Global regularity of the 4D restricted Euler equations

We are concerned with the critical threshold phenomena in the restricted Euler (RE) equations. Using the spectral and trace dynamics we identify the critical thresholds for the 3D and 4D restricted Euler equations. It is well known that the 3D RE solutions blow up. Projected on the 3-sphere, the set of initial eigenvalues which give rise to bounded stable solutions is reduced to a single point, which confirms that the 3D RE blowup is generic. In contrast, we identify a surprisingly rich set of the initial spectrum on the 4-sphere which yields global smooth solutions; thus, 4D regularity is generic.     

An optimised molecular model for ammonia

Based on molecular dynamics (MD) computer simulations we investigate the dynamic behaviour of a model complex fluid suspension consisting of large (A) particles (the ‘solute’) immersed in a bath of smaller ‘solvent’ (B) particles. The goal is to identify the effect of systematic simplifications (coarse-graining) of the solvent on typical microscopic time correlation functions characterizing the single-particle and collective dynamics of the solute. As a reference system we employ a binary Lennard–Jones mixture of spherical particles with significant differences in particle sizes (σ_A>σ_B) and masses (m _A>m _B). We then replace the original B particles step by step by a reduced number of larger and heavier particles such that the mass and volume fraction of B particles is kept constant. At each step of coarse-graining, the intermolecular interactions between A particles are chosen such that the static A–A structure of the reference system is preserved. Our MD results indicate that coarse-graining has a profound influence on both the single-particle dynamics as reflected by the self-diffusion constant and the collective dynamics represented by the distinct part of the van Hove time correlation function. The latter holds only at intermediate packing fractions, whereas the collective dynamics turns out to be essentially insensitive to coarse-graining at high packing fractions.     

Point-vortex cluster formation in the plane and on the sphere: an energy bifurcation condition

The dynamics of a system of point vortices is considered in the plane and on the sphere. Particular attention is given to the formation of vortex clusters and to global vortex dynamics, especially in the spherical case. For integrable systems and systems with given symmetries, we show the existence of a critical energy above or below which (depending on the geometry of the surface) the system splits into clusters and vortex dynamics is confined to a particular region. The case of nonidentical vortices is of particular interest since we observe quite different global dynamics depending on the energy and the initial conditions. Furthermore we identify all the relative equilibria configurations as critical points of the reduced energy and we give an instability criterion to deduce instability for certain configurations.     

Quench dynamics of two one-dimensional harmonically trapped bosons bridging attraction and repulsion

ABSTRACT

We unravel the nonequilibrium quantum dynamics of two harmonically confined bosons in one spatial dimension when performing an interaction quench from finite repulsive to attractive interaction strengths and vice versa. A closed analytical form of the expansion coefficients of the time-evolved two-body wavefunction is derived, while its dynamics is determined in terms of an expansion over the postquench eigenstates. For both quench scenarios the temporal evolution is analysed by inspecting the one- and two-body reduced density matrices and densities, the momentum distribution and the fidelity. Resorting to the fidelity spectrum and the eigenspectrum we identify the dominant eigenstates of the system that govern the dynamics. Monitoring the dynamics of the above-mentioned observables we provide signatures of the energetically higher-lying states triggered by the quench.     

Canonical formulation of pp-waves

We construct a Hamiltonian formulation for the class of plane-fronted gravitational waves with parallel rays (pp-waves). Because of the existence of a light-like Killing vector, the dynamics is effectively reduced to a 2+1 evolution with “time” chosen to be light-like. In spite of the vanishing action this allows us to geometrically identify a symplectic form as well as dynamical Hamiltonian, thus casting the system into canonical form.     

Electric field effect in the spin dynamics of self-assembled InAs/GaAs quantum dots

We identify fundamental mechanisms of electron and hole dynamics in self-organized InAs/GaAs quantum dots (QDs) subject to vertical electric fields by photocurrent investigations. We propose a spin–flip mechanism involving a spin exchange between neighboring QDs. The spin–flip process is revealed in the photocurrent dynamics when the exciton population increases unexpectedly with reverse bias.     

