Step Of Calculations Research Articles

FILTERING OF AN INTERRUPTED SIGNAL ON APPROXIMATION BY GAMMA DISTRIBUTION UNDER THE INFLUENCE OF ADDITIVE MULTIPLICATIVE INTERFERENCE

The problem of constructing an algorithm for recognizing and filtering a continuous-valued Markov process measured in a mixture with random additive and multiplicative interference under conditions of random information interruptions is considered. The Bayes principle and the well-known two-stage filtering method “forecast-correction” are applied, supplemented by procedures for identifying the number of the structure, in which the system is located in the current and next time intervals. At the forecast stage, identification is based on calculating the probabilities of the future state of the system based on a priori information about the probabilities of its transitions from structure to structure, as well as on the current values of estimates of these probabilities. At the correction stage, identification is based on the use of probability prediction results and a priori known information about the reliability of the information of the system status indicator. In addition, the values of the probability densities of the measuring information in each structure are used, the expressions for which are obtained on the basis of a priori known laws of distribution of additive and multiplicative interference, as well as the predicted probability density of the Markov process in each structure at the next step of calculations. To obtain a practically realizable algorithm, expressions for the predicted and a posteriori densities of the Markov process probabilities are obtained based on their approximation by the probability density of the gamma distribution, completely determined by the first two initial moments. This made it possible to obtain a closed system of recurrent equations for estimating the probability of information interruption, mathematical expectations and variances of the Markov process in each structure.

Adiabatic Trajectory Approximation within the Framework of Mixed Quantum/Classical Theory.

A hierarchy of approximate methods is proposed for solving the equations of motion within a framework of the mixed quantum/classical theory (MQCT) of inelastic molecular collisions. Of particular interest is a limiting case: the method in which the classical-like equations of motion for the translational degrees of freedom (scattering) are decoupled from the quantum-like equations for time evolution of the internal molecular states (rotational and vibrational). In practice, trajectories are pre-computed during the first step of calculations with driving forces determined solely by the potential energy surface of the entrance channel, which is an adiabatic trajectory approximation. Quantum state-to-state transition probabilities are computed in the second step of calculations with an expanded basis and very efficient step-size adjustment. Application of this method to H2O + H2 rotationally inelastic scattering shows a significant computational speedup by 2 orders of magnitude. The results of this approximate propagation scheme are still rather accurate, as demonstrated by benchmarking against more rigorous calculations in which the quantum and classical equations of motion are held coupled and against the full-quantum coupled-channel calculations from the literature. It is concluded that the AT-MQCT method (the adiabatic trajectory version of MQCT) represents a promising tool for the computational treatment of molecular collisions and energy exchange.

Silicon Photonics Codesign for Deep Learning

Deep learning is revolutionizing many aspects of our society, addressing a wide variety of decision-making tasks, from image classification to autonomous vehicle control. Matrix multiplication is an essential and computationally intensive step of deep-learning calculations. The computational complexity of deep neural networks requires dedicated hardware accelerators for additional processing throughput and improved energy efficiency in order to enable scaling to larger networks in the upcoming applications. Silicon photonics is a promising platform for hardware acceleration due to recent advances in CMOS-compatible manufacturing capabilities, which enable efficient exploitation of the inherent parallelism of optics. This article provides a detailed description of recent implementations in the relatively new and promising platform of silicon photonics for deep learning. Opportunities for multiwavelength microring silicon photonic architectures codesigned with field-programmable gate array (FPGA) for pre- and postprocessing are presented. The detailed analysis of a silicon photonic integrated circuit shows that a codesigned implementation based on the decomposition of large matrix-vector multiplication into smaller instances and the use of nonnegative weights could significantly simplify the photonic implementation of the matrix multiplier and allow increased scalability. We conclude this article by presenting an overview and a detailed analysis of design parameters. Insights for ways forward are explored.

A 2×2 MIMO Throughput Analytical Model for RF Front End Optimization

With a given communication protocol, performance optimization of a multiple-input multipleoutput (MIMO) wireless system mainly lies on the design of the radio frequency (RF) front end. Currently, the optimization is mainly achieved based on experiences, such as promoting the multiple antenna gains and reducing their correlations. This experience-based method works to a certain extent, but is inefficient since the final performance impact by each sub-system is not quantified. The challenge lies on how to find the most limiting factor that restricts the overall communication throughput. This paper presents an analytical model for throughput calculations of 2 × 2 MIMO wireless system, which is built on a first step of maximum rate calculated under the chosen protocol and channel, followed by a second step of throughput baseline measurement, and continued with the third step of throughput calculations of the overall system according to the actual settings of subsystems. The model can provide a detailed diagnostic report of each RF factor, which will directly point out the imperfections and make the troubleshooting and debugging much more effective. Besides, throughput is analyzed in a mathematical approach that allows the performance more predictable during the design phase.

