In this article, the dynamics of the qubits states based on solution of the time-dependent Schrödinger equation is investigated. Using the Magnus method we obtain an explicit interpolation representation for the propagator, which allows to find wave function at an arbitrary time. To illustrate the effectiveness of the approach, the population of the levels a single and two coupled qubits have been calculated by applying the Magnus propagator and the result has been compared with the numerical solution of the Schrödinger equation. As a measure of the approximation of the wave function, we calculate fidelity, which indicates proximity when the exact and approximate evolution operator acts on the initial state. We discuss the possibility of extending the developed methods to a multi-qubits system when highspeed calculation methods of the operators of evolution are particularly relevant

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.

A measurement of CP-violating weak phase *s *and meson decay width difference with decays in the ATLAS experiment is presented. It is based on integrated luminosity of 14.3 fb−1 collected by the ATLAS detector from 8 TeV *pp* collisions at the LHC. The measured values are statistically combined with those from 4.9 fb−1 of 7 TeV collisions data, yielding an overall Run-1 ATLAS result.

The density functional theory is applied for the calculation of the dependence of pressure and profiles of proton–proton pair correlation function of hydrogen on density in the range 1.14–2.0 g/cm3 at temperature 100 K. The calculated range of pressures is 300–2600 GPa, which corresponds to the solid phase of hydrogen. The transition at pressure 607 GPa is found, which is characterized by a noticeable jump of electrical conductivity and a sharp decrease in the number of molecules of H2. The structural transition is characterized by the first peak of the pair correlation function at a distance of 0.92 ˚A, which corresponds to the interatomic distance in the ion H+3 and does not depend on density. Therefore, the nature of the transition combines ionization with structural changes.

The warm dense hydrogen is studied by means of the ab initio molecular dynamics simulation in the region of fluid–fluid phase transition. The metastable states of two isotherm of 700 and 1000 K are calculated. The metastable ranges by pressure are 470 and 320 kbar respectively. The existence of metastability is a strong criterion that the transition is a first order phase transition.

We investigate synchronisation aspects of an optimistic algorithm for parallel discrete event simulations (PDES). We present a model for the time evolution in optimistic PDES. This model evaluates the local virtual time profile of the processing elements. We argue that the evolution of the time profile is reminiscent of the surface profile in the directed percolation problem and in unrestricted surface growth. We present results of the simulation of the model and emphasise predictive features of our approach.

Pressure of plasma is calculated by using classical molecular dynamics method. The formula based on virial theorem was used. Spectrum pressure's fluctuations of singly ionized non-ideal plasma are studied. 1/*f*-like spectrum behavior is observed. In other words, flicker noise is observed in fluctuations of pressure equilibrium non-ideal plasma. Relations between the obtained result and pressure fluctuations within the Gibbs and Einstein approaches are discussed. Special attention is paid to features of calculating the pressure in strongly coupled systems.

A new idea is developed that the fluid–fluid phase transition in warm dense hydrogen is related to the partial ionization of molecular hydrogen H2 with formation of molecular ions H2+ and H3+ . Conventional ab initio quantum modeling is applied. Proton pair correlation functions (PCF) obtained are used for the nonconventional diagnostics of the phase transition and elucidation of its nature for temperatures 700-1500 K. Short- and longrange changes of PCF’s are studied. H2 molecules ionization and molecular ions H2+ and H3+ appearance is revealed. The validity of the soft sphere model is tested for the long-range order.

The article shows that large artificial neural networks can be used for mutual ordering of a set of multi-dimensional patterns of the same nature (handwritten text, voice, smells, taste). Each neural network must be pre-trained to recognize one of the patterns. As a measure of ordering one can use the entropy of patterns "Strangers" that are input to a neural network trained to recognize only examples of the pattern "familiar". The neural network after training reduces the entropy of the examples of the pattern "Familiar" and increases the entropy of examples of pattern "Stranger." It is shown that the entropy measure of the ordering always has two global minima. The first minimum corresponds to the pattern "Familiar", the second to the inversion of the pattern "Familiar". It is also shown that the Hamming distance between the patterns belonging to two different groups (groups of the two global minima) is always as large as possible.