Simplectic Geometry and the Canonical Variables for Dirac–Nambu–Goto and Gauss–Bonnet System in String Theory

Using a strongly covariant formalism given by Carter for the deformations dynamics of p-branes in a curved background and a covariant and gauge invariant geometric structure constructed on the corresponding Witten's phase space, we identify the canonical variables for Dirac–Nambu–Goto (DNG) and Gauss–Bonnet (GB) system in string theory. Future extensions of the present results are outlined.     

Nonlinear voter models: the transition from invasion to coexistence

In nonlinear voter models the transitions between two states depend in a nonlinear manner on the frequencies of these states in the neighborhood. We investigate the role of these nonlinearities on the global outcome of the dynamics for a homogeneous network where each node is connected to m = 4 neighbors. The paper unfolds in two directions. We first develop a general stochastic framework for frequency dependent processes from which we derive the macroscopic dynamics for key variables, such as global frequencies and correlations. Explicit expressions for both the mean-field limit and the pair approximation are obtained. We then apply these equations to determine a phase diagram in the parameter space that distinguishes between different dynamic regimes. The pair approximation allows us to identify three regimes for nonlinear voter models: (i) complete invasion; (ii) random coexistence; and – most interestingly – (iii) correlated coexistence. These findings are contrasted with predictions from the mean-field phase diagram and are confirmed by extensive computer simulations of the microscopic dynamics.     

How confinement affects the dynamics of c60 in carbon nanopeapods

The dynamics of confined systems is of major concern for both fundamental physics and applications. In this Letter, the dynamics of C60 fullerene molecules inside single walled carbon nanotubes is studied using inelastic neutron scattering. We identify the C60 vibrations and highlight their sensitivity to temperature. Moreover, a clear signature of rotational diffusion of the C60 is evidenced, which persists at lower temperature than in 3D bulk C60. It is discussed in terms of confinement and of reduced dimensionality of the C60 chain.     

Reduced System Complexity of Heart Rate Dynamics in Patients with Hyperthyroidism: A Multiscale Entropy Analysis

Studying heart rate dynamics would help understand the effects caused by a hyperkinetic heart in patients with hyperthyroidism. By using a multiscale entropy (MSE) analysis of heart rate dynamics derived from one-channel electrocardiogram recording, we aimed to compare the system complexity of heart rate dynamics between hyperthyroid patients and control subjects. A decreased MSE complexity index (CI) computed from MSE analysis reflects reduced system complexity. Compared with the control subjects (n = 37), the hyperthyroid patients (n = 37) revealed a significant decrease (p < 0.001) in MSE CI (hyperthyroid patients 10.21 ± 0.37 versus control subjects 14.08 ± 0.21), sample entropy for each scale factor (from 1 to 9), and high frequency power (HF) as well as a significant increase (p < 0.001) in low frequency power (LF) in normalized units (LF%) and ratio of LF to HF (LF/HF). In conclusion, besides cardiac autonomic dysfunction, the system complexity of heart rate dynamics is reduced in hyperthyroidism. This finding implies that the adaptability of the heart rate regulating system is impaired in hyperthyroid patients. Additionally, it might explain the exercise intolerance experienced by hyperthyroid patients. In addition, hyperthyroid patients and control subjects could be distinguished by the MSE CI computed from MSE analysis of heart rate dynamics.     

Propagation and ghosts in the classical kagome antiferromagnet

We investigate the classical spin dynamics of the kagome antiferromagnet by combining Monte Carlo and spin dynamics simulations. We show that this model has two distinct low temperature dynamical regimes, both sustaining propagative modes. The expected gauge invariance type of the low energy, low temperature, out-of-plane excitations is also evidenced in the nonlinear regime. A detailed analysis of the excitations allows us to identify ghosts in the dynamical structure factor, i.e., propagating excitations with a strongly reduced spectral weight. We argue that these dynamical extinction rules are of geometrical origin.     

The Effective Dynamics of the Volume Preserving Mean Curvature Flow

We consider the dynamics of small closed submanifolds (‘bubbles’) under the volume preserving mean curvature flow. We construct a map from (\(\text {n}+1\))-dimensional Euclidean space into a given (\(\text {n}+1\))-dimensional Riemannian manifold which characterizes the existence, stability and dynamics of constant mean curvature submanifolds. This is done in terms of a reduced area function on the Euclidean space, which is given constructively and can be computed perturbatively. This allows us to derive adiabatic and effective dynamics of the bubbles. The results can be mapped by rescaling to the dynamics of fixed size bubbles in almost Euclidean Riemannian manifolds.     

