Molecular orbital ab initio and density functional theoretical study on reaction between PH2 and NO

The theoretical study of reaction between PH₂ and NO on the ground state potential energy surface is reported by using molecular orbital ab initio calculation and density function theory (DFT). Equilibrium structural parameters, harmonic vibrational frequencies, total energies and zero point energies of all species during reaction are computed by HF, MP2 (full) and B3LYP theory levels with the medium basis set 6-31G*. Theoretical results indicate that intermediate IM1(H₂PNO) is firstly formed by overcoming a small energy barrier TS1, and then two four-membered ring transient states TS2 and TS5, with energy barriers 103.3 and 102.6 kJ/mol respectively, then H-migration and isomerization are completed and the products PN and H₂O are formed. The reaction is exothermic one with −189.6 kJ/mol released.     

Modelling lumped-parameter sorption kinetics and diffusion dynamics of odour-causing VOCs to dust particles

An analytical algorithm is presented for fast simulation of the adsorption kinetics and diffusion dynamics of odour-causing volatile organic compounds (VOC-odour) which originate in the stored swine manure to airborne dust particles in a ventilated airspace. The model is an extension to the well-known lumped-parameter model (LPM) that incorporates a Langmuir–Hinshelwood (LH) kinetic concept dependent on VOC-odour concentration with diffusion limitation. The basic idea behind the model implementation is to couple the calculations of the two major processes in the VOC-odour/dust particle system: VOC-odour diffusion based on the homogeneous surface diffusion model (HSDM) and surface reaction based on the LH kinetics in an LPM scheme. The LPM employs Laplace transforms and gamma distributions of the rate coefficient to produce a lumped-parameter gamma model (LPGM) for kinetic equation of VOC-odour adsorption to airborne dust particles, whereas the HSDM incorporates the age and size distributions of airborne dust for evaluating the dust-borne VOC-odour dynamics. The integrate assessment of VOC-odour sorption kinetics and diffusion dynamics allows to relate the adsorption rate coefficient, reaction order, and surface effective diffusivity in a complex VOC-odour/dust particle system. The LPGM fitted well with the data obtained numerically from HSDM and successfully determined the adsorption rate coefficient and reaction order for each sorption process.     

A tensor model for liquid crystals on a spherical surface

Rod-like molecules confined on a spherical surface can organize themselves into nematic liquid crystal phases. This can give rise to novel textures displayed on the surface, which has been observed in experiments. An important theoretical question is how to find and predict these textures. Mathematically, a stable configuration of the nematic fluid corresponds to a local minimum in the free energy landscape. By applying Taylor expansion and Bingham approximation to a general molecular model, we obtain a closed-form tensor model, which gives a free energy form that is different from the classic Landau-de Gennes model. Based on the tensor model, we implement an efficient numerical algorithm to locate the local minimum of the free energy. Our model successfully predicts the splay, tennis-ball and rectangle textures. Among them, the tennis-ball configuration has the lowest free energy.     

Can classical equations simulate quantum-mechanical behavior? a molecular dynamics investigation of a diatomic molecule with a morse potential

In a recent paper, we presented a new computational method for molecular dynamics which uses the Backward-Euler scheme to solve the classical Langevin dynamics equations. Parameters for the simulation include a target temperature T, a time step Δt, and a cutoff frequency ω_c. We showed for a harmonic oscillator system that the cutoff frequency can be set as ω_c = kT/h in order to mimic quantum-mechanical behavior. We now continue this investigation for a nonlinear case: a diatomic molecule governed by a Morse bond potential. Since approximate quantum-mechanical energy levels are explicitly known for this model, a comparison of energies can be made with molecular dynamics results. By performing dynamics runs for a wide range of temperatures and calculating mean energies, we find a very good agreement between these energies and quantum mechanical predictions. Vibrational excitation begins at temperatures around 800 K, and for higher temperatures both energy curves (molecular dynamics and quantum mechanics) approach the classical prediction of 7/2kT energy per molecule. Future investigations will focus on more general nonlinear potential functions employed in force fields of nucleic acids and proteins.     

