Solvation dynamics in a Brownian dipolar lattice. Comparison between computer simulation and various molecular theories of solvation dynamics

Several recent theoretical and computer simulation studies have considered solvation dynamics in a Brownian dipolar lattice which provides a simple model solvent for which detailed calculations can be carried out. In this article a fully microscopic calculation of the solvation dynamics of an ion in a Brownian dipolar lattice is presented. The calculation is based on the non‐Markovian molecular hydrodynamic theory developed recently. The main assumption of the present calculation is that the two‐particle orientational correlation functions of the solid can be replaced by those of the liquid state. It is shown that such a calculation provides an excellent agreement with the computer simulation results. More importantly, the present calculations clearly demonstrate that the frequency‐dependent dielectric friction plays an important role in the long time decay of the solvation time correlation function. We also find that the present calculation provides somewhat better agreement than either the dynamic mean spherical approximation (DMSA) or the Fried–Mukamel theory which use the simulated frequency‐dependent dielectric function. It is found that the dissipative kernels used in the molecular hydrodynamic approach and in the Fried–Mukamel theory are vastly different, especially at short times. However, in spite of this disagreement, the two theories still lead to comparable results in good agreement with computer simulation, which suggests that even a semiquantitatively accurate dissipative kernel may be sufficient to obtain a reliable solvation time correlation function. A new wave vector and frequency‐dependent dissipative kernel (or memory function) is proposed which correctly goes over to the appropriate expressions in both the single particle and the collective limits. This form is expected to lead to better results than all the existing descriptions.

Ultrafast underdamped solvation: Agreement between computer simulation and various theories of solvation dynamics

A theoretical analysis of the three currently popular microscopic theories of solvation dynamics, namely, the dynamic mean spherical approximation (DMSA), the molecular hydrodynamic theory (MHT), and the memory function theory (MFT) is carried out. It is shown that in the underdamped limit of momentum relaxation, all three theories lead to nearly identical results when the translational motions of both the solute ion and the solvent molecules are neglected. In this limit, the theoretical prediction is in almost perfect agreement with the computer simulation results of solvation dynamics in the model Stockmayer liquid. However, the situation changes significantly in the presence of the translational motion of the solvent molecules. In this case, DMSA breaks down but the other two theories correctly predict the acceleration of solvation in agreement with the simulation results. We find that the translational motion of a light solute ion can play an important role in its own solvation. None of the existing theories describe this aspect. A generalization of the extended hydrodynamic theory is presented which, for the first time, includes the contribution of solute motion towards its own solvation dynamics. The extended theory gives excellent agreement with the simulations where solute motion is allowed. It is further shown that in the absence of translation, the memory function theory of Fried and Mukamel can be recovered from the hydrodynamic equations if the wave vector dependent dissipative kernel in the hydrodynamic description is replaced by its long wavelength value. We suggest a convenient memory kernel which is superior to the limiting forms used in earlier descriptions. We also present an alternate, quite general, statistical mechanical expression for the time dependent solvation energy of an ion. This expression has remarkable similarity with that for the translational dielectric friction on a moving ion.

Real-time Computer Simulation of Three Dimensional Elastostatics using the Finite Point Method

Real-time simulation of deformable solids is essential for some applications such as biological organ simulations for surgical simulators. In this work, deformable solids are approximated to be linear elastic, and an easy and straight forward numerical technique, the Finite Point Method (FPM), is used to model three dimensional linear elastostatics. Graphics Processing Unit (GPU) is used to accelerate computations. Results show that the Finite Point Method, together with GPU, can compute three dimensional linear elastostatic responses of solids at rates suitable for real-time graphics, for solids represented by reasonable number of points.

