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Wyniki wyszukiwania dla: TIME-DEPENDENT SCHROEDINGER EQUATION
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Very accurate time propagation of coupled Schrödinger equations for femto- and attosecond physics and chemistry, with C++ source code
PublikacjaIn this article, I present a very fast and high-precision (up to 33 decimal places) C++ implementation of the semi-global time propagation algorithm for a system of coupled Schrödinger equations with a time-dependent Hamiltonian. It can be used to describe time-dependent processes in molecular systems after excitation by femto- and attosecond laser pulses. It also works with an arbitrary user supplied Hamiltonian and can be used...
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Entropy Production Associated with Aggregation into Granules in a Subdiffusive Environment
PublikacjaWe 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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Evaluation of technical efficiency of heat and electric power generation
PublikacjaThis paper presents an evaluation of technical efficiency and time-dependent changes in productivity of Polish professional electric power and heat&electric power stations by using Data Envelopment Analysis non-parametric method. The research covered the enterprises whose total available electric power amounted to about 98% of that of all professional thermal electric power stations in this country. The analysis has concerned...
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Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
PublikacjaIn this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained...
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Identification of Parameters Influencing the Accuracy of the Solution of the Nonlinear Muskingum Equation
PublikacjaTwo nonlinear versions of the Muskingum equation are considered. The difference between both equations relates to the exponent parameter. In the first version, commonly used in hydrology, this parameter is considered as free, while in the second version, it takes a value resulting from the kinematic wave theory. Consequently, the first version of the equation is dimensionally inconsistent, whereas the proposed second one is consistent. It...
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Flexomagnetic response of buckled piezomagnetic composite nanoplates
PublikacjaIn this paper, the equation governing the buckling of a magnetic composite plate under the influence of an in-plane one-dimensional magnetic field, assuming the concept of flexomagnetic and considering the resulting flexural force and moment, is investigated for the first time by different analytical boundary conditions. To determine the equation governing the stability of the plate, the nonlocal strain gradient theory has been...
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Methodology of generation of CFD meshes and 4D shape reconstruction of coronary arteries from patient-specific dynamic CT
PublikacjaDue to the difficulties in retrieving both the time‑dependent shapes of the vessels and the generation of numerical meshes for such cases, most of the simulations of blood flow in the cardiac arteries use static geometry. The article describes a methodology for generating a sequence of time‑dependent 3D shapes based on images of different resolutions and qualities acquired from ECG‑gated coronary artery CT angiography. The precision...
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Numerical modelling and experimental verification of compressible squeeze film pressure
PublikacjaThe 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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Systems, Environments, and Soliton Rate Equations: Toward Realistic Modeling
PublikacjaIn order to solve a system of nonlinear rate equations one can try to use some soliton methods. The procedure involves three steps: (1) find a ‘Lax representation’ where all the kinetic variables are combined into a single matrix ρ, all the kinetic constants are encoded in a matrix H; (2) find a Darboux–Bäcklund dressing transformation for the Lax representation iρ˙=[H,f(ρ)], where f models a time-dependent environment; (3) find...
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Impact of Boundary Conditions on Acoustic Excitation of EntropyPerturbations in a Bounded Volume of Newtonian Gas
PublikacjaExcitation 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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Balance errors generated by numerical diffusion in the solution of non-linear open channel flow equations
PublikacjaThe paper concerns the untypical aspect of application of the dissipative numerical methods to solve nonlinear hyperbolic partial differential equations used in open channel hydraulics. It is shown that in some cases the numerical diffusion generated by the applied method of solution produces not only inaccurate solution but as well as a balance error. This error may occur even for an equation written in the conservative form not...
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DL_MG: A Parallel Multigrid Poisson and Poisson–Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution
PublikacjaThe 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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Effects of deviations from thermo-rheologically simple behavior of asphalt mixes in creep on developing of master curves of their stiffness modulus
PublikacjaThe paper presents the deviations from the thermo-rheologically simple behavior of asphalt mixes and their effects on the developing of master curves of stiffness modulus. Eleven different mixes were tested in three point bending test under constant load at temperatures –20°C, –10 °C and 0 °C, and in some cases at +10 °C. The test method was developed at the Gdansk University of Technology, Poland. The applied stress level was...
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Calculations of labyrinth seals with and without diagnostic extraction in fluid-flow machines
PublikacjaLabyrinth seals are essential components of steam turbine unit constructions. Two types of labyrinth seals can be named, the first of which is the seal without diagnostic steam extraction, and the second – with extraction. The distribution of flow parameters along the packing is affected remarkably by the average seal clearance. The presence of diagnostic extraction leads to the equation system which is determinable and can be...