Symplectic ray tracing based on Hamiltonian optics in gradient-index media.

A method based on Hamiltonian optics for ray tracing through gradient-index (GRIN) media is proposed. The ray equation that describes light-ray paths can be written in the form of the Hamiltonian equations. Although the Hamiltonian equations can be numerically calculated using a finite-difference explicit method, deviations from the exact equations are generally inevitable at subsequent time steps. An optical Hamiltonian can be constructed of two independent terms, i.e., one term dependent on position and the other term dependent on momentum. The symplectic integrator is applicable to such a separable optical Hamiltonian system and makes the optical Hamiltonian equations form invariant at each time step of numerical calculations. Accuracies of light-ray paths calculated using the first-order symplectic ray tracing in GRIN lenses approximate those calculated on the basis of the fourth-order Runge-Kutta algorithm, which shows the promising potential of the symplectic-ray-tracing method.

Визуализация линейных смещений узловых точек при реализации мгновенных состояний различных конфигураций руки андроидного робота

During planning the movement of an android robot arm in an organized space, there is a need in reducing calculation time of the trajectory in the space of generalized coordinates. The indicated time significantly depends on calculation time the vector of increments of the generalized coordinates at each step of calculations in the synthesis of movements along the velocity vector. In this paper, geometric studies were carried out based on the visualization of patterns of changes in the average displacement of the nodal points of the hand mechanism of an android robot while implementing instantaneous states. On the basis of the geometric analysis of the indicated displacements, a method is proposed which makes it possible to reduce the time of iterative search for the increment vector of generalized coordinates. Also images are shown of multiple positions of arm mechanism links on the frontal and horizontal projections when implementing instantaneous states. This images allows to make a graphic interpretation of manipulator mechanism maneuverability at each point of the configuration space. Hypersurfaces in four-dimensional space are used to establish the analytical dependencies reflecting the relationship of the average displacement of manipulator mechanism nodal points and the generalized coordinates that defining the positions of the manipulator configurations. For this purpose, the equations of interpolating polynomials located in three mutually perpendicular planes are used. Based on these three interpolating polynomials, a third-order hypersurface equation is obtained, which reflects the interrelation of geometric and kinematic parameters. The article also presents the results of virtual modeling of android robot hand mechanism movement, taking into account the position of the restricted area in the AutoCAD system. The results of calculations using the obtained analytical dependencies showed a reduction in the calculation time of test tasks. The conducted studies can be used in the development of intelligent motion control systems for autonomously functioning android robots in an organized environment without the participation of a human operator.

Axial-anomaly in noncommutative QED and Pauli–Villars regularization

We calculate the [Formula: see text](1) axial-anomaly in two and four dimensions using a modified path integral method coupled to a Pauli–Villars regulator field in the noncommutative QED. Pauli–Villars regularization method provides us with unambiguous way to connect the modified path integral formalism with perturbative axial Ward identities at each step of calculations.

Energy exchange rate coefficients in modeling carbon dioxide kinetics: calculation optimization

In this paper considers algorithms for calculating vibrational energy exchange rate coefficients for collisions of carbon dioxide molecules are considered. For numerical modeling of CO2 vibrational kinetics in the state-to-state approach, it is necessary to solve a system of several thousands of differential equations for level populations of three vibrational CO2 modes at an each step of calculations. The right hand parts of these kinetic equations contain energy exchange rate coefficients for collisions of molecules from different levels of three vibrational CO2 modes. There are hundreds of thousands of these coefficients due to the large number of energy exchanges. From the numerical point of view, this modeling qualifies as Big Data and requires the development of rapid numerical methods or pre-calculations. Such an amount of data also requires a quick access data structure. Until now for the state-to-state description of CO2 vibrational relaxation has used only simplified kinetic schemes with a limited numbers of vibrational levels and energy transitions have been used. In the present paper the problem is solved in the complete formulation. An effective scheme for calculating the coefficients is proposed on the basis of parallel computations and convolute code optimization, together with an optimal data structure for their storage.

