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Search results for: INTEGRO-DIFFERENTIAL EQUATION
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Integrate-and-fire models with an almost periodic input function
PublicationWe investigate leaky integrate-and-fire models (LIF models for short) driven by Stepanov and μ-almost periodic functions. Special attention is paid to the properties of the firing map and its displacement, which give information about the spiking behavior of the considered system. We provide conditions under which such maps are well-defined and are uniformly continuous. We show that the LIF models with Stepanov almost periodic...
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The cohomological span of LS-Conley index
PublicationIn this paper we introduce a new homotopy invariant – the cohomological span of LS-Conley index. We prove the theorems on the existence of critical points for a class of strongly indefinite functionals with the gradient of the form Lx+K(x), where L is bounded linear and K is completely continuous. We give examples of Hamiltonian systems for which our methods give better results than the Morse inequalities. We also give a formula...
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Homoclinic solutions for a class of the second order Hamiltonian systems
PublicationW niniejszej pracy badamy istnienie orbit homoklinicznych dlaukładu Hamiltonowskiego drugiego rzędu: q^{..} + V_{q}(t,q) = f(t), gdzie V z iloczynu kartezjańskiego R x R^{n} do R jest postaciV(t,q) = -K(t,q) + W(t,q). Zakładamy, ze V jest T-okresowe ze względuna zmienną t, K spełnia tzw. ''pinching'' warunek, W jest superliniowew nieskończoności, a norma f w L^{2} jest wystarczająco mała.Orbitę homokliniczną takiego układu znajdujemy...
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Time-of-flight electron scattering from molecular hydrogen: Benchmark cross sections for excitation of the X1Σ+g→b3Σ+u transition
PublicationThe electron impact X1Σ+g to b3Σ+u transition in molecular hydrogen is one of the most important dissociation pathways to forming atomic hydrogen atoms, and is of great importance in modeling astrophysical and industrial plasmas where molecular hydrogen is a substantial constituent. Recently it has been found that the convergent close-coupling (CCC) cross sections of Zammit et al. [Phys. Rev. A 95, 022708 (2017)] are up to a factor...
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Numerical Simulations and Tracer Studies as a Tool to Support Water Circulation Modeling in Breeding Reservoirs
PublicationThe article presents a proposal of a method for computer-aided design and analysis of breeding reservoirs in zoos and aquariums. The method applied involves the use of computer simulations of water circulation in breeding pools. A mathematical model of a pool was developed, and a tracer study was carried out. A simplified model of two-dimensional flow in the form of a biharmonic equation for the stream function (converted into...
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The finite-difference simulation of x-rays propagation through a system of lenses
PublicationThe propagation of X-ray waves through an optical system consisting of 33 aluminum X-ray refractive lenses is considered. For solving the problem, a finite-difference method is suggested and investigated. It is shown that very small steps of the difference grid are necessary for reliable computation of propagation of X-ray waves through the system of lenses. It is shown that the wave phase is a function very quickly increasing...
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Entropy Production Associated with Aggregation into Granules in a Subdiffusive Environment
PublicationWe study the entropy production that is associated with the growing or shrinking of a small granule in, for instance, a colloidal suspension or in an aggregating polymer chain. A granule will fluctuate in size when the energy of binding is comparable to k_{B}T, which is the “quantum” of Brownian energy. Especially for polymers, the conformational energy landscape is often rough and has been commonly modeled as being self-similar...
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Application of non-classical operational calculus to indicate hazards in numerical solutions of engineering problems
PublicationThe article addresses the application of non- classical operational calculus to approximative solutions of engineering problems. The engineering-sound examples show that a continuous–discrete problem transformation from differential unequivocal problem to a differential wildcard problem, triggering a change in solution quality. A number of approximative methods are capable to alter both quantitative and qualitative...
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Thermal properties of VO2 and V2O3 nanostructures
Open Research DataThe DataSet contains the DSC and TG curves of VO2 and V2O3 nanostructures obtained by the sol-gel with different reaction conditions. The information about xerogel powder synthesis is described in the Journal of Nanomaterials. The xerogel powder was annealing under argon atmosphere at the selected temperature: 500C, 600C, and 1000C.
