic ion-electron plasmas. But the fate of the initial magnetic energy in a reconnection event remains poorly known: what is the amount given to kinetic energy, the ion/electron repartition, and the hardness of the particle distributions? We explore these questions with 2D particle-in-cell simulations of ion-electron plasmas. We find that 45 to 75% of the total initial magnetic energy ends up in kinetic energy, this fraction increasing with the inflow magnetization. Depending on the guide field strength, ions get from 30 to 60% of the total kinetic energy. Particles can be separated into two populations that only weakly mix: (i) particles initially in the current sheet, heated by its initial tearing and subsequent contraction of the islands; and (ii) particles from the background plasma that primarily gain energy via the reconnection electric field when passing near the X-point. Particles (ii) tend to form a power-law with an index $p=-d\log n(\gamma)/d\log\gamma$, that depends mostly on the inflow Alfv\'en speed $V_A$ and magnetization $\sigma_s$ of species $s$, with for electrons $p=5$ to $1.2$ for increasing $\sigma_e$. The highest particle Lorentz factor, for ions or electrons, increases roughly linearly with time for all the relativistic simulations. This is faster, and the spectra can be harder, than for collisionless shock acceleration. We discuss applications to microquasar and AGN coronae, to extragalactic jets, and to radio lobes. We point out situations where effects such as Compton drag or pair creation are important.

V1309 Sco—UNDERSTANDING A MERGER

One of the two outcomes of a common envelope event is a merger of the two stars. To date, the best known case of a binary merger is the V1309 Sco outburst, where the orbital period was known and observed to decay up to the outburst. Using the hydrodynamical code StarSmasher, we study in detail which characteristics of the progenitor binary affect the outburst and produce the best match with observations. We have developed a set of tools in order to quantify any common envelope event. We consider binaries consisting of a 1.52$M_\odot$ giant and a 0.16$M_\odot$ companion with $P_{\rm orb}\sim1.4$ days, varying the nature of the companion and its synchronization. We show that all considered progenitor binaries evolve towards the merger primarily due to the Darwin instability. The merger is accompanied by mass ejection that proceeds in several separate mass outbursts and takes away a few percent of the donor mass. This very small mass, nonetheless, is important as it is not only sufficient to explain the observed light-curve, but it also carries away up to 1/3 of the both initial total angular momentum and initial orbital energy. We find that all synchronized systems experience $L_2$ mass loss that operates during just a few days prior to merger and produces ring-shaped ejecta. The formed star is always a strongly heated radiative star that differentially rotates. We conclude that the case of a synchronized binary with a main-sequence companion gives the best match with observations of V1309 Sco.

Collective dynamics in a non-dissipative two-coupled pendulum system

We study the collective dynamics of a non-dissipative two-coupled pendulum system, including phase synchronization (PS) and measure synchronization (MS). We find that as the coupling intensity between the two pendulums increases, the PS happens prior to the MS. We also present a three-dimensional phase space representation of MS, from which a more detailed information about evolution can be obtained. Furthermore, the order parameters are introduced to describe the phase transition between PS and MS. Finally, through the analysis of the Poincaré sections, we show that the system exhibits separatrix crossing behavior right at the MS transition point, and as the total initial energy increases, the Hamiltonian chaos will arise with separatrix chaos at the chaotic MS transition point.

Global well-posedness and stability of semilinear Mindlin–Timoshenko system

We study long-term behavior of Reissner–Mindlin–Timoshenko (RMT) plate systems, focusing on the interplay between nonlinear viscous damping and source terms. The sources may represent restoring forces, but may also be focusing thus potentially amplifying the total energy which is the primary scenario of interest. This work complements [28] which established local well-posedness of this problem, global well-posedness when damping dominates the sources (in an appropriate sense) and a blow-up in the complementary scenario assuming negative “total” initial energy. The current paper develops the potential well theory for the RMT system: it proves global existence for potential well solutions without restricting the source exponents, derives explicit energy decay rates dependent on the order of the damping exponents, and verifies a blow-up result for positive total initial energy.

On the ultracold plasma evolution

The time evolution of the Coulomb system whose initial total energy is zero is considered. The solution for a system of 2000 particles in the range of 8000 inverse plasma frequencies was obtained by themolecular dynamicsmethod. It is shown that under conditions typical of experiments with ultracold plasma the nonideality parameter of the plasma cannot reach large values due to recombination heating, and the relaxation process itself is not described within the conventional model of three-body recombination.