Downscaling of wave climate in the western Black Sea

This study presents the south-west Black Sea wave climatology based on a downscaling approach of a long-term 31-year SWAN model wave hindcast using telescoping nested grids. At all domains the SWAN model is forced with the CFSR winds. Sensitivity tests are conducted on domain size, computational resolutions, the physical formulations and their adjustable coefficients for deep water source terms, time step of non-stationary calculation, and wind forcing for all domains. For each nested grid the physical and numerical settings were determined separately by calibration against wave buoy measurements at six locations (Gelendzhik, Hopa, Sinop, Gloria, Filyos, and Karaburun) in appropriate domains. Model validation is also conducted for the long-term data using the unused measurements in the calibration. Using the calibrated nested models, a 31-year long-term wave hindcast is conducted. Two-hourly sea state parameters of significant wave height (Hm0), wave energy period (Tm-10), spectral period (Tm01), zero-crossing period (Tm02), peak period (Tp), wind speed components, and mean wave direction (DIR) were collected over three sub-grid domains. Using this database normal and extreme wave conditions in the three sub-grid domains were determined. Finally, extreme waves with different return periods were determined and compared with those presented in the Wind and Deep Water Wave Atlas of Özhan and Abdalla (2002).The present study demonstrates the sensitivity of the SWAN model towards different GEN3 physics options and its adjustable whitecapping parameter Cds and time step of the non-stationary calculations. It is shown that the developed wave model set-up with a nested grid system performs quite satisfactorily and storms are also well-captured. This study yields higher extreme waves in the western part of our area of interest and lower extremes in the eastern part in comparison with those of the presently used Wind and Deep Water Wave Atlas.

Numerical Model of Two-Phase Flow in Dissolvable Porous Media and Simulation of Reservoir Acidizing

Mathematical model of porous media dissolution coupled with two-phase flow is proposed. The model is based on the conception of dissolvable porous medium with deformable mass-variable porous skeleton. Model can be used for simulation of coupled chemo- and hydrogeomechanical processes which are difficult to examine experimentally. Acidizing of calcite oil reservoir is used as an example of the process. Water solution of hydrochloric acid and oil are two fluid phases of the model with several components. Dissolvable porous media is treated as deformable mass-variable solid phase. Change in mass of the solid phase is caused by hydrochloric acid dissolving the calcite part of the solid phase. Dissolution is supposed to be congruent; kinetics is governed by the Nernst law. Software for numerical solution of the model is developed. It uses AmgCL parallel library for high-performance computing in order to deal with large algebraic systems on the each time step of calculations. The library uses algebraic multigrid methods for preconditioning and parallel iterative solvers. NVidia CUDA framework is used as a backend to perform GPGPU calculations, because it proved to be faster than OpenCL framework on this problem. Numerical experiments on the basis of data set from real reservoirs are conducted with the developed software. Good correlation between field and calculated data is achieved. Numerical experiments for different configurations of heterogeneous layer are performed. Acidizing of layers with highly permeable conduit and with random distribution of permeability is modeled.

Estimation of Sand Production Rate Using Geomechanical and Hydromechanical Models

This paper aims to develop a numerical model that can be used in sand control during production phase of an oil and gas well. The model is able to predict not only the onset of sand production using critical bottom hole pressure inferred from geomechanical modelling, but also the mass of sand produced versus time as well as the change of porosity versus space and time using hydromechanical modelling. A detailed workflow of the modelling was presented with each step of calculations. The empirical parameters were calibrated using laboratory data. Then the modelling was applied in a case study of an oilfield in Cuu Long basin. In addition, a sensitivity study of the effect of drawdown pressure was presented in this paper. Moreover, a comparison between results of different hydromechanical models was also addressed. The outcome of this paper demonstrated the possibility of modelling the sand production mass in real cases, opening a new approach in sand control in petroleum industry.

Low cost, high accuracy real-time simulation used for rapid prototyping and testing control algorithms on example of BLDC motor

AbstractThis article presents the simulation of a BLDC motor and its closed control system in FPGA. The simulation is based on a mathematical model of the motor, including the electromagnetic torque, phase currents, back electromotive force, etc. In order to ensure calculation precision, the equations describing the motor were solved using a floating point representation of real numbers, and a small step of numerical calculations of 1 μs was assumed. The time step selection methodology has been discussed in detail. The motor model was executed with the use of Textual Programming Languages (with HDL codes).