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Impact of Boundary Conditions on Acoustic Excitation of EntropyPerturbations in a Bounded Volume of Newtonian Gas
PublicationExcitation of the entropy mode in the field of intense sound, that is, acoustic heating, is theoreticallyconsidered in this work. The dynamic equation for an excess density which specifies the entropy mode,has been obtained by means of the method of projections. It takes the form of the diffusion equation withan acoustic driving force which is quadratically nonlinear in the leading order. The diffusion coefficient isproportional...
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On the Buckling Response of Axially Pressurized Nanotubes Based on a Novel Nonlocal Beam Theory
PublicationIn the present study, the buckling analysis of single-walled carbon nanotubes (SWCNT) on the basis of a new refined beam theory is analyzed. The SWCNT is modeled as an elastic beam subjected to unidirectional compressive loads. To achieve this aim, the new proposed beam theory has only one unknown variable which leads to one equation similar to Euler beam theory and is also free from any shear correction factors. The equilibrium...
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On various modelling approaches to real-time visualisation of blood flow
PublicationThis paper reviews various modelling approaches to real-time visualisation of blood flow. These include classic, macroscale approach based on the momentum conservation equation together with a proper constitutive equation. Moreover, modern micro- and mesoscale approaches, such as molecular dynamics and dissipative particle dynamics, are discussed. Advantages and disadvantages of the discussed methods are highlighted with particular...
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Analytical Buckling of FG Nanobeams on The Basis of A New One Variable First-Order Shear Deformation Beam Theory
PublicationIn this work, buckling analysis of functionally graded (FG) nanobeams based on a new refined beam theory has been analyzed. The beam is modeled as an elastic beam subjected to unidirectional compressive loads. To achieve this aim, the new obtained beam theory has only one variable which leads to one equation similar to the Euler beam theory and also is free of any shear correction factor. The equilibrium equation has been...
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Vortex flow caused by periodic and aperiodic sound in a relaxing maxwell fluid
PublicationThis paper concerns the description of vortex flow generated by periodic and aperiodic sound in relaxing Maxwell fluid. The analysis is based on governing equation of vorticity mode, which is a result of decomposition of the hydrodynamic equations for fluid flow with relaxation and thermal conductivity into acoustical and non-acoustical parts. The equation governing vorticity mode uses only instantaneous, not averaged over sound...
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Magnetic disturbances caused by magnetic contamination of plastics
PublicationIn the study of low magnetic fields precision magnetometers working in a differential system are used. Two optically pumped magnetometers working in a differential system allow for precise measuring of disturbances in the magnetic field. In order to attain high accuracy of magnetic field measurement, it is necessary to use appropriate materials for the construction of a magnetometric system, particularly of those located closely...
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A high-accuracy complex-phase method of simulating X-ray propagation through a multi-lens system
PublicationThe propagation of X-ray waves through an optical system consisting of many X-ray refractive lenses is considered. For solving the problem for an electromagnetic wave, a finite-difference method is applied. The error of simulation is analytically estimated and investigated. It was found that a very detailed difference grid is required for reliable and accurate calculations of the propagation of X-ray waves through a multi-lens...
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A significance of multi slip condition for inclined MHD nano-fluid flow with non linear thermal radiations, Dufuor and Sorrot, and chemically reactive bio-convection effect
PublicationThe aim of this research is to discuss the significance of slip conditions for magnetized nanofluid flow with the impact of nonlinear thermal radiations, activation energy, inclined MHD, sorrot and dufour, and gyrotactic micro motile organisms over continuous stretching of a two-dimensional sheet. The governing equations emerge in the form of partial differential equations. Since the resultant governing differential equations...
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On solvability of initial boundary-value problems of micropolar elastic shells with rigid inclusions
PublicationThe problem of dynamics of a linear micropolar shell with a finite set of rigid inclusions is considered. The equations of motion consist of the system of partial differential equations (PDEs) describing small deformations of an elastic shell and ordinary differential equations (ODEs) describing the motions of inclusions. Few types of the contact of the shell with inclusions are considered. The weak setup of the problem is formulated...
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The α-µ model of the multipath fading channel
Open Research DataThe dataset contains the results of simulations that are part of the research on modelling the multipath fading in the communication channel. The envelope of the α-µ fading process is generated using the Monte-Carlo simulation (MCS) in the LabVIEW programming environment.