In this work we discuss complex dynamics arising in a model describing behavior of an encapsulated bubble contrast agent oscillating close to an elastic wall. We demonstrate presence of three coexisting attractors in the system. We propose an efficient numerical procedure based on the continuation method that can be used to locate the area of coexistence of these attractors in the parameters space. We provide area of coexistence of three attractors obtained by means of the proposed procedure.

When combined with error-correction codes reception techniques based on nonparametric hypothesis testing and order statistics provide strong immunity to different types of interference including multiuser interference. That makes communication systems using such reception techniques most appealing candidates for various applications such as Machine-to-Machine (M2M) communications and Internet Of Things (IOT). Unfortunately analytical treatment of communication systems with nonparametric reception remains a cumbersome task. Therefore simulation remains the main tool for the development of such systems. For multiuser systems supporting hundreds of active users and operating in fading channels (e.g. IOT) time spending grows drastically hampering the design process. Thus the development of simplified multiuser channel models is of great interest. In this paper two simplified mathematical models of multiuser interference for the case of a single user nonparametric reception are proposed. The effectiveness of the proposed models is compared by means of modulation. Special attention is paid to the problem of software implementation of the models proposed.

The CRAYFIS experiment proposes to use privately owned mobile phones as a ground detector array for Ultra High Energy Cosmic Rays. Upon interacting with Earth’s atmosphere, these events produce extensive particle showers which can be detected by cameras on mobile phones. A typical shower contains minimally-ionizing particles such as muons. As these particles interact with CMOS image sensors, they may leave tracks of faintly-activated pixels that are sometimes hard to distinguish from random detector noise. Triggers that rely on the presence of very bright pixels within an image frame are not efficient in this case. We present a trigger algorithm based on Convolutional Neural Networks which selects images containing such tracks and are evaluated in a lazy manner: the response of each successive layer is computed only if activation of the current layer satisfies a continuation criterion. Usage of neural networks increases the sensitivity considerably comparable with image thresholding, while the lazy evaluation allows for execution of the trigger under the limited computational power of mobile phones.

In this volume we have collected papers based on the presentations given at the International Conference on Computer Simulations in Physics and beyond (CSP2015), held in Moscow, September 6-10, 2015. We hope that this volume will be helpful and scientifically interesting for readers.

The Conference was organized for the first time with the common efforts of the Moscow Institute for Electronics and Mathematics (MIEM) of the National Research University Higher School of Economics, the Landau Institute for Theoretical Physics, and the Science Center in Chernogolovka. The name of the Conference emphasizes the multidisciplinary nature of computational physics. Its methods are applied to the broad range of current research in science and society. The choice of venue was motivated by the multidisciplinary character of the MIEM. It is a former independent university, which has recently become the part of the National Research University Higher School of Economics.

Current mechanisms of radiation-induced chromosomal aberration (CA) formation suggest misrepair of chromosomal lesions being in spatial proximity. In this case CAs have to depend on pattern of chromosomal contacts and on chromosome spatial organization in a cell nucleus. We were interested in whether variation of nucleus 3D organization results in difference of radiation induced CA formation frequency. Experimental data available do not provide information sufficient for definite conclusions. To have more deep insight in this issue we developed the biophysical modeling technique taking into account different levels of chromosome/nuclear organization and radiation damage of DNA and chromosomes. Computer experiments on gamma irradiation were carried out for two types of cells with different 3D organization of nuclei, preferentially peripheral and internal. CA frequencies were found to depend on spatial positioning of chromosomes within a nucleus which determines a pattern of interchromosomal contacts. For individual chromosomes this effect can be more pronounced than for genome averaged. Since significant part of aberrations, for example dicentrics, results in cell death, the proposed technique is capable of evaluating radiosensitivity of cells, both normal and cancer, with the incorporation of 3D genome information. This predictive technology allows to reduce uncertainties of prognosis of biological effects of radiation compared to phenomenological methods and may have variety of biomedical applications, in particular, in cancer radiation therapy.

High-energy physics experiments rely on reconstruction of the trajectories of particles produced at the interaction point. This is a challenging task, especially in the high track multiplicity environment generated by p-p collisions at the LHC energies. A typical event includes hundreds of signal examples (interesting decays) and a significant amount of noise (uninteresting examples). This work describes a modification of the Artificial Retina algorithm for fast track finding: numerical optimization methods were adopted for fast local track search. This approach allows for considerable reduction of the total computational time per event. Test results on simplified simulated model of LHCb VELO (VErtex LOcator) detector are presented. Also this approach is well-suited for implementation of paralleled computations as GPGPU which look very attractive in the context of upcoming detector upgrades.

