Self-adjusting entropy-stable scheme for compressible Euler equations

In this work,a self-adjusting entropy-stable scheme is proposed for solving compressible Euler equations.The entropy-stable scheme is constructed by combining the entropy conservative flux with a suitable diffusion operator.The entropy has to be preserved in smooth solutions and be dissipated at shocks.To achieve this,a switch function,which is based on entropy variables,is employed to make the numerical diffusion term be automatically added around discontinuities.The resulting scheme is still entropy-stable.A number of numerical experiments illustrating the robustness and accuracy of the scheme are presented.From these numerical results,we observe a remarkable gain in accuracy.     

Multi-symplectic method for generalized fifth-order KdV equation

This paper considers the multi-symplectic formulations of the generalized fifth-order KdV equation in Hamiltonian space. Recurring to the midpoint rule, it presents an implicit multi-symplectic scheme with discrete multi-symplectic conservation law to solve the partial differential equations which are derived from the generalized fifth-order KdV equation numerically. The results of the numerical experiments show that this multi-symplectic algorithm is good in accuracy and its long-time numerical behaviour is also perfect.     

Lie group analysis,numerical and non-traveling wave solutions for the(2+1)-dimensional diffusion–advection equation with variable coefficients

In this paper, the variable-coefficient diffusion–advection(DA) equation, which arises in modeling various physical phenomena, is studied by the Lie symmetry approach. The similarity reductions are derived by determining the complete sets of point symmetries of this equation, and then exact and numerical solutions are reported for the reduced second-order nonlinear ordinary differential equations. Further, an extended(G /G)-expansion method is applied to the DA equation to construct some new non-traveling wave solutions.     

Periodic oscillation of quantum diffusion in coupled one-dimensional systems

We analytically show that quantum diffusion in the coupled system composed of two identical chains exhibits a well-defined periodic oscillation in both transverse and longitudinal directions with a frequency determined by the interchain hopping strength, no matter whether the chains are periodic or non-periodic. We illustrate the result through numerical work on the coupled periodic chains and the quasiperiodic Aubry-Andre-Harper(AAH) chains with various modulations of onsite potentials supporting extended, critical, and localized states. We further numerically show that quantum diffusion in the coupled chains of different degrees of disorder W exhibits an exponential decay oscillation similar to the behavior of an underdamped harmonic oscillator, with a decay time inversely proportional to the square of W and a slight frequency change proportional to the square of W. Moreover, quantum diffusions in the coupled systems composed of two different chains are numerically studied, including periodic/disordered chains, periodic/AAH chains, and two different AAH chains, which exhibit the same behavior of underdamped periodic oscillation if the onsite potential difference between two chains is smaller than the interchain hoping strength.Existence of this universal periodic oscillation is a result of spectral splitting of the iso-spectra of two chains determined by interchain hopping, independent of system size, boundary condition, and intrachain onsite potentials. Because the oscillation frequency and spreading distance of wavepacket can be tuned separately by interchain hopping and intrachain potentials, the periodic oscillation of quantum diffusion in coupled chains is expected to find applications in control of quantum states and in designing nanoscale quantum devices.     

Pattern formation in superdiffusion Oregonator model

Pattern formations in an Oregonator model with superdiffusion are studied in two-dimensional(2D) numerical simulations. Stability analyses are performed by applying Fourier and Laplace transforms to the space fractional reaction–diffusion systems. Antispiral, stable turing patterns, and travelling patterns are observed by changing the diffusion index of the activator. Analyses of Floquet multipliers show that the limit cycle solution loses stability at the wave number of the primitive vector of the travelling hexagonal pattern. We also observed a transition between antispiral and spiral by changing the diffusion index of the inhibitor.     

Transient grating study of the intermolecular dynamics of liquid nitrobenzene

Femtosecond time-resolved transient grating(TG) technique is used to study the intermolecular dynamics in liquid phase. Non-resonant excitation of the sample by two crossing laser pulses results in a transient Kerr grating, and the molecular motion of liquid can be detected by monitoring the diffraction of a third time-delayed probe pulse. In liquid nitrobenzene(NB), three intermolecular processes are observed with lifetimes of 37.9±1.4 ps, 3.28±0.11 ps, and 0.44±0.03 ps, respectively. These relaxations are assigned to molecular orientational diffusion, dipole/induced dipole interaction, and libration in liquid cage, respectively. Such a result is slightly different from that obtained from OKE experiment in which the lifetime of the intermediate process is measured to be 1.9 ps. The effects of electric field on matter are different in TG and optical Kerr effect(OKE) experiments, which should be responsible for the difference between the results of these two types of experiments. The present work demonstrates that TG technique is a useful alternative in the study of intermolecular dynamics.     