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Examples of numerical simulations of two-dimensional unsaturated flow with VS2DI code using different interblock conductivity averaging schemes
PublicationFlow in unsaturated porous media is commonly described by the Richards equation. This equation is strongly nonlinear due to interrelationships between water pressure head (negative in unsaturated conditions), water content and hydraulic conductivity. The accuracy of numerical solution of the Richards equation often depends on the method used to estimate average hydraulic conductivity between neighboring nodes or cells of the numerical...
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Temperature-dependent structure-property modeling of viscosity for ionic liquids
PublicationIn this paper we present the methodology for assessing the ionic liquids' viscosity at six temperature points (25, 35, 45, 50, 60 and 70 [C]), which utilizes only the in silico approach. The main idea of such assessment is based on the "correction equation" describing the correlation between experimentally measured viscosity and theoretically derived density (calculated with use of molecular mechanics), given at 6 different temperature...
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Influence of heterogeneous air entry pressure on large scale unsaturated flow in porous media
PublicationThe paper presents numerical simulations of water infiltration in unsaturated porous media containing coarse-textured inclusions embed- ded in fine-textured background material. The calculations are performed using the two-phase model for water and air flow and a simplified model known as the Richards equation. It is shown that the Richards equation cannot correctly describe flow in the presence of heterogeneities. How- ever, its...
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Existence and uniqueness of solutions for single-population McKendrick-von Foerster models with renewal
PublicationWe study a McKendrick-von Foerster type equation with renewal. This model is represented by a single equation which describes one species which produces young individuals. The renewal condition is linear but takes into account some history of the population. This model addresses nonlocal interactions between individuals structured by age. The vast majority of size-structured models are also treatable. Our model generalizes a number...
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Numerical modelling and experimental verification of compressible squeeze film pressure
PublicationThe validity of using the Reynolds equation for compressible squeeze film pressure was tested with computational fluid dynamics (CFD). A squeeze film air bearing was instrumented with pressure sensors and non-contacting displacement probes to provide transient measurements of film thickness and pressure. The film thickness measurements also provided input parameters to the numerical prediction. However, numerical results showed...
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Analytical Buckling of FG Nanobeams on The Basis of A New One Variable First-Order Shear Deformation Beam Theory
PublicationIn this work, buckling analysis of functionally graded (FG) nanobeams based on a new refined beam theory has been analyzed. The beam is modeled as an elastic beam subjected to unidirectional compressive loads. To achieve this aim, the new obtained beam theory has only one variable which lead to one equation similar to Euler beam theory and also is free of any shear correction factor. The...
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Improvement of Thrust Bearing Calculation Considering the Convectional Heating within the Space between the Pads
PublicationA modern thrust bearing tool is used to estimate the behavior of tilting pad thrust bearings not only in the oil film between pad and rotating collar, but also in the space between the pads. The oil flow in the space significantly influences the oil film inlet temperature and the heating of pad and collar. For that reason, it is necessary to define an oil mixing model for the space between the pads. In the bearing tool, the solutions...
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Jakub Golik dr
PeopleJakub Golik currently works as a Research & Teaching Assistant at the Faculty of Management and Economics, Department of Entrepreneurship, Gdańsk University of Technology. Jakub does research in Utility-maximizing Models in Economy, Entrepreneurial Economics, Career Choice and Decision/Risk Theory. In his research he utilises mainly quantitative and experimental research methods including Conjoint Analysis and Structural Equation...
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Fourier transform infrared spectroscopy (FTIR) of pre- PXBS (0 h) and PXBS during the crosslinking process (24 h–288 h)
Open Research DataThe goal of this research was developing biodegradable and biocompatibile xylitol-based copolymers with improved mechanical properties, and investigating the change in their thermal and chemical properties withprogress of the cross-linking process. Using a raw material of natural origin such as xylitol, a prepolymer wasobtained by esterification and...
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Thermal behaviour of vanadium xerogel powder under oxidizing atmosphere
Open Research DataThe DataSet contains the results of the thermal behavior of the vanadium xerogel powder. The information about xerogel powder synthesis is described in the Journal of Nanomaterials.
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Thermal behaviour of vanadium xerogel powder under argon atmosphere
Open Research DataThe DataSet contains the results of the thermal behavior of the vanadium xerogel powder. The information about xerogel powder synthesis is described in the Journal of Nanomaterials.