乙醇在TiO2(110)表面光催化解离的动力学和超快电子动态学 (cited: 2)

采用实时双光子光电子能谱和时间分辨双光子光电子能谱技术分别研究了乙醇在该表面光催化解离的动力学和超快电子动态学过程. 通过测量与乙醇光催化解离相关的电子激发态随时间的演化,发现这个反应满足分型动力学. 乙醇在还原性TiO₂(110)上的光催化解离比在氧化性表面快,这归结于缺陷的存在降低了反应能垒. 这样一个反应的加速过程很可能是与缺陷电子相关的. 通过干涉双脉冲相关的测量,得到了乙醇-TiO₂界面电子激发态的超快动态学. 与甲醇的情况类似,这个电子激发态的寿命为24 fs. 激发态的出现为TiO₂和它周围环境的电子转移提供了一个通道.     

A new technology for studying multicomponent liquids using a quartz crystal resonator: Theory and applications

A new technique for analyzing multicomponent liquids is suggested. It is based on recording “electronic autographs” of liquids and thereby allows one to identify and certify them. In this technique, information comes from the dynamics of the complex process of self-organization in drying drops, this dynamics being dependent on the composition and structure of the liquid. Detecting the self-organization dynamics as acoustomechanical impedance, one can reveal quantitative distinctions between liquids and thereby test their quality by comparing with a reference.     

Border between regular and chaotic quantum dynamics

We identify a border between regular and chaotic quantum dynamics. The border is characterized by a power-law decrease in the overlap between a state evolved under chaotic dynamics and the same state evolved under a slightly perturbed dynamics. For example, the overlap decay for the quantum kicked top is well fitted with [1+(q-1)(t/tau)2](1/(1-q)) (with the nonextensive entropic index q and tau depending on perturbation strength) in the region preceding the emergence of quantum interference effects. This region corresponds to the edge of chaos for the classical map from which the quantum chaotic dynamics is derived.     

Development of a united-atom force field for 1-ethyl-3-methylimidazolium tetracyanoborate ionic liquid

Three united-atom (UA) force fields are presented for the ionic liquid 1-ethyl-3-methylimidazolium tetracyanoborate, abbreviated as [EMIM]⁺[B(CN)₄]^?. The atomistic charges were calculated based on the restrained electrostatic potential (RESP) of the isolated ions (abbreviated as force field 1, FF-1) and the ensemble averaged RESP (EA-RESP) method from the most stable ion pair configurations obtained by MP2/6-31G*+ calculations (abbreviated as FF-2 and FF-3). Non-electrostatic parameters for both ions were taken from the literature and Lennard–Jones parameters for the [B(CN)₄]^? anion were fitted in two different ways to reproduce the experimental liquid density. Molecular dynamics (MD) simulations were performed over a wide temperature range to identify the effect of the electrostatic and non-electrostatic potential on the liquid density and on transport properties such as self-diffusion coefficient and viscosity. Predicted liquid densities for the three parameter sets deviate less than 0.5% from experimental data. The molecular mobility with FF-2 and FF-3 using reduced charge sets is appreciably faster than that obtained with FF-1. FF-3 presents a refined non-electrostatic potential that leads to a notable improvement in both transport properties when compared to experimental data.     

Bifurcation and chaos in simple jerk dynamical systems

In recent years, it is observed that the third-order explicit autonomous differential equation, named as jerk equation, represents an interesting sub-class of dynamical systems that can exhibit many major features of the regular and chaotic motion. In this paper, we investigate the global dynamics of a special family of jerk systems {ie075-01}, whereG(x) is a non-linear function, which are known to exhibit chaotic behaviour at some parameter values. We particularly identify the regions of parameter space with different asymptotic dynamics using some analytical methods as well as extensive Lyapunov spectra calculation in complete parameter space. We also investigate the effect of weakening as well as strengthening of the non-linearity in theG(x) function on the global dynamics of these jerk dynamical systems. As a result, we reach to an important conclusion for these jerk dynamical systems that a certain amount of non-linearity is sufficient for exhibiting chaotic behaviour but increasing the non-linearity does not lead to larger regions of parameter space exhibiting chaos.