The infinite hierarchy of differential-recurrence relations for ensemble averages of the spherical harmonics pertaining to the noninertial rotational Brownian motion of an ensemble of polar and anisotropically polarizable molecules in a strong external dc electric field is derived by averaging the underlying Langevin equation. This procedure avoids recourse to the Fokker-Planck equation, the so...

When using the explicit dynamic relaxation approach (DRA) to model quasi-static rock breakage, fragmentation, and flow problems, especially top-coal caving question, introducing numerical damping into solution equation is inevitable for reducing vibration frequency impact speed of mesh nodes, which significantly affect fidelity computation results. Although DRA has been widely adopted simulate ...

A major issue in Lagrangian relaxation for integer programming problems is to maximize the dual function which is piece-wise linear, and consists of many facets. Available methods include the subgradient method, the bundle method, and the recently developed surrogate subgradient method. Each of the above methods, however, has its own limitations. Based on the insights obtained from these method...

Here we show a heterogeneous energy landscape approach to describing the Kohlrausch-Williams-Watts (KWW) relaxation function. For a homogeneous dynamic process, the distribution of free energy landscape is first proposed, revealing the significance of rugged fluctuations. In view of the heterogeneous relaxation given in two dynamic phases and the transmission coefficient in a rate process, we o...

Dynamic relaxation of the XY model quenched from a high temperature state to the critical temperature or below is investigated with Monte Carlo methods. When a non-zero initial magnetization is given, in the short-time regime of the dynamic evolution the critical initial increase of the magnetization is observed. The dynamic exponent θ is directly determined. The results show that the exponent ...

Most metallic glasses (MGs) exhibit weak evidence of slow β-relaxation in their dynamic mechanical spectroscopy spectra. In contrast to other MGs, the La-based MGs we report here show a distinct slow β-relaxation peak in the mechanical relaxation measurements. We find that the slow β-relaxation behavior can be tuned by modification of the chemical composition and fragility. The structural origi...

Real-time physics simulation has been extensively used in computer games, but its potential has yet to be fully realized in design and education. We present an interactive 3D physics engine with a wide variety of applications. In common with traditional FEM, the use of a local element stiffness matrix is retained. However, unlike typical non-linear FEM routines elements forces, moments and iner...

The dynamic behavior of macromolecular networks dominates the mechanical properties of soft materials and influences biological processes at multiple length scales. In hydrogels prepared from self-assembling artificial proteins, stress relaxation and energy dissipation arise from the transient character of physical network junctions. Here we show that subtle changes in sequence can be used to p...