First-order neutron-deuteron scattering in a three-dimensional approach

The description of the neutron-deuteron scattering process has been possible using the partial wave approach since the 1980s (Few-Body Syst. 3, 123 (1988); Phys. Rep. 274, 107 (1996); Acta Phys. Pol. B 28, 1677 (1997)). In recent years the so-called “three-dimensional” formalism was developed, where the calculations are performed with operators acting directly on the three-dimensional degrees of freedom of the nucleons. This approach avoids a tedious step of the classical calculations, the partial wave decomposition of operators, and in this paper is applied to the neutron-deuteron scattering process. The calculations presented here are a first step toward a new calculation scheme that would make it possible to easily produce precise predictions for a wide range of nuclear force models. This paper is a continuation of the work presented in Eur. Phys. J. A 43, 339 (2010) where the breakup channel was considered in detail. The theoretical formulation used in this paper is very closely related to the formalism introduced in Eur. Phys. J. A 43, 339 (2010) and Phys. Rev. C 68, 054003 (2003), however, we work directly with the matrix representation of operators in the joined isospin-spin space of the three-nucleon system and use only the driving term of the three-nucleon Faddeev equations. This greatly simplifies the numerical realization of the calculation and allows us to consider also the elastic channel of the reaction.

VIBRATIONS RESONANCE ESTIMATION IN MARINE STRUCTURES

Dynamic analyses of marine structures are one of the most important during design process as well as during exploitation. Typically, two parts of vibrations calculations are performed. Firstly, natural vibrations frequencies and modes are determined. Forced vibrations analysis is the second step of calculations. Natural vibrations give us information about possibility (e.g. at which main engine speed) of dangerous vibrations amplitudes (resonances threat). Exact values of vibrations amplitudes are results of forced vibrations analysis. Confidence level (error value) of forced vibration calculations is much lower in comparison to uncertainty of natural vibration analysis. What is more, form engineering practice point of view, natural vibrations frequencies estimation (resonance avoidance) is the most important during dynamic analysis of marine structures with propulsion systems. In the paper some examples of dynamic characteristics estimation and their changing methods (possibility) was presented. Utility of relatively simple models, with low degree of freedom number, was discussed. Modelling methods depending on the analysis target of marine slow-speed crankshafts was presented. Advantages and disadvantages of subcritical and supercritical design of marine propulsion system were discussed. An example of propulsion system natural torsional vibrations simplified analysis was presented. Location of the main torsional resonance is one of the most important decisions during design process of the marine propulsion system. Methods of fast and easy estimation as well as changing possibility of natural vibrations frequencies of marine structures is the main objective of presented paper.

Extension of the free energy workflow FEW towards implicit solvent/implicit membrane MM–PBSA calculations

BackgroundThe number of high-resolution structures of pharmacologically relevant membrane proteins has been strongly increasing. This makes computing relative affinities of chemically similar compounds binding to a membrane protein possible in order to guide decision making in drug design. However, the preparation step of such calculations is time-consuming and complex. MethodsWe extended the free energy workflow tool FEW, available in AMBER, towards facilitating the setup of molecular dynamics simulations with explicit membrane, and the setup and execution of effective binding energy calculations according to a 1-trajectory implicit solvent/implicit membrane MM-PBSA approach for multiple ligands binding to the same membrane protein. ResultsWe validated the implemented protocol initially on two model systems, a sodium ion in the presence of an implicit membrane slab and a proton traversing the M2 proton-channel of the influenza A virus. For the latter, we found a good agreement for several important events along the proton pathway with those obtained in a recent computational study. Finally, we performed a case study on effective binding energy calculations for a set of inhibitors binding to the M2 proton-channel. ConclusionsFrom the case study, we estimate a considerable speed up in the setup and analysis times for implicit solvent/implicit membrane MM-PBSA calculations by the extended version of FEW compared to a manual preparation. General significanceTogether with the overall runtime and the analysis results, this suggests that such type of calculations can be valuable in later stages of drug design projects on membrane proteins. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

A Regression-Based Method for Estimating Risks and Relative Risks in Case-Base Studies

Both the absolute risk and the relative risk (RR) have a crucial role to play in epidemiology. RR is often approximated by odds ratio (OR) under the rare-disease assumption in conventional case-control study; however, such a study design does not provide an estimate for absolute risk. The case-base study is an alternative approach which readily produces RR estimation without resorting to the rare-disease assumption. However, previous researchers only considered one single dichotomous exposure and did not elaborate how absolute risks can be estimated in a case-base study. In this paper, the authors propose a logistic model for the case-base study. The model is flexible enough to admit multiple exposures in any measurement scale—binary, categorical or continuous. It can be easily fitted using common statistical packages. With one additional step of simple calculations of the model parameters, one readily obtains relative and absolute risk estimates as well as their confidence intervals. Monte-Carlo simulations show that the proposed method can produce unbiased estimates and adequate-coverage confidence intervals, for ORs, RRs and absolute risks. The case-base study with all its desirable properties and its methods of analysis fully developed in this paper may become a mainstay in epidemiology.

