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In this paper, we describe the Desmos supercomputer that consists of 32 hybrid nodes connected by a low-latency highbandwidth Angara interconnect with torus topology. This supercomputer is aimed at cost-effective classical molecular dynamics calculations. Desmos serves as a test bed for the Angara interconnect that supports 3D and 4D torus network topologies, and verifies its ability to unite massively-parallel programming systems speeding-up effectively MPI-based applications. We describe the Angara interconnect presenting typical MPI benchmarks. Desmos benchmarks results for GROMACS, LAMMPS, VASP and CP2K are compared with the data for other HPC systems. Also, we consider the job scheduling statistics for several months of Desmos deployment.
Single-point mutations in the transmembrane (TM) region of receptor tyrosine kinases (RTKs) can lead to abnormal ligand-independent activation. We use a combination of computational modeling, NMR spectroscopy and cell experiments to analyze in detail the mechanism of how TM domains contribute to the activation of wild-type (WT) PDGFRA and its oncogenic V536E mutant. Using a computational framework, we scan all positions in PDGFRA TM helix for identification of potential functional mutations for the WT and the mutant and reveal the relationship between the receptor activity and TM dimerization via different interfaces. This strategy also allows us design a novel activating mutation in the WT (I537D) and a compensatory mutation in the V536E background eliminating its constitutive activity (S541G). We show both computationally and experimentally that single-point mutations in the TM region reshape the TM dimer ensemble and delineate the structural and dynamic determinants of spontaneous activation of PDGFRA via its TM domain. Our atomistic picture of the coupling between TM dimerization and PDGFRA activation corroborates the data obtained for other RTKs and provides a foundation for developing novel modulators of the pathological activity of PDGFRA.
A stratified liquid with two layers separated by a fast oscillating interface in the case of Raleigh--Taylor instability is considered. The averaged equations are derived, and it is shown that a mushy region of a certain density appears after averaging. The similarity between this fact and the case of unstable jump decay is discussed.
The transmission and the circular transmission are investigated for a ring of quantum dots (in a benzene-type configuration) connected to external leads in the meta-configuration. A computational method utilizing the tight-binding approximation to the Schrödinger equation is used to solve for the transmission probabilities as a function of the electron energy and external magnetic flux. The flux dependence is incorporated into the model using a standard procedure involving the Aharonov–Bohm effect. The positions of the transmission zeros and poles in the complex energy plane, and their possible interference with or even complete cancellation of each other, are shown to correlate with the amplitude and structure of the circular transmission resonances. Large-amplitude resonances of the circular transmission are found to occur when two poles of the transmission are separated along the imaginary axis. These resonances demonstrate a high degree of flux sensitivity at specific energy values and flux ranges. A small change in flux causes the orientation of the resonance poles in the complex energy plane to rotate parallel to the real energy axis, resulting in a concurrent decrease in the circular transmission amplitude. The flux-dependent interference between the transmission poles and zeros in the complex energy plane leads to a decrease of the circular transmission resonance amplitudes. The circular transmission and its corresponding current–voltage characteristic provide more information related to the external flux than can be obtained from the normal transmission alone.
The article investigates one‐dimensional (1D) suspension‐colloidal transport of size distributed particles with particle attachment. A population balance approach is presented for computing the particle transport and capture by porous media. The occupied area of each attached particle is particle‐size dependent. The main model assumption is the retention‐rate dependency of the overall vacancy concentration for all particle sizes. For the first time, we derive an exact averaging (upscaling) procedure resulting in a closed system of large‐scale equations for average concentrations of suspended and retained particles, and of occupied rock surface area. The resulting large‐scale 3x3 system significantly differs from the traditional 2x2 deep bed filtration model. However, the traditional model becomes a particular case that corresponds to an equal occupied area for all particles. The averaging yields the appearance of two empirical suspension and site‐occupation functions, which govern the kinetics of particle retention and site occupation, respectively. 1D flow problems for the averaged equations are essentially non‐linear. However, they allow for exact solutions. We derive novel exact solutions for three 1D problems: continuous injection of particulate colloidal suspension, injection of colloidal suspension bank with particle‐free chase drive, and fines migration induced by high‐rate flows. The analytical model for continuous injection closely matches three series of laboratory tests on nano‐fluid transport.