Charmonia and bottomonia in asymmetric magnetized hot nuclear matter

We investigate the mass-shift of P-wave charmonium(χ_(c0),χ_(c1)),and S and P-wave bottomonium(η_b,■,χ_(b0),and χ_(b1)) states in magnetized hot asymmetric nuclear matter using the unification of QCD sum rules(QCDSR)and the chiral S U(3) model.Within QCDSR,we use two approaches,i.e.,the moment sum rule and the Borel sum rule.The magnetic field induced scalar gluon condensate α_s/πG_(μν)~aG~(aμν) and the twist-2 gluon operatorα_s/πG_(μσ)~aG~a ν~σcalculated in the chiral S U(3) model are utilised in QCD sum rules to calculate the in-medium mass-shift of the above mesons.The attractive mass-shift of these mesons is observed,which is more sensitive to magnetic field in the high density regime for charmonium,however less so for bottomonium.These results may be helpful to understand the decay of higher quarkonium states to the lower quarkonium states in asymmetric heavy ion collision experiments.     

Atomic diffusion across NisoTiso-Cu explosive welding interface： Diffusion layer thickness and atomic concentration distribution

Molecular dynamics simulations are carried out to study atomic diffusion in the explosive welding process of NisoTis0-Cu （at.%）. By using a hybrid method which combines molecular dynamics simulation and classical diffusion the- ory, the thickness of the diffusion layer and the atomic concentration distribution across the welding interface are obtained. The results indicate that the concentration distribution curves at different times have a geometric similarity. According to the geometric similarity, the atomic concentration distribution at any time in explosive welding can be calculated. NisoTis0- Cu explosive welding and scanning electron microscope experiments are done to verify the results. The simulation results and the experimental results are in good agreement.     

Temporal and Spectral Properties of Subcycle THz Pulses in Near-Field Zone

In a novel generation and detection configuration of terahertz (THz) radiation, we investigate experimentally and numerically the properties of sub-cycle THz pulses in the near field. It is found that the sub-cycle THz pulses experience significant spectral and temporal deformation in the near-field zone. The variations of both the pulse waveform and spectral distribution of the THz electric field are clearly observed in our experiments when the spot size of source is changed. Numerical simulations based on Gaussian distribution are performed to explain the details of the data and lead to an excellent agreement with the experimental results.     

Sawtooth-Stabilization and Snake-Excitation during LHCD on the HL-1M

Lower-hybrid current drive (LHCD) experiments were carried out in the HL-1M hydrogen plasmas.The suppression of sawtooth instabilities by LHCD has been observed in the sawtoothing discharges;an improvement in the global energy confinement time of up to 20％ is observed.There is an optimal rf-power range for the complete suppression of the central MHD instabilities.Possible mechanisms for the stabilization of the sawtooth instability are discussed from the measurement of internal inductance and current profile reconstruction using an equilibrium code.A large long-lived snake-like oscillation is newly observed at the end of the sawtooth-stabilization phase of the LHCD operation in the HL-1M tokamak.It is evident that such perturbation is due to a temperature depression caused by impurity accumulation during LHCD.     

Spin-orbit coupling, spin relaxation, and spin diffusion in organic solids

We develop a systematic approach of quantifying spin-orbit coupling (SOC) and a rigorous theory of carrier spin relaxation caused by the SOC in disordered organic solids. The SOC mixes up and down spin in the polaron states and can be characterized by an admixture parameter γ2. This mixing effects spin flips as polarons hop from one molecule to another. The spin relaxation time is τ(sf) = R2/(16γ2 D), and the spin diffusion length is L(s) = R/4|γ|, where R is the mean polaron hopping distance and D the carrier diffusion constant. The SOC in tris-(8-hydroxyquinoline) aluminum (Alq3) is particularly strong due to the orthogonal arrangement of the three ligands. The theory quantitatively explains the temperature-dependent spin diffusion in Alq3 from recent muon measurements.     