Novel Area Optimization in FPGA Implementation Using Efficient VHDL Code

A new novel method for area efficiency in FPGA implementation is presented. The method is realized through flexibility and wide capability of VHDL coding. This method exposes the arithmetic operations such as addition, subtraction and others. The design technique aim to reduce occupies area for multi stages circuits by selecting suitable range of all value involved in every step of calculations. Conventional and efficient VHDL coding methods are presented and the synthesis result is compared. The VHDL code which limits range of integer values is occupies less area than the one which is not. This VHDL coding method is suitable for multi stage circuits.

Numerical modelling of vandalistic action on footbridge for pedestrians and bicycles

The paper deals with numerical modelling of dynamic load acting on a footbridge. Two cases of loads caused by passing people have been considered: the load caused by crowd of people and by random stream of people. Moreover, two cases of vandalistic actions have been taken into account. Vandalistic action is such purposeful human action which leads to damage or destruction of an object. Numerical analyses have been carried out for the real footbridge for pedestrians and bicycles traffic over Vistula River in Cracow. Modal analysis was the first step of calculations and on this basis various variants of dynamic actions have been assumed. All computations have been performed with use of FEM system - ALGOR.

Estimation of Peak Ground Acceleration and Its Uncertainty for Northern Indian Region

In the present study the authors evaluate uncertainties in the seismic hazard assessment for the Northern Indian region, based on the probabilistic seismic hazard analysis (PSHA). The newly compiled earthquake data has been treated for the quality, consistency, and homogeneity in a systematic manner to find out the uncertainties in every step of calculations. Based on the geological and tectonic setup, seismicity and other geophysical anomalies, a seismotectonic model of the region has been developed. The seismic hazard parameters are calculated based on giving proper weight to specific region. The peak ground acceleration (PGA) is estimated for various return periods for the Northern Indian region using a logic tree approach. The variation at the input level in terms of the source models and different Ground Motion Prediction Equations (GMPEs) is used. To examine into the effect of source modelling and GMPEs, the Coefficient of Variation (COV) maps have been generated. To encompass the region and for better resolution, the peak ground acceleration (PGA) is estimated at 15 minute intervals. The COV values due to all branch points in the logic tree decrease with distance from the source and conspicuous increase toward fault boundaries are observed.

Interfacing ab initio Quantum Mechanical Method with Classical Drude Osillator Polarizable Model for Molecular Dynamics Simulation of Chemical Reactions.

In order to further improve the accuracy and applicability of combined quantum mechanical/molecular mechanical (QM/MM) methods, we have interfaced the ab initio QM method with the classical Drude oscillator polarizable MM force field (ai-QM/MM-Drude). Different coupling approaches have been employed and compared: 1. the conventional dual self-consistent-field (SCF) procedure; 2. the direct SCF scheme, in which QM densities and MM Drude positions are converged simultaneously; 3. the micro-iterative SCF scheme, in which the Drude positions of the polarizable model are fully converged during each self-consistent field (SCF) step of QM calculations; 4. the one-step-Drude-update scheme, in which the MM Drude positions are updated only once instead of fully converged during each molecular dynamics (MD) step. The last three coupling approaches are found to be efficient and can achieve the desired convergence in a similar number of QM SCF steps comparing with the corresponding QM method coupled to a non-polarizable force field. The feasibility and applicability of the implemented ai-QM/MM-Drude approach have been demonstrated by carrying out Born-Oppenheimer molecular dynamics simulations with the umbrella sampling method to determine potentials of mean force for both the methyl transfer reaction of the methyl chlorine-chlorine ion system and the glycine intra-molecular proton transfer reaction in aqueous solution. Our results indicate that the ai-QM/MM-Drude approach is very promising, which provides a better description of QM/MM interactions while can achieve quite similar computational efficiency in comparison with the corresponding conventional ab initio QM/MM method.