A novel method of finding and classifying irreducible invariant surfaces of non-autonomous polynomial dynamical systems in the plane is presented. The general structure of irreducible invariant surfaces and their cofactors is found. The complete set of irreducible invariant surfaces for the classical forced Duffing-van der Pol oscillator is obtained. It is proved that the forced Duffing-van der Pol oscillator possesses only one independent generalized Darboux first integral provided that a constraint on the parameters is valid. In other cases generalized Darboux first integrals do not exist. Consequently, the forced Duffing-van der Pol oscillator is not integrable with two independent generalized Darboux first integrals.
We present a nonlocal statistical field theory of a diluted solution of dipolar particles which are capable of forming chain-like clusters in accordance with the ’head-to-tail’ mechanism. As in our previous study [Yu.A. Budkov 2018 J. Phys.: Condens. Matter 30 344001], we model dipolar particles as dimers comprised of oppositely charged point-like groups, separated by fluctuating distance. For the special case of the Yukawa-type distribution function of distance between the charged groups of dipolar particles we obtain an analytical expression for the electrostatic free energy of solution within the random phase approximation. We show that an increase in the association constant leads to a decrease in the absolute value of the electrostatic free energy of solution, preventing its phase separation which is in agreement with the former computer simulations and theoretical results. We obtain a non-linear integro-differential equation for the self-consistent field potential created by the fixed external charges in a solution medium, taking into account the association of dipolar particles. As a consequence of the derived self-consistent field equation, in regime of weak electrostatic interactions, we obtain an analytical expression for the electrostatic potential of the pointlike test ion, surrounded by the chain-like clusters of the dipolar particles. We show that in the mean-field approximation the association does not change the bulk dielectric permittivity of the solution, but increases the solvation radius of the point-like charge, relative to the theory of non-associating dipolar particles.
This paper generalizes assertion that a consistent process is a supermartingale with respect to any equivalent martingale probability measure if and only if it admits a Doob uniform expansion with respect to any measure from a given class.
This book constitutes the refereed proceedings of the 9th International Conference on Optimization and Applications, OPTIMA 2018, held in Petrovac, Montenegro, in October 2018.The 35 revised full papers and the one short paper presented were carefully reviewed and selected from 103 submissions. The papers are organized in topical sections on mathematical programming; combinatorial and discrete optimization; optimal control; optimization in economy, finance and social sciences; applications.
A new method of solubility estimations, applied to sparingly dissolved compounds in supercritical carbon dioxide has been introduced in this paper. The method is based on determination of solubility contributions along the thermodynamic path consisting of sublimation and solvation processes. The contribution of the sublimation process is taken from the experiment, while the free energy of solvation is calculated from the classical density functional theory based on the fundamental measure theory. The parameterization of potential was performed using the Weeks-Chandler-Anderson procedure, where the Lennard-Jones parameters were obtained from the thermodynamics data of solute and solvent critical points. The introduced method can efficiently predict the pressure crossover on solubility curve of sparingly dissolved compounds in supercritical carbon dioxide.
We consider the Wiener algebra A(T^d) of absolutely convergent Fourier series on the d-torus. For phase functions \phi of a certain special form we obtain lower bounds for the A -norms of e^{i\lambda\varphi} as \lambda tends to \infty.
Formation of carbon nanoparticles is an important type of complex non-equilibrium processes that require precise atomistic theoretical understanding. In this work, we consider the process of ultrafast cooling of pure carbon gas that results in nucleation of an onion-like fullerene. The model is based on molecular dynamics simulation with the interaction between carbon atoms described via a reactive ReaxFF model. We study the consecutive stages of fullerene-like nanoparticle formation and identify the corresponding temperature ranges. Analysis of hybridization and graphitization reveals the underlying microscopic mechanisms connected with rearrangements of dihedral angles and density changes.