High-energy physics experiments rely on reconstruction of the trajectories of particles produced at the interaction point. This is a challenging task, especially in the high track multiplicity environment generated by p-p collisions at the LHC energies. A typical event includes hundreds of signal examples (interesting decays) and a significant amount of noise (uninteresting examples). This work describes a modification of the Artificial Retina algorithm for fast track finding: numerical optimization methods were adopted for fast local track search. This approach allows for considerable reduction of the total computational time per event. Test results on simplified simulated model of LHCb VELO (VErtex LOcator) detector are presented. Also this approach is well-suited for implementation of paralleled computations as GPGPU which look very attractive in the context of upcoming detector upgrades.

We consider N-component synchronization models defined in terms of stochastic particle systems with special interaction. For general (nonsymmetric) Markov models we discuss phenomenon of the long time stochastic synchronization. We study behavior of the system in different limit situations related to appropriate changes of variables and scalings. For N = 2 limit distributions are found explicitly.

We investigate combinatorial properties of a higher invariant of magnetic lines. Assume that a 3-component link L is modeled by a magnetic eld B, which is represented by 3 closed magnetic lines. Main Theorem relates the integral invariant M(B) and a combinatorial invariant ~M (L), dened from the Conway polynomial. As a corollary of Main Theorem, asymptotic properties for combinatorial links are proposed. The combinatorial invariant ~M satises these asymptotic properties.

The paper refers to the area of morphological processing of projection images and its goal is to design some computer models of basic operations, geometric properties and methods of pulsed optical tomography which provide a high-speed production operational control and sorting of each micro-objet (MO) of nuclear fuel in their flow according to their size and shape: image approximation of a three-dimensional MO and spatial geometric properties of its size and shape; generation operations of the pulsed discrete projection images of an MO and determination of the representative number and optimal view of images; operations of numerical determination of the optimal basic properties of each projection image; methods of dynamic reconstruction of spatial geometric properties of an MO based on the basic properties of its discrete projection images. Based on the proposed computer models, a precision laser method of industrial differential control and quality control of MO flow of nuclear fuel was developed and experimentally tested. The method uses the statistical reconstruction of the size (D) and shape (K) of each micro-object and take into account the overall dimensions of the outlines of three mutually orthogonal two-dimensional pulsed discrete projection images of a micro-object. The processing speed of this method is 100 MO/s in the diameter range of 400 – 1500 mkm. The relative error of an MO diameter control is no more than 0.25% (at the reliability of PD = 0.7 and K = 1.3 relative units), and the relative error of the non-sphericity coefficient control lies in the range of 2.3% (PK = 0.7 and K = 1.3 relative units) to 0.6% (PK = 0.96 and K = 1.05 relative units).

L´evy stochastic processes and related fine analytic properties of probability distributions such as infinite divisibility play an important role in construction of stochastic models of various distributed networks (e.g., local clock synchronization), of some physical systems (e.g., anomalous diffusions, quantum probability models), of finance etc. Nevertheless, little is known about limit probability laws resulted from the long time behavior of such stochastic systems. In this paper we will focus on the impact of interaction graph topologies on limit laws of multicomponent synchronization models.

We review recent advances in the analysis of the Wang–Landau algorithm, which is designed for the direct Monte Carlo estimation of the density of states (DOS). In the case of a discrete energy spectrum, we present an approach based on introducing the transition matrix in the energy space (TMES). The TMES fully describes a random walk in the energy space biased with the Wang–Landau probability. Properties of the TMES can explain some features of the Wang–Landau algorithm, for example, the flatness of the histogram. We show that the Wang–Landau probability with the true DOS generates a Markov process in the energy space and the inverse spectral gap of the TMES can estimate the mixing time of this Markov process. We argue that an efficient implementation of theWang–Landau algorithm consists of two simulation stages: the original Wang–Landau procedure for the first stage and a 1/t modification for the second stage. The mixing time determines the characteristic time for convergence to the true DOS in the second simulation stage. The parameter of the convergence of the estimated DOS to the true DOS is the difference of the largest TMES eigenvalue from unity. The characteristic time of the first stage is the tunneling time, i.e., the time needed for the system to visit all energy levels.