Nonlinear Amplification and Decay of Phase-Mixed Waves in Compressing Plasma

Through particle-in-cell simulations, we show that plasma waves carrying trapped electrons can be amplified manyfold via compressing plasma perpendicularly to the wave vector. These simulations are the first abinitio demonstration of the conservation of nonlinear action for such waves, which contains a term independent of the field amplitude. In agreement with the theory, the maximum of amplification gain is determined by the total initial energy of the trapped-particle average motion but otherwise is insensitive to the particle distribution. Further compression destroys the wave; electrons are then untrapped at suprathermal energies and form a residual beam. As compression continues, the bump-on-tail instability is triggered each time one of the discrete modes comes in resonance with this beam. Hence, periodic bursts of the electrostatic energy are produced until a wide quasilinear plateau is formed.

Synchronization and phase transition in the Frenkel–Kontorova-type model system

A coupled Hamiltonian system of the Frenkel–Kontorova model is studied in this paper, including the measure synchronization and the complete synchronization of the model. The measure synchronization depends not only on the coupling strength but also on the initial conditions. In a certain range of initial conditions, complete synchronization is reached when the system is in the measure synchronization, which means that as the coupling strength increases the energy can be transferred from one particle to another more easily. In other words, the average vibration amplitude of two particles tends to be identical as the coupling strength increases. The critical point Kc depends on both the initial total energy of two particles and the initial energy difference between two particles. Moreover, it is also related to the initial velocity directions of the two particles.

Collisional Penrose Process near the Horizon of Extreme Kerr Black Holes

Collisions of particles in black hole ergospheres may result in an arbitrarily large center-of-mass energy. This led recently to the suggestion [M. Bañados, J. Silk, and S. M. West, Phys. Rev. Lett. 103, 111102 (2009)] that black holes can act as ultimate particle accelerators. If the energy of an outgoing particle is larger than the total energy of the infalling particles, the energy excess must come from the rotational energy of the black hole and hence, a Penrose process is involved. However, while the center-of-mass energy diverges, the position of the collision makes it impossible for energetic particles to escape to infinity. Following an earlier work on collisional Penrose processes [T. Piran and J. Shaham, Phys. Rev. D 16, 1615 (1977)], we show that even under the most favorable idealized conditions the maximal energy of an escaping particle is only a modest factor above the total initial energy of the colliding particles. This implies that one should not expect collisions around a black hole to act as spectacular cosmic accelerators.

Approach to Ground State and Time-Independent Photon Bound for Massless Spin-Boson Models

It is widely believed that an atom interacting with the electromagnetic field (with total initial energy well-below the ionization threshold) relaxes to its ground state while its excess energy is emitted as radiation. Hence, for large times, the state of the atom + field system should consist of the atom in its ground state, and a few free photons that travel off to spatial infinity. Mathematically, this picture is captured by the notion of asymptotic completeness. Despite some recent progress on the spectral theory of such systems, a proof of relaxation to the ground state and asymptotic completeness was/is still missing, except in some special cases (massive photons, small perturbations of harmonic potentials). In this paper, we partially fill this gap by proving relaxation to an invariant state in the case where the atom is modelled by a finite-level system. If the coupling to the field is sufficiently infrared-regular so that the coupled system admits a ground state, then this invariant state necessarily corresponds to the ground state. Assuming slightly more infrared regularity, we show that the number of emitted photons remains bounded in time. We hope that these results bring a proof of asymptotic completeness within reach.

A non-adiabatic wavepacket dynamical study of the low energy charge transfer process in the S3+ + H collision

The collisional system S3++H→S2++H+ has been studied using a time-dependent wavepacket methodology in two-dimensions. Using available potential energy surfaces and coupling matrix elements obtained from multireference ab initio calculations, five non-adiabatically coupled electronic states of 1Π symmetry have been included in the dynamical simulations. The collision has been studied in the low energy regime of 1–10eV. The wavepacket treatment accounts for the description of the collision including all possible impact parameters simultaneously in all spatial directions of the considered plane. The molecular movie of the scattered products arising from charge transfer yields the angular distribution and the total charge transfer probability vs. initial kinetic energy of the projectile. A detailed analysis of the forward, sideways, and backward scattering mechanisms showing different patterns is presented.

Instabilities in a nonstationary model of self-gravitating disks. III. The phenomenon of lopsidedness and a comparison of perturbation modes

This is an examination of the gravitational instability of the major large-scale perturbation modes for a fixed value of the azimuthal wave number m = 1 in nonlinearly nonstationary disk models with isotropic and anisotropic velocity diagrams for the purpose of explaining the displacement of the nucleus away from the geometric center (lopsidedness) in spiral galaxies. Nonstationary analogs of the dispersion relations for these perturbation modes are obtained. Critical diagrams of the initial virial ratio are constructed from the rotation parameters for the models in each case. A comparative analysis is made of the instability growth rates for the major horizontal perturbation modes in terms of two models, and it is found that, on the average, the instability growth rate for the m = 1 mode with a radial wave number N = 3 almost always has a clear advantage relative to the other modes. An analysis of these results shows that if the initial total kinetic energy in an isotropic model is no more than 12.4% of the initial potential energy, then, regardless of the value of the rotation parameter Ω, an instability of the radial motions always occurs and causes the nucleus to shift away from the geometrical center. This instability is aperiodic when Ω = 0 and is oscillatory when Ω ≠ 0 . For the anisotropic model, this kind of structure involving the nucleus develops when the initial total kinetic energy in the model is no more than 30.6% of the initial potential energy.