Translational and rotational motion in molecular liquids: A computer simulation study of Lennard-Jones ellipsoids

In order to understand the translational and rotational motion in dense molecular liquids, detailed molecular dynamics simulations of Lennard-Jones ellipsoids have been carried out for three different values of the aspect ratio kappa. For ellipsoids with an aspect ratio equal to 2, the product of the translational diffusion coefficient (D-T) and the average orientational correlation time of the l-th rank harmonics (tau(lR)), converges to a nearly constant value at high density. Surprisingly, this density independent value of D-T tau(lR) is within 5% of the hydrodynamic prediction with the slip boundary condition. This is despite the fact that both D-T and tau(lR) themselves change nearly by an order of magnitude in the density range considered, and the rotational correlation function itself is strongly nonexponential. For small aspect ratios (kappa less than or equal to 1.5), the rotational correlation function remains largely Gaussian even at a very large density, while for a large aspect ratio (kappa greater than or equal to 3), the transition to the nematic liquid-crystalline phase precludes the hydrodynamic regime. Thus, the rotational dynamics of ellipsoids show great sensitivity to the aspect ratio. At low density, tau(lR) goes through a minimum value, indicating the role of interactions in enhancing the rate of orientational relaxation. (C) 1997 American Institute of Physics. [S0021-9606(97)50142-5].

Computer simulation of liquid crystals

In this article we review the current status in the modelling of both thermotropic and lyotropic Liquid crystal. We discuss various coarse-graining schemes as well as simulation techniques such as Monte Carlo (MC) and Molecular dynamics (MD) simulations.In the area of MC simulations we discuss in detail the algorithm for simulating hard objects such as spherocylinders of various aspect ratios where excluded volume interaction enters in the simulation through overlap test. We use this technique to study the phase diagram, of a special class of thermotropic liquid crystals namely banana liquid crystals. Next we discuss a coarse-grain model of surfactant molecules and study the self-assembly of the surfactant oligomers using MD simulations. Finally we discuss an atomistically informed coarse-grained description of the lipid molecules used to study the gel to liquid crystalline phase transition in the lipid bilayer system.

Development of experimental setup for study of adsorption characteristics of porous materials down to 4.2 K

The knowledge of adsorption characteristics of activated carbon (porous material) in the temperature range from 5 to 20 K is essential when used in cryosorption pumps for nuclear fusion applications. However, such experimental data are very scarce in the literature, especially below 77 K. So, an experimental system is designed and fabricated to measure the adsorption characteristics of porous materials under variable cryogenic temperatures (from 5 K to 100 K). This is based on the commercially available micropore-analyser coupled to a closed helium cycle two-stage Gifford McMahon (GM) Cryocooler, which allows the sample to be cooled to 4.2 K. The sample port is coupled to the Cryocooler through a heat switch, which isolates this port from the cold head of the Cryocooler. By this, the sample temperature can now be varied without affecting the Cryocooler. The setup enables adsorption studies in the pressure range from atmospheric down to 10(-4) Pa. The paper describes the details of the experimental setup and presents the results of adsorption studies at 77 K for activated carbon with nitrogen as adsorbate. The system integration is now completed to enable adsorption studies at 4.2 K.

Dependence of collision frequency on distance between two hard-sphere particles estimated by computer simulation

A Monte Carlo simulation is performed to study the dependence of collision frequency on interparticle distance for a system composed of two hard-sphere particles. The simulation quantitatively shows that the collision frequency drops down sharply as the distance between two particles increases. This characteristic provides a useful evidence for the collision-reaction dynamics of aggregation process for the two-particle system described in the other reference.

Rapidly Infrared-Assisted Cooperatively Self-Assembled Highly Ordered Multiscale Porous Materials

In this paper, cooperative self-assembly (CSA) of colloidal spheres with different sizes was studied. It was found that a complicated jamming effect makes it difficult to achieve an optimal self-assembling condition for construction of a well-ordered stacking of colloidal spheres in a relatively short growth time by CSA. Through the use of a characteristic infrared (IR) technique to significantly accelerate local evaporation on the growing interface without changing the bulk growing environment, a concise three-parameter (temperature, pressure, and IR intensity) CSA method to effectively overcome the jamming effect has been developed. Mono- and multiscale inverse opals in a large range of lattice scales can be prepared within a growth time (15-30 min) that is remarkably shorter than the growth times of several hours for previous methods. Scanning electron microscopy images and transmittance spectra demonstrated the superior crystalline and optical qualities of the resulting materials. More importantly, the new method enables optimal conditions for CSA without limitations on sizes and materials of multiple colloids. This strategy not only makes a meaningful advance in the applicability and universality of colloidal crystals and ordered porous materials but also can be an inspiration to the self-assembly systems widely used in many other fields, such as nanotechnology and molecular bioengineering.

