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✖There is a gap in the proof of the main theorem in the article [5] on optimal bounds for the Morse lemma in Gromov-hyperbolic spaces. We correct this gap, showing that the main theorem of [5] is true. We also describe a computer certification of this result.
The mathematical model describing the dynamics of HIV in the human body is a nonlinear system of differential equations. This model takes into account the effect of drugs on the body. Thus, it is possible to obtain ”optimal” treatment regimens for patients, which cause minimal harm to the body. In the work for constructing suboptimal control of the supply of drugs, the method of ”extended linearization” is used, which makes it possible to switch from a nonlinear model to a linear model, but with parameters that depend on the state. To solve the resulting equation Riccati and search for control actions, a method is proposed for the formation of optimization algorithms for nonlinear control systems based on the application of functions of admissible values of control actions.
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.
We study properties of generalized $K$-functionals and generalized moduli of smoothness in $L_p(\R)$ spaces with $1 \le p \le +\infty$. We obtain the direct Jackson type estimate and the inverse Bernstein type estimate for them. We state equivalence between approximation error of convolution integrals generated by an arbitrary generator with compact support generalized $K$-functionals generated by homogeneous function and generalized moduli of smoothness generated by $2\pi$-periodic generator subject to equivalence of their generators. We show that generalized $K$-functionals and generalized moduli of smoothness contain, as their special cases many well-known constructions of $K$-functionals and moduli of smoothness with an appropriate choice of the generators.
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.
Modern Elbrus-4S and Elbrus-8S processors show floating point performance comparable to the popular Intel processors in the field of high-performance computing. Tasks oriented to take advantage of the VLIW architecture show even greater efficiency on Elbrus processors. In this paper the efficiency of the most popular materials science codes in the field of classical molecular dynamics and quantum-mechanical calculations is considered. A comparative analysis of the performance of these codes on Elbrus processor and other modern processors is carried out.
A Euclidean distance matrix D(α) is defined by D_ij=(α_i−α_j)^2, where α=(α_1,…,α_n) is a real vector. We prove that D(α) cannot be written as a sum of [2sqrt(n)−2] nonnegative rank-one matrices, provided that the coordinates of α are algebraically independent. As a corollary, we provide an asymptotically optimal separation between the complexities of quantum and classical communication protocols computing a given matrix in expectation.
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.
The results of numerical calculations for the mathematical model proposed for describing the magnetization in a thin film of a ferromagnetic semiconductor at temperatures below the Curie temperature in the presence of an external electric field are presented. The theoretical prediction of the existence of a piecewise continuous solution, which describes the presence of the phase transition boundary for magnetization inside the film, is confirmed. The location of this phase transition boundary depends on the external electric field and temperature.
A theoretical model describing the spontaneous magnetization of a ferromagnetic semiconductor (InMn)As film in the presence of an external electric field directed across the film is considered. It is assumed that the ions of a manganese impurity with spin 5/2 are acceptors, have a uniform spatial distribution inside the semiconductor, and do not change their position under the action of an external field. The motion of holes with spin ½ changes their spatial distribution under the action of the field. The exchange interaction between manganese ions and holes allows the formation of magnetization that is non-uniform across the film thickness.
In particular, the existence of a piecewise continuous solution describing the presence of a phase transition boundary for magnetization inside a ferromagnetic semiconductor film is shown.
This volume collects the referred papers based on plenary, invited, and oral talks, as well on the posters presented at the Third International Conference on Computer Simulations in Physics and beyond (CSP2018), which took place September 24-27, 2018 in Moscow. The Conference continues the tradition started by an inaugural conference in 2015. It took place on the campus of A.N. Tikhonov Moscow Institute of Electronics and Mathematics in Strogino, was jointly organized by the National Research University Higher School of Economics, the Landau Institute for Theoretical Physics and Science Center in Chernogolovka.
The Conference is a multidisciplinary meeting, with a focus on computational physics and related subjects. Indeed, methods of computational physics prove useful in a broad spectrum of research in multiple branches of natural sciences, and this volume provides a sample.
We hope that this volume will interest readers, and we are already looking forward to the next conference in the series.
Moscow, Russia
November, 2018
CSP2018 Conference Chair and Volume Editor
Lev Shchur
We present the theory of many-body corrections to cyclotron transition energies in graphene in strong magnetic field due to Coulomb interaction, considered in terms of the renormalized Fermi velocity. A particular emphasis is made on the recent experiments where detailed dependencies of this velocity on the Landau level filling factor for individual transitions were measured. Taking into account the many-body exchange, excitonic corrections and interaction screening in the static random-phase approximation, we successfully explained the main features of the experimental data, in particular that the Fermi velocities have plateaus when the 0th Landau level is partially filled and rapidly decrease at higher carrier densities due to enhancement of the screening. We also explained the features of the nonmonotonous filling-factor dependence of the Fermi velocity observed in the earlier cyclotron resonance experiment with disordered graphene by taking into account the disorder-induced Landau level broadening.
Matrix multiplication is one of the core operations in many areas of scientific computing. We present the results of the experiments with the matrix multiplication of the big size comparable with the big size of the onboard memory, which is 1.5 terabyte in our case. We run experiments on the computing board with two sockets and with two Intel Xeon Platinum 8164 processors, each with 26 cores and with multi-threading. The most interesting result of our study is the observation of the perfect scalability law of the matrix multiplication, and of the universality of this law.
In this manuscript, we study the electrically induced breathing of Metal-Organic Framework (MOF) within a 2D lattice model. The Helmholtz free energy of the MOF in electric eld consists of two parts: the electrostatic energy of the dielectric body in the external electric eld and elastic energy of the framework. The rst contribution is calculated from the rst principles of statistical mechanics with an account of MOF symmetry. By minimizing the obtained free energy and solving the resulting system of equations, we obtain the local electric eld and the parameter of the unit cell (angle ). The paper also studies the cross-section area of the unit cell and the polarization as functions of the external electric eld. We obtain the hysteresis in the region of the structural transition of the framework. Our results are in qualitative agreement with the literature data of the molecular dynamics (MD) simulation of MIL-53(Cr).
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.
We consider an initial{boundary value problem for a simple semilinear ltration equation with nonunique characteristics and prove that uniqueness nevertheless holds for the solution of this problem. The solution is then constructed by quadratures.
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.
We consider a bilayer system of two-dimensional Bose-Einstein-condensed dipolar dark excitons (upper layer) and bright ones (bottom layer). We demonstrate that the interlayer interaction leads to a mixing between excitations from different layers. This mixing leads to the appearance of a second spectral branch in the spectrum of bright condensate. The excitation spectrum of the condensate of dark dipolar excitons then becomes optically accessible during luminescence spectra measurements of the bright condensate, which allows one to probe its kinetic properties. This approach is relevant for experimental setups, where detection via conventional techniques remains challenging; in particular, the suggested method is useful for studying dark dipolar excitons in transition metal dichalcogenide monolayers.