We reply to the comment on our paper by Budkov (2018 J. Phys.: Condens. Matter 30 344001).
How is a water-soluble globular protein able to spontaneously cross a cellular membrane? It is commonly accepted that it undergoes significant structural rearrangements on the lipid-water interface, thus acquiring membrane binding and penetration ability. In this study molecular dynamics (MD) simulations have been used to explore large-scale conformational changes of the globular viscumin A chain in a complex environment – comprising urea and chloroform/methanol (CHCl3/MeOH) mixture. Being well-packed in aqueous solution, viscumin A undergoes global structural rearrangements in both organic media. In urea, the protein is “swelling” and gradually loses its long-distance contacts, thus resembling the “molten globule” state. In CHCl3/MeOH, viscumin A is in effect turned “inside out”. This is accompanied with strengthening of the secondary structure and surface exposure of hydrophobic epitopes originally buried inside the globule. Resulting solvent-adapted models were further subjected to Monte Carlo simulations with an implicit hydrophobic slab membrane. In contrast to only a few point surface contacts in water and two short regions with weak protein-lipid interactions in urea, MD-derived structures in CHCl3/MeOH reveal multiple determinants of membrane interaction. Consequently it is now possible to propose a specific pathway for the structural adaptation of viscumin A with respect to the cell membrane – a probable first step of its translocation into cytoplasmic targets.
We study the stability conditions of the multiserver queueing system in which each customer requires a random number of servers simultaneously. The input flow is supposed to be a regenerative one and service times of a given customer are independent at the occupied servers. The service time has an exponential, phase-type or hyper-exponential distribution. We define an auxiliary service process that is the number of completed services by all m servers under the assumption that there are always customers in the system. Then we construct the sequence of common regeneration points for the regenerative input flow and the auxiliary service process. It allows us to deduce the stability criterion of the model under consideration. It turns out that the stability condition does not depend on the structure of the input flow, only the rate of this process plays a role. Nevertheless the distribution of the service time is a very important factor. We give examples which show that the stability condition can not be expressed in terms of the mean of the service time.
This paper derives upper and lower bounds of the price in the optimal stopping problem for a consistent random sequence in the case of finite horizon. As is demonstrated below, the bounds can be found by solving the maximax and maximin setups of optimal stopping problems. For these setups, we obtain conditions under which 1) a recurrent relation is satisfied for the upper (lower) truncated sequence of optimal stopping prices; 2) an optimality criterion is constructed for the stopping times; 3) the structure and invariance of the optimal stopping times are established. Some examples with explicit solutions of the maximax and maximin setups of optimal stopping problems are given.
We present a study of viscosities of methane, n-butane and their mixtures by the non-equilibrium molecular dynamics simulations and derivation of semiempirical volume-based mixing rules. The Batchinski equation $\eta = C / (V - b)$ is used to describe the viscosities of pure components, with parameters fitted to reproduce molecular dynamics results. Cubic root, Arrhenius and Batchinski mixing rules are tested for mixtures. The viscosities of pure components used in mixing equations are expressed as functions of volume of component rather than pressure. This allows to apply the mixing rules to metastable and stable liquids, dense supercritical fluids and solutions of gas in liquid. To obtain volumes of components in mixture, molecular dynamics method is used. The mixing rules predictions are compared against direct non-equilibrium molecular dynamics calculations of mixture viscosities. The best agreement with the molecular dynamics data is found when Batchinski mixing is used. The proposed viscosity model predictions are in agreement with the experimental data on viscosities of methane-butane mixtures. The model can be used for the interpretation and interpolation of the experimental data on viscosities of liquids, which is demonstrated on the example of methane + propane system.