Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

Physical Review B

Nonlinear mathematical models are becoming increasingly important for new
applications of low-dimensional semiconductor structures. Examples of such
structures include
quasi-zero-dimensional quantum dots that have potential
applications ranging from quantum computing to nano-biological devices. In
this contribution, we analyze presently dominating linear models for
bandstructure calculations and demonstrate why nonlinear models are required
for characterizing adequately optoelectronic properties of self-assembled
quantum dots.

/pdf/accounting-for-nonlinearities-in-mathematical-modelling-of-24b6jwvd1z.pdf

Accounting for nonlinearities in mathematical modelling of quantum dot molecules

Nonlinearities and hysteresis effects in a re- ciprocal ultrasound system is examined by a dynamical mathematical model on the basis of phase-transition theory. In particular, we consider the perovskite piezoelectric ceramic where the polarization process in the material can be modeled by minimizing the Helmholtz free energy function, i.e., each polarization state is associated with a minimum of the free energy function. Based on the free-energy function, nonlinear constitutive laws can be obtained accounting for effects such as hysteresis. The elastic field is assumed to be coupled linearly with other fields while the electric field is nonlinearly coupled to the electric displacement. We present step-response results for the transmitter and receiver of a reciprocal-transducer system and identify the influence of nonlinearities on the system dynamics. components) is modelled with nonlinear constitutive laws capable of capturing the hysteresis features in the E-D relations. The proposed model is based on polarization switching theory employing the Landau - Ginzburg theory so as to characterize different polarization directions. Ther- modynamical equilibrium conditions allow the constitutive laws to be obtained. We finally present the dynamical behaviour of a one-dimensional reciprocal system using the proposed model.

Nonlinearities and hysteresis phenomena in reciprocal ultrasound systems

The influence of different model parameters describing a multilayer transducer model is addressed by altering each single simulation parameter within ±20 % in steps of 2 % and by calculating the pressure and the intensity at a field point located 112 mm from the source. The simulations are compared with a hydrophone measured pressure pulse and intensity from a single element of a 128 element convex medical transducer. Results show that mainly the lens material and the ceramic material are of importance for errors in the pressure pulse prediction. Specifically the thickness, the density, and the stiffness constants are of significance. Among the results it is found that a −4 % change in lens stiffness yields a 6 % relative error change and a −4 % change in ceramic stiffness yields a −1.2 % relative error change. When calculating intensity the piezoceramic and electronic driving circuits are of importance, where a similar change in the lens and the ceramic stiffness shows a −0.1% and a −12% relative error change, respectively.

/pdf/parameter-sensitivity-study-of-a-field-ii-multilayer-23nvsxf4ap.pdf

Parameter sensitivity study of a Field II multilayer transducer model on a convex transducer

In this paper we analyze the acoustic flow in periodic structures for general time-dependent problems. Mathematically, the acoustic problem reduces to analysis of the linearized Helmholtz equations of an ideal barotropic fluid in the neighbourhood of the stationary background flow. We show that in the linear approximation stationary flows are generally unstable. Explicit unbounded solutions are determined and, in some cases, expressions for the general solution of the acoustic problem are stated.

Flow acoustics and linearized equations for ideal barotropic fluid flows

A simple one-dimensional differential equation in the centerline coordinate of an arbitrarily curved quantum waveguide with a varying cross section is derived using a combination of differential geometry and perturbation theory. The model can tackle curved quantum waveguides with a cross-sectional shape and dimensions that vary along the axis. The present analysis generalizes previous models that are restricted to either straight waveguides with a varying cross-section or curved waveguides, where the shape and dimensions of the cross section are fixed. We carry out full 2D wave simulations on a number of complex waveguide geometries and demonstrate excellent agreement with the eigenstates and energies obtained using our present 1D model. It is shown that the computational benefit in using the present 1D model to calculate both 2D and 3D wave solutions is significant and allows for the fast optimization of complex quantum waveguide design. The derived 1D model renders direct access as to how quantum waveguide eigenstates depend on varying cross-sectional dimensions, the waveguide curvature, and rotation of the cross-sectional frame. In particular, a gauge transformation reveals that the individual effects of curvature, thickness variation, and frame rotation correspond to separate terms in a geometric potential only. Generalization of the present formalism to electromagnetics and acoustics, accounting appropriately for the relevant boundary conditions, is anticipated.

/pdf/quantum-eigenstates-of-curved-and-varying-cross-sectional-3fpmw8yyh0.pdf

Morten Willatzen

Papers

Accounting for nonlinearities in mathematical modelling of quantum dot molecules

Nonlinearities and hysteresis phenomena in reciprocal ultrasound systems

Parameter sensitivity study of a Field II multilayer transducer model on a convex transducer

Flow acoustics and linearized equations for ideal barotropic fluid flows

Quantum Eigenstates of Curved and Varying Cross-Sectional Waveguides