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DL_MG: A Parallel Multigrid Poisson and Poisson–Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution
PublicationThe solution of the Poisson equation is a crucial step in electronic structure calculations, yielding the electrostatic potential -- a key component of the quantum mechanical Hamiltonian. In recent decades, theoretical advances and increases in computer performance have made it possible to simulate the electronic structure of extended systems in complex environments. This requires the solution of more complicated variants of the...
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ESTIMATING AVERSION TO RANK INEQUALITY UNDERLYING SELECTED ITALIAN INDICES OF INCOME INEQUALITY
PublicationIn this paper, we estimate aversion to rank inequality (ATRI) underlying selected Italian income inequality indices, I, notably the Pietra index, the Bonferroni index and the “new” Zenga index. We measure ATRI by the parameter v of the generalised Gini index G(v). ATRI is distinct from aversion to income inequality, as measured by parameter ε of Atkinson’s index A(ε). We propose eliciting v from the equation I = GE(v). As, in general,...
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Modelowanie przepływu ustalonego niejednostajnego w sieciach kanałów otwartych z uwzględnieniem obiektów hydrotechnicznych
PublicationW pracy sformułowano zagadnienie brzegowe dla równania energii opisującego przepływ ustalony niejednostajny i przedstawiono sposób jego rozwiązania przy pomocy metody różnicowej. Zaproponowana metoda obliczeń nadaje się do analizy przepływu w dendrycznych i pierścieniowych sieciach kanałów otwartych. Ponadto na przykładzie przelewu prostokątnego zaproponowano metodę uwzględnienia w obliczeniach zabudowy hydrotechnicznej. Słowa...
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Parabolic Equations with Functional Dependence
PublicationWe consider the Cauchy problem for nonlinear parabolic equations with functional dependence and prove theorems on the existence of solutions to parabolic differential-functional equations.
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Mountain pass solutions to Euler-Lagrange equations with general anisotropic operator
PublicationUsing the Mountain Pass Theorem we show that the problem \begin{equation*} \begin{cases} \frac{d}{dt}\Lcal_v(t,u(t),\dot u(t))=\Lcal_x(t,u(t),\dot u(t))\quad \text{ for a.e. }t\in[a,b]\\ u(a)=u(b)=0 \end{cases} \end{equation*} has a solution in anisotropic Orlicz-Sobolev space. We consider Lagrangian $\Lcal=F(t,x,v)+V(t,x)+\langle f(t), x\rangle$ with growth conditions determined by anisotropic G-function and some geometric conditions...
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A Quasi-2D MOSFET Model — 2D-to-Quasi-2D Transformation
PublicationA quasi-two-dimensional (quasi-2D) representation of the MOSFET channel is proposed in this work. The representation lays the foundations for a quasi 2D MOSFET model. The quasi 2D model is a result of a 2D into quasi 2D transformation. The basis for the transformation are an analysis of a current density vector field and such phenomena as Gradual Channel Detachment Effect (GCDE), Channel Thickness Modulation Effect (CTME), and...
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Induction machine behavioral modeling for prediction of EMI propagation.
PublicationThis paper presents the results of wideband behavioral modeling of an induction machine (IM). The proposed solution enables modeling the IM differential- and common-mode impedance for a frequency range from 1 kHz to 10 MHz. Methods of parameter extraction are derived from the measured IM impedances. The developed models of 1.5 kW and 7.5 kW induction machines are designed using the Saber Sketch scheme editor and simulated in the...
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The Suzuki model of the multipath fading channel
Open Research DataThe dataset contains the results of simulations that are part of the research on modelling the multipath fading in the communication channel. The Suzuki fading envelope is generated using the Monte-Carlo simulation (MCS) in the LabVIEW programming environment.
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On the Existence of Homoclinic Type Solutions of a Class of Inhomogenous Second Order Hamiltonian Systems
PublicationWe show the existence of homoclinic type solutions of a class of inhomogenous second order Hamiltonian systems, where a C1-smooth potential satisfies a relaxed superquadratic growth condition, its gradient is bounded in the time variable, and a forcing term is sufficiently small in the space of square integrable functions. The idea of our proof is to approximate the original system by time-periodic ones, with larger and larger...
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Local fixed point indices of iterations of planar maps
PublicationW artykule podana zostaje postać indeksów iteracji dla pewnej klasy odwzorowań planarnych. Podstawowymi narzędziami stosowanym w pracy są liczba Nielsena i indeks Conleya.