Statistical inference for functions of the covariance matrix in the stationary Gaussian time-orthogonal principal components model

We consider inference for functions of the marginal covariance matrix under a class of stationary vector time series models, referred to as time-orthogonal principal components models. The main application which motivated this work involves the estimation of configurational entropy from molecular dynamics simulations in computational chemistry, where current methods of entropy estimation involve calculations based on the sample covariance matrix. The theoretical results we obtain provide a basis for approximate inference procedures, including confidence interval calculations for scalar quantities of interest; these results are applied to the molecular dynamics application, and some further applications are discussed briefly.     

Free vibrations and stability of hydraulic cylinder fixed elastically on both ends

The boundary value problem of the stability and free vibration of a hydraulic cylinder has been formulated and solved in this paper. The considered hydraulic cylinder has been elastically fixed at both ends and loaded by Euler force. An elastical fixation has been modelled by rotational springs. The mentioned above hydraulic cylinder consists of a piston rod and cylinder replaced by rods. There are conditions of continuity between the rods. The boundary value problem has been formulated on the basis of minimum potential energy (static problem) and on the basis of Hamilton's principle (free vibration problem). In this paper example results of numerical calculations of the stability and free vibration have been presented. Experimental research has been performed in order to verify the correctness of the assumed mathematical model. Professional measuring apparatus and special stand for research into the slender systems have been used in experiment. Natural frequencies have been measured in dependence on the values of an external load. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Adaptive accuracy control for Car-Parrinello simulations

Summary. The Car-Parrinello (CP) approach to ab initio molecular dynamics serves as an approximation to time-dependent Born-Oppenheimer (BO) calculations. It replaces the explicit minimization of the energy functional by a fictitious Newtonian dynamics and therefore introduces an artificial mass parameter which controls the electronic motion. A recent theoretical investigation shows that the CP-error, i.e., the deviation of the CP–solution from the BO-solution decreases like asymptotically. Since the computational effort increases like , the choice of has to find a compromise between efficiency and accuracy. The asymptotical result is used in this paper to construct an easily implemented algorithm which automatically controls : the parameter is repeatedly adapted during the simulation by choosing as large as possible while pushing an error measure below a user-given tolerance. The performance and reliability of the algorithm is illustrated by a typical example. Received March 10, 1998     

Dynamics and Stability of Surface Waves with Bulk-Soluble Surfactants

In this paper we study the dynamics of a layer of incompressible viscous fluid bounded below by a rigid boundary and above by a free boundary, in the presence of a uniform gravitational field. We assume that a mass of surfactant is present both at the free surface and in the bulk of the fluid, and that conversion from one species to the other is possible. The surfactants couple to the fluid dynamics through the coefficient of surface tension, which depends on the surface density of surfactants. Gradients in this concentration give rise to Marangoni stress on the free surface. In turn, the fluid advects the surfactants and distorts their concentration through geometric distortions of the free surface. We model the surfactants in a way that allows absorption and desorption of surfactant between the surface and bulk. We prove that small perturbations of the equilibrium solutions give rise to global-in-time solutions that decay to equilibrium at an exponential rate. This establishes the asymptotic stability of the equilibrium solutions.

     

Molecular conformation of n-alkanes using terrain/funneling methods

Understanding molecular conformation is a first step in understanding the waxing (or formation of crystals) of petroleum fuels. In this work, we study the molecular conformation of typical fuel oils modeled as pure n-alkanes. A multi-scale global optimization methodology based on terrain methods and funneling algorithms is used to find minimum energy molecular conformations of united atom n-alkane models for diesel, home heating, and residual fuel oils. The terrain method is used to gather average gradient and average Hessian matrix information at the small length scale while funneling is used to generate conformational changes at the large length scale that drive iterates to a global minimum on the potential energy surface. In addition, the funneling method uses a mixture of average and point-wise derivative information to produce a monotonically decreasing sequence of objective function values and to avoid getting trapped at local minima on the potential energy surface. Computational results clearly show that the calculated united atom molecular conformations are comprised of zigzag structure with considerable wrapping at the ends of the molecule and that planar zigzag conformations usually correspond to saddle points. Furthermore, the numerical results clearly demonstrate that our terrain/funneling approach is robust and fast.     