Computer simulation of influence of sedimentation on rapid coagulation

A computer simulation was performed to explore the features and effects of sedimentation on rapid coagulation. To estimate the accumulated influence of gravity on coagulation for dispersions, a sedimentation influence ratio is defined. Some factors possibly related to the influence of sedimentation were considered in the simulation and analysed by comparing the size distribution of aggregates, the change in collision number, and coagulation rates at different gravity levels (0 g, 1 g and more with g being the gravitational constant).

Computer simulation on the collision-sticking dynamics of two colloidal particles in an optical trap

Collisions of a particle pair induced by optical tweezers have been employed to study colloidal stability. In order to deepen insights regarding the collision-sticking dynamics of a particle pair in the optical trap that were observed in experimental approaches at the particle level, the authors carry out a Brownian dynamics simulation. In the simulation, various contributing factors, including the Derjaguin-Landau-Verwey-Overbeek interaction of particles, hydrodynamic interactions, optical trapping forces on the two particles, and the Brownian motion, were all taken into account. The simulation reproduces the tendencies of the accumulated sticking probability during the trapping duration for the trapped particle pair described in our previous study and provides an explanation for why the two entangled particles in the trap experience two different statuses. (c) 2007 American Institute of Physics.

Collective evolution characteristics and computer simulation of short fatigue cracks

Fatigue testing was conducted using a kind of triangular isostress specimen to obtain the short-fatigue-crack behaviour of a weld low-carbon steel. The experimental results show that short cracks continuously initiate at slip bands within ferrite grain domains and the crack number per unit area gradually increases with increasing number of fatigue cycles. The dispersed short cracks possess an orientation preference, which is associated with the crystalline orientation of the relevant slip system. Based on the observed collective characteristics, computer modelling was carried out to simulate the evolution process of initiation, propagation and coalescence of short cracks. The simulation provides progressive displays which imitate the appearance of experimental observations. The results of simulation indicate that the crack path possesses a stable value of fractal dimension whereas the critical value of percolation covers a wide datum band, suggesting that the collective evolution process of short cracks is sensitive to the pattern of crack site distribution.

Dynamic failure in ductile porous materials

In this paper, a mathematical model of dynamic fracture in porous ductile materials under intense dynamic general loading is developed. The mathematical model includes the influence of inertial effects and material rate sensitivity, as well as the contribution of surface energy of a void and material work-hardening. In addition, the condition of the void compaction is considered as well. The threshold stresses for the void growth and compaction are obtained. A simple criterion for ductile fracture which is associated with material distention and plastic deformation is adopted. As an application of the theoretical model, the processes of two-dimensional spallation in LY12 aluminum alloy are successfully simulated by means of two-dimensional finite-difference Lagrangian code.

TUNPOP, a computer simulation model of the yellowfin tuna population and the surface tuna fishery of the Eastern Pacific Ocean

ENGLISH: Mathematical documentation of TUNP0P, an age-structured computer simulation model of the yellowfin tuna population and surface tuna fishery of the eastern Pacific Ocean, is described. Example runs of the model are presented and discussed, and the sensitivity of the model output to changes in various parameters is examined. SPANISH: Se describe la documentación matemática de TUNP0P, un modelo computador de simulación basado en la edad de la población del atún aleta amarilla y de la pesca atunera epipelágíca del Océano Pacífico oriental. Se presentan y se discuten ejemplos de las pasadas del modelo, y se examina la sensibilidad de los resultados de salida con relación a los cambios de varios parámetros. (PDF contains 47 pages.)