Differentiation of high-grade and low-grade intra-axial brain tumors by time-dependent diffusion MRI

IntroductionOscillating gradient spin-echo (OGSE) sequences enable acquisitions with shorter diffusion times. There is growing interest in the effect of diffusion time on apparent diffusion coefficient (ADC) values in patients with cancer. However, little evidence exists regarding its usefulness for differentiating between high-grade and low-grade brain tumors. The purpose of this study is to investigate the utility of changes in the ADC value between short and long diffusion times in distinguishing low-grade and high-grade brain tumors.Material and methodsEleven patients with high-grade brain tumors and ten patients with low-grade brain tumors were scanned using a 3 T magnetic resonance imaging with diffusion-weighted imaging (DWI) using OGSE and PGSE (effective diffusion time [Δ_eff]: 6.5 ms and 35.2 ms) and b-values of 0 and 1000 s/mm². Using a region of interest (ROI) analysis of the brain tumors, we measured the ADC for two Δeff (ADC_Δeff) values and computed the subtraction ADC (ΔADC = ADC_{6.5 ms} − ADC_{35.2 ms}) and the relative ADC (ΔADC = (ADC_{6.5 ms} − ADC_{35.2 ms}) / ADC_{35.2 ms} × 100). The maximum values for the subtraction ADC (ΔADC_max) and the relative ADC (rADC_max) on the ROI were compared between low-grade and high-grade tumors using the Wilcoxon rank-sum test. A P-value <.05 was considered significant. The ROIs were also placed in the normal white matter of patients with high- and low-grade brain tumors, and ΔADC_max values were determined.ResultsHigh-grade tumors had significantly higher ΔADC_max and rADC_max than low-grade tumors. The ΔADC_max values of the normal white matter were lower than the ΔADC_max of high- and low-grade brain tumors.ConclusionThe dependence of ADC values on diffusion time between 6.5 ms and 35.2 ms was stronger in high-grade tumors than in low-grade tumors, suggesting differences in internal tissue structure. This finding highlights the importance of reporting diffusion times in ADC evaluations and might contribute to the grading of brain tumors using DWI.     

Measurement of persistence in 1D diffusion

Using a novel NMR scheme we observed persistence in 1D gas diffusion. Analytical approximations and numerical simulations have indicated that for an initially random array of spins undergoing diffusion, the probability p(t) that the average spin magnetization in a given region has not changed sign (i.e., "persists") up to time t follows a power law t(-straight theta), where straight theta depends on the dimensionality of the system. Using laser-polarized 129Xe gas, we prepared an initial "quasirandom" 1D array of spin magnetization and then monitored the ensemble's evolution due to diffusion using real-time NMR imaging. Our measurements are consistent with analytical and numerical predictions of straight theta approximately 0.12.     

Energy diffusion in strongly driven quantum chaotic systems

The energy evolution of a quantum chaotic system under a perturbation that harmonically depends on time is studied in the case of a large perturbation in which the transition rate calculated from the Fermi golden rule exceeds the frequency of the perturbation. It is shown that the energy evolution retains its diffusive character, with a diffusion coefficient that is asymptotically proportional to the magnitude of the perturbation and to the square root of the density of states. The results are supported by numerical calculation. Energy absorption by the system and quantum-classical correlations are discussed. The text was submitted by author in English.     

Diffusion in ion-implanted solids with non-uniform diffusion parameters

Abstract

There is increasing evidence that diffusion phenomena in ion-implanted solids do not follow normal diffusion kinetics at high doses. For example, diffusion profiles are sometimes found to move towards the surface with increasing temperature, while the diffusion temperature widths tend to be up to a factor-of-3 too narrow. Such results can be self-consistently explained by recognizing that the diffusion detrapping energy will ordinarily be greater in the vicinity of the damage mean range than deeper in. One way of treating this analytically is to idealize a bombarded target as consisting of the sequence surface/damage/no-damage. It is shown that the interface damage/no-damage then acts as a nearly impermeable barrier and thus tends to prevent inward motion. Alternatively, one can approximate the detrapping energy as varying continuously with depth, ΔH = ΔH ₀(1-gx), the problem then becoming one of solving the equation ?C/?t = D (?² C/?s ² -?C/s?s), where s=exp (-ΔH ₀ gx/2RT). The interesting result now is that the integral concentration follows as having a time-independent shape roughly of the form exp(-ΔH ₀ gx/RT), so that surface-directed motion again follows naturally provided g is large enough. These arguments also apply to ion depth distributions at high doses which are anomalous with respect either to being too shallow or to being temperature dependent. It is necessary only to assume that prolonged ion impact on a solid surface causes radiation-enhanced diffusion.     