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A Strategy to Locate Fixed Points and Global Perturbations of ODE’s: Mixing Topology with Metric Conditions
PublicationIn this paper we discuss a topological treatment for the planar system z' = f (t, z) + g(t, z) where f and g are T -periodic in time and g(t, z) is bounded. Namely, we study the effect of g(t, z) in two different frameworks: isochronous centers and time periodic systems having subharmonics. The main tool employed in the proofs consists of a topological strategy to locate fixed points in the class of orientation preserving embedding...
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Theoretical and experimental study on scattering of low-energy electrons by dimethyl and diethyl ethers
PublicationWe report a joint theoretical and experimental investigation on low-energy electron scattering by dimethyl and diethyl ethers. The experimental elastic differential cross sections were measured at impact energies from 1 eV up to 30 eV and scattering angle range of 10◦ to 130◦. Theoretical elastic differential, integral and momentum-transfer cross sections are calculated at impact energies up to 30 eV, employing the Schwinger multichannel...
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Biomass estimation using a length-weight relationship in beetle larvae (Coleoptera: Aphodiidae, Histeridae, Hydrophilidae, Staphylinidae) obtained from cow dung
PublicationThis research enabled the relationship between length and dry body mass to be determined for 158 beetle larvaetaken from cow dung in north-eastern Poland. The larvae were divided into three morphological types, for which the power and linear function of the body length-weight relationship were determined. The linear regression equation characterizes the relationship between body weight and...
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Numerical Test for Stability Evaluation of Discrete-Time Systems
PublicationIn this paper, a new numerical test for stability evaluation of discrete-time systems is presented. It is based on modern root-finding techniques at the complex plane employing the Delaunay triangulation and Cauchy's Argument Principle. The method evaluates if a system is stable and returns possible values and multiplicities of unstable zeros of the characteristic equation. For state-space discrete-time models, the developed test...
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Elastic electron scattering and vibrational excitation of isoxazole molecules in the energy range from 2 to 20 eV
PublicationDifferential cross sections for elastic electron scattering and the excitation of the C-H vibrational modes of isoxazole molecules were measured in the energy range from 2 to 20 eV and over the scattering angle range from 10◦ to 180◦. The cross sections at the scattering angles of and above 90◦ were accessible with the use of a magnetic angle changer. The differential cross sections were integrated to yield integral and momentum...
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Use of Sensory Analysis Methods to Evaluate the Odor of Food and Outside Air
PublicationSensory analysis is applied in many areas of daily life. It is used to carry out the sensory evaluation of foodstuffs or other products and to evaluate the properties of odors present in the environment. The authors attempt to summarize the knowledge on the classification and application of sensory analysis methods to evaluate the odor nuisance of air, which allows the identification of sensory impressions and determination of...
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Raman spectra and electrochemical data of carbon nanowall with tailored defects
Open Research DataThis dataset comprises of Raman spectra aquired with different excitation laser sources and the electrochemical data of defect-induced carbon nanowall electrodes (CNW).
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Projekt mechanizmu różnicowego do pojazdu samochodowego z zachowaniem wymogów jakościowych ISO/TS 16949
PublicationW artykule przedstawiono proces projektowania mechanizmu różnicowego. Dokonano wyboru koncepcji z pośród istniejących rozwiązań stosowanych obecnie w pojazdach samochodowych. Skupiono się przede wszystkim na przebiegu procesu wykonania prototypu z zachowaniem wymogów i standardów ISO/TS 16949 dla produktu i projektu.
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Convergence of Monte Carlo algorithm for solving integral equations in light scattering simulations
PublicationThe light scattering process can be modeled mathematically using the Fredholm integral equation. This equation is usually solved after its discretization and transformation into the system of algebraic equations. Volume integral equations can be also solved without discretization using the Monte Carlo (MC) algorithm, but its application to the light scattering simulations has not been sufficiently studied. Here we present implementation...
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Interaction of Acoustic and Thermal Modes in the Vibrationally Relaxing Gases. Acoustic Cooling
PublicationThe dynamic equation which governs an excess temperature associated with the thermal mode in vibrationally relaxing gas is derived. The nonlinear transfer of acoustic energy to the energy of the thermal mode in a relaxing gas causes slow variation of temperature with time. The nal dynamic equation is instantaneous. All types of sound, including aperiodic, may be considered as an acoustic source of corresponding heating or cooling....