Structure and thermodynamic characteristics of small inert gas clusters

The relaxation dynamics of small groups of identical atoms interacting according to the Lennard-Jones law was studied experimentally. It is shown that for a fixed number of atoms, the probabilities of the formation of clusters with different structures depend on the random initial distribution of atoms in space, i.e., on the initial total energy and geometry of the particle distribution. Probabilities of the emergence of different structures of clusters vary greatly and do not contradict classical statistics. Except in extraordinary cases (e.g., N = 13), distances between the nearest atoms in clusters are different and change with the addition of each subsequent atom. The thermodynamics is constructed from the canonical ensembles of clusters with different numbers of particles. The resulting dependence of the cluster energy on the number of particles proves to be a smooth function, since only pair interactions were taken into account.

Application of conditional non-linear optimal perturbations to tropical cyclone adaptive observation using theWeather Research Forecasting (WRF) model

Conditional non-linear optimal perturbation (CNOP), which is a natural extension of the linear singular vector into the non-linear regime, has been suggested to identify data-sensitive regions in the adaptive observation strategy. CNOP is the global maximum of a cost function, whereas, local CNOP is the local maximum of the cost function if the local maximum exists. The potential application of CNOPs to tropical cyclone adaptive observation is researched. The CNOPs and the first singular vector (FSV) are numerically obtained by a spectral projected gradient algorithm with the Weather Research Forecasting (WRF) model. This paper examines two tropical cyclone cases, a fast straight moving typhoon Matsa (2005) and a slow moving recurving typhoon Shanshan (2006). The CNOPs and FSVs are obtained using the norms of background error at initial time and total dry energy at final time with a 36-h optimization time interval. The spatial structures of CNOPs, their energies, non-linear evolutions and impacts on track simulations are compared with those of the FSVs. The results show that both the CNOPs and the FSVs are localized, and evolve into the verification area at the final time with the upscale growth of perturbations. However, the CNOPs are different from the FSVs in spatial patterns, wind maximum distribution, growth rate of energy and impact on track simulation. Compared to FSV, CNOP and local CNOP have greater impact on the forecast in the verification region at the final time in terms of total energy, and have larger, at least similar impact on track simulation too. This indicates the CNOP method with constraint of the norm of background error at initial time and total energy norm at final time is a reasonable candidate in tropical cyclone adaptive observation. Therefore, both CNOP and local CNOP are suggested to be considered in tropical cyclone adaptive observation.

Large Data Existence Result for Unsteady Flows of Inhomogeneous Shear-Thickening Heat-Conducting Incompressible Fluids

We consider unsteady flows of inhomogeneous, incompressible, shear-thickening and heat-conducting fluids where the viscosity depends on the density, the temperature and the shear rate, and the heat conductivity depends on the temperature and the density. For any values of initial total mass and initial total energy we establish the long-time existence of weak solution to internal flows inside an arbitrary bounded domain with Lipschitz boundary.

Global existence and exponential stability of solutions in [formula omitted] for the compressible Navier–Stokes equations with the cylinder symmetry

This paper is concerned with the global existence and exponential stability of solutions in H 4 for the compressible Navier–Stokes equations with the cylinder symmetry in R 3 when the initial total energy is sufficiently small. Moreover, the global existence and exponential stability of the classical solution can be also derived.

Exponential stability for the compressible Navier–Stokes equations with the cylinder symmetry in [formula omitted

This paper is concerned with the exponential stability in H 1 and H 2 of global weak solutions to the compressible Navier–Stokes equations with the cylinder symmetry in R 3 when the initial total energy is sufficiently small. Such a circular coaxial cylinder symmetric domain in R 3 is an unbounded domain, but under our assumptions on the solutions depending only on one radial spatial variable r ∈ G = { r ∈ R + , 0 < a < r < b < + ∞ } , the related domain G to equations is a bounded domain. The Matsumura and Nishida result in R 3 requires the smallness of initial data, while our result does not need the smallness of density.

On the Asymptotic Behaviour of the Solutions of the Equations of Linear Elastodynamics in Unbounded Domains

We prove, among other things, that if the acoustic tensor satisfies a suitable growth condition at infinity (the hyperbolicity condition) and the total initial energy is summable with a suitable weight, then the solution to the initial boundary value problem of linear elastodynamics in unbounded domains decays at infinity, at every instant, with a rate depending on the weight. Moreover, we show that the hyperbolicity condition is necessary and sufficient for the equipartition in mean of the total energy.