A new computer-oriented approach to molecular mechanics

A new dynamical theory for atomic and molecular dynamics is formulated and discussed. The associated nonlinear differential system is derived from general atomic and molecular stability properties and from aspects of modern particle theory, especially as it relates to the structure of the electron. Computer experiments are described for developing a new model of the water molecule.     

Numerical and experimental simulation of wave formation during explosion welding

The results of numerical and experimental simulation of wave formation under an oblique impact of metal plates during explosion welding are presented. The numerical simulation was carried out on the basis of the Maxwell relaxation model and by a molecular dynamics method. In the experiments, the impact of metal plates was investigated with X-ray radiography of phenomena in front of and behind the point of contact, and the preserved samples were studied metallographically. It is shown that the numerical simulation correctly reproduces the formation and evolution of waves on the contact boundary. Simultaneously, constraints are pointed out that prohibit the use of the elastoplastic model in the impact zone of the plates starting from the moment when the material of the plate in this zone is decomposed into thin jets. In this zone, the dependence of the specific deformation energy E on the tensor C _j ⁱ is no longer described by a convex function. It is this fact that motivated the transition to the molecular dynamics model.     

Simulation of seepage flows from channels

Plane steady-state seepage in a homogeneous isotropic ground from channels through a layer of soil with an underlying highly permeable pressurized water-bearing layer when the ground possesses capillarity and there is evaporation from the free surface is considered in a hydrodynamic formulation. To investigate it, a mixed multiparametric boundary-value problem of the theory of analytical functions is formulated, which is solved using the Polubarinova-Kochina method and conformal mapping of the regions of a special form, typical of problems of underground hydromechanics. On the basis of this model, an algorithm for calculating the capillary spreading of water and seepage flow is developed in situations when the ground capillarity is taken into account in the seepage of water from channels, as well as evaporation from the free surface of the ground waters, and also backwater of the underlying highly permeable stratum. Using the exact analytical relations obtained and numerical calculations, a hydrodynamic analysis of the structure and characteristic features of the simulated process, and also of the effect of all the physical parameters of the system on the seepage characteristics, is carried out. Limit and special cases, related to the absence of one or two of the three factors, characterizing the simulated process are considered: the ground capillarity, evaporation from the free surface, and also backwater of the underlying highly permeable water-bearing layer. The results of the calculations are compared with similar seepage characteristics with a similar scheme, but in which the flow region is underlaid by an impenetrable base.     

Calculation of damage and of force relaxation in amorpho-crystalline polymers

The dynamics of damage and of the relaxing force in amorpho-crystalline polymers under constant strain are calculated using the formulas for the probability of rupture of a deformed polymer molecule and a model representation of amorphous interlayers. The main parameters of the model are the maximum and minimum possible deformations of molecular chains, the energy of rupture activation, the function of the chain length distribution, the temperature, the macroscopic strain, and the relative dimensions of the amorphous interlayer. The conformity of the theoretical model and the association of the relaxation spectrum with the internal molecular and structural characteristics of the material are established.Zhambyl Technical Institute of Light and Food Industry, Taraz, Kazakhstan. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 499–508, July–August, 1999.     

A free energy based mathematical study for molecular motors

We present a Parrondo’s paradox for free energy in a classical flashing ratchet model and use it as an alternative way to interpret the working mechanism of molecular motors. We also study the efficiency of molecular motors measured by their free energies. Our example demonstrates that a molecular motor can gain up to 20% in its free energy during the process. In addition, we report a noise induced free energy increasing phenomenon, which is similar to the stochastic resonance, in flashing ratchet models.     

A stick-slip/Rouse hybrid model for viscoelasticity in polymers

A Rouse model for polymer chains is incorporated into the linear continuous stick-slip molecular-based tube reptation ideas of Doi–Edwards and Johnson–Stacer. This treats the physically constrained (PC) molecular stretches as internal strain variables for the overall PC/chemically cross-linked (CC) system. It yields an explicit system of stress–strain equations for the system permitting simple calculations of complex stress–strain relations. The model that is developed here treats PC molecule as entrapped within a constraining tube, which is comprised of both CC and PC molecules. The model is compared with experimental data sets from the literature.     