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NUMERICAL SIMULATION OF CRATER CREATING PROCESS IN DYNAMIC REPLACEMENT METHOD BY SMOOTH PARTICLE HYDRODYNAMICS
PublikacjaA theoretical base of SPH method, including the governing equations, discussion of importance of the smoothing function length, contact formulation, boundary treatment and finally utilization in hydrocode simulations are presented. An application of SPH to a real case of large penetrations (crater creating) into the soil caused by falling mass in Dynamic Replacement Method is discussed. An influence of particles spacing on method...
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A New Expression for the 3-D Dyadic FDTD-Compatible Green's Function Based on Multidimensional Z-Transform
PublikacjaIn this letter, a new analytic expression for the time-domain discrete Green's function (DGF) is derived for the 3-D finite-difference time-domain (FDTD) grid. The derivation employs the multidimensional Z-transform and the impulse response of the discretized scalar wave equation (i.e., scalar DGF). The derived DGF expression involves elementary functions only and requires the implementation of a single function in the multiple-precision...
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Simulation of unsteady flow over floodplain using the diffusive wave equation and the modified finite element method
PublikacjaWe consider solution of 2D nonlinear diffusive wave equation in a domain temporarily covered by a layer of water. A modified finite element method with triangular elements and linear shape functions is used for spatial discretization. The proposed modification refers to the procedure of spatial integration and leads to a more general algorithm involving a weighting parameter. The standard finite element method and the finite difference...
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Numerical Solution of the Two-Dimensional Richards Equation Using Alternate Splitting Methods for Dimensional Decomposition
PublikacjaResearch on seepage flow in the vadose zone has largely been driven by engineering and environmental problems affecting many fields of geotechnics, hydrology, and agricultural science. Mathematical modeling of the subsurface flow under unsaturated conditions is an essential part of water resource management and planning. In order to determine such subsurface flow, the two-dimensional (2D) Richards equation can be used. However,...
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Parametric method applicable in assessing breakout force and time for lifting slender bodies from seabed
PublikacjaThe article presents a parametric method applicable in assessing the suction force of a slender body to the seabed, and prognosing the body extrication time. Along with the body weight in water, the information on the suction force is essential for assessing the force needed to lift the object from the seabed. Based on the Foda theory and the resulting integral equation, which relates the maximum suction force with basic parameters...
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MONITORING OF PERMANENT GPS STATIONS AT THE SUDETY MOUNTAINS
PublikacjaThe aim of this paper is to show time-dependent baseline variation between GPS stations situated in South-East Poland. This study was based on daily data analysis of selected GPS stations: WROC, GOPE, MOPI, KRAW and KATO. The start date of the analysis is linked at every station with the beginning of its operation and the closing date of the operation is in 2006. The multiresolution signal decomposition method has been used to...
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Multi-objective Weather Routing with Customised Criteria and Constraints
PublikacjaThe paper presents a weather routing algorithm utilising a multi-objective optimisation with constraints, namely the Multi-objective Evolutionary Weather Routing Algorithm (MEWRA). In the proposed approach weather route recommendations can be made simultaneously e.g. for passage time, fuel consumption and safety of passage by means of Pareto optimisation. The sets of criteria and constraints in the optimisation process are fully...
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Analysis of Floodplain Inundation Using 2D Nonlinear Diffusive Wave Equation Solved with Splitting Technique
PublikacjaIn the paper a solution of two-dimensional (2D) nonlinear diffusive wave equation in a partially dry and wet domain is considered. The splitting technique which allows to reduce 2D problem into the sequence of one-dimensional (1D) problems is applied. The obtained 1D equations with regard to x and y are spatially discretized using the modified finite element method with the linear shape functions. The applied modification referring...
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Ultrawideband transmission in physical channels: a broadband interference view
PublikacjaThe superposition of multipath components (MPC) of an emitted wave, formed by reflections from limiting surfaces and obstacles in the propagation area, strongly affects communication signals. In the case of modern wideband systems, the effect should be seen as a broadband counterpart of classical interference which is the cause of fading in narrowband systems. This paper shows that in wideband communications, the time- and frequency-domain...
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Coherent-wave Monte Carlo method for simulating light propagation in tissue
PublikacjaSimulating propagation and scattering of coherent light in turbid media, such as biological tissues, is a complex problem. Numerical methods for solving Helmholtz or wave equation (e.g. finite-difference or finite-element methods) require large amount of computer memory and long computation time. This makes them impractical for simulating laser beam propagation into deep layers of tissue. Other group of methods, based on radiative...
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On the Structure of Time in Computational Semantics of a Variable-Step Solver for Hybrid Behavior Analysis
PublikacjaHybrid dynamic systems combine continuous