Asymptotic-preserving scheme for highly anisotropic non-linear diffusion equations

Heat transfer in magnetically confined plasmas is a process characterized by non-linear and extremely high anisotropic diffusion phenomena. Standard numerical methods, successfully employed in the numerical treatment of classical diffusion problems, are generally inefficient, or even prone to break down, when such high anisotropies come into play, leading thus to the need of new numerical techniques suitable for this kind of problems.In the present paper, the authors propose a numerical scheme based on an asymptotic-preserving (AP) reformulation of this non-linear evolution problem, generalizing the ideas introduced in a previous paper for the case of elliptic anisotropic problems [P. Degond, A. Lozinski, J. Narski, C. Negulescu, An asymptotic-preserving method for highly anisotropic elliptic equations based on a micro–macro decomposition, J. Comput. Phys. 231 (7) (2012) 2724–2740]. The performances of the here proposed AP scheme are tested numerically; in particular it is shown that the scheme is capable to deal with problems characterized by a high degree of anisotropy, thus proving to be suitable for the study of anisotropic diffusion in magnetically confined plasmas.     

CPMG relaxation by diffusion with constant magnetic field gradient in a restricted geometry: numerical simulation and application

Carr-Purcell-Meiboom-Gill (CPMG) measurements are the primary nuclear magnetic resonance (NMR) technique used for evaluating formation properties and reservoir fluid properties in the well logging industry and laboratory sample analysis. The estimation of bulk volume irreducible (BVI), permeability, and fluid type relies on the accurate interpretation of the spin-spin relaxation time (T(2)) distribution. The interpretation is complicated when spin's self-diffusion in an inhomogeneous field and restricted geometry becomes dominant. The combined effects of field gradient, diffusion, and a restricted geometry are not easily evaluated analytically. We used a numerical method to evaluate the dependence of the free and restricted diffusion on the system parameters in the absence of surface relaxation, which usually can be neglected for the non-wetting fluids (e.g., oil or gas). The parameter space that defines the relaxation process is reduced to two dimensionless groups: D* and tau*. Three relaxation regimes: free diffusion, localization, and motionally averaging regimes are identified in the (log(10)D*, log(10)tau*) domain. The hypothesis that the normalized magnetization, M*, relaxes as a single exponential with a constant dimensionless relaxation time T*(2) is justified for most regions of the parameter space. The numerical simulation results are compared with the analytical solutions from the contour plots of T*(2). The locations of the boundaries between different relaxation regimes, derived from equalizing length scales, are challenged by observed discrepancies between numerical and analytical solutions. After adjustment of boundaries by equalizing T*(2), numerical simulation result and analytical solution match each other for every relaxation regime. The parameters, fluid diffusivity and pore length, can be estimated from analytical solutions in the free diffusion and motionally averaging regimes, respectively. Estimation of the parameters near the boundaries of the regimes may require numerical simulation.     

A theory of modulational diffusion

Modulational diffusion, a weak instability that frequently occurs in many-dimensional, nonlinear Hamiltonian systems, is studied both analytically and numerically. Modulational diffusion arises when an oscillation in one of the degrees of freedom is phase modulated at a slow driving frequency, producing a “modulational layer” of overlapping resonances in phase spaces. Because the motion within this layer is chaotic, any coupling to the oscillation of another degree of freedom produces a long-time diffusion of its associated action along the layer. The diffusion rate for this process is evaluated analytically, and is compared with numerical calculations for a model, two-degree-of-freedom, nonautonomous Hamiltonian. The diffusion coefficient is found to vary in a series of descending steps as the frequency difference between the two oscillators is increased. Good agreement between analytical and numerical results has been obtained over many orders of magnitude in the diffusion coefficient.