On the conservativeness of two-stage symmetric-symplectic Runge-Kutta methods and the Störmer-Verlet method

In the present paper, we discuss the problem on the total energy conservation for the numerical solution of the Cauchy problem for the equations of classical molecular dynamics by symplectic and symmetric methods. We consider the methods from a one-parameter family of two-stage symmetric-symplectic Runge-Kutta methods and the Störmer-Verlet method. In particular, we show that a numerical algorithm preserving the total energy of the system on the approximate solutions of the model Cauchy problem almost on the entire trajectory can be constructed on the basis of the one-parameter family of two-stage symmetric-symplectic Runge-Kutta methods.     

Persistence of undercompressive phase boundaries for isothermal Euler equations including configurational forces and surface tension

The persistence of subsonic phase boundaries in a multidimensional Van der Waals fluid is analyzed. The phase boundary is considered as a sharp free boundary that connects liquid and vapor bulk phase dynamics given by the isothermal Euler equations. The evolution of the boundary is driven by effects of configurational forces as well as surface tension. To analyze this problem, the equations and trace conditions are linearized such that one obtains a general hyperbolic initial boundary value problem with higher‐order boundary conditions. A global existence theorem for the linearized system with constant coefficients is shown. The proof relies on the normal mode analysis and a linear form in suitable spaces that is defined using an associated adjoint problem. Especially, the associated adjoint problem satisfies the uniform backward in time Kreiss–Lopatinski? condition. A new energy‐like estimate that also includes surface energy terms leads finally to the uniqueness and regularity for the found solutions of the problem in weighted spaces. Copyright © 2016 John Wiley & Sons, Ltd.     

Application of the string method to compute minimum energy paths for a chain of bi-stable elements using the finite element method and molecular dynamics

Activated processes are frequently found in solid state mechanics. The energy landscape of such processes show a non-convex behaviour, and therefore the computation of energy barriers between two stable minima is of importance. Such barriers are revealed by computing minimum energy paths. The string method is a simple and efficient algorithm to move curves over an energy landscape and to identify minimum energy paths. A hierarchical two-scale model recently introduced to the literature (molecular dynamics coupled with the finite element method) is used in this paper to investigate the string method in a model phase transition in a copper single crystal. To do so, bi-stable elements are constructed and the energetic behaviour of a two-elements chain is investigated. We identify successfully the minimum energy path between two local stable minima of the chain and demonstrate thereby the performance of the string method applied to a complex multiscale model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A sigma coordinate 3D k– model for turbulent free surface flow over a submerged structure

A fully three-dimensional unsteady flow model is developed to simulate free surface flow over a submerged structure. A new sigma coordinate is used to map the physical domain containing the wavy free surface and uneven bottom to a rectangular prism, and to keep the size of the submerged block unchanged in the sigma coordinate system. The numerical difficulty encountered in the conventional sigma coordinate system in which the block changes dynamically due to the time varying free surface is thus eliminated. A split operator scheme is used in the numerical solution so that different numerical schemes can be purposely chosen to deal with the distinctive mathematical and physical characteristics of the phenomena at different steps. k– model is used in the parameterization of turbulence due to its efficiency and reasonable performance. The model is applied to simulate the propagation of a solitary wave with good results. It is subsequently used to simulate a free surface flow against a submerged cube with one face perpendicular (or 45° inclined) to the flow. The numerical results compare favorably with the experimental measurements. In particular, no excessive turbulent kinetic energy is accumulated at the impingement regions.     

Dynamics on the Double Morse Potential: A Paradigm for Roaming Reactions with no Saddle Points

In this paper we analyze a two-degree-of-freedom Hamiltonian system constructed from two planar Morse potentials. The resulting potential energy surface has two potential wells surrounded by an unbounded flat region containing no critical points. In addition, the model has an index one saddle between the potential wells. We study the dynamical mechanisms underlying transport between the two potential wells, with emphasis on the role of the flat region surrounding the wells. The model allows us to probe many of the features of the “roaming mechanism” whose reaction dynamics are of current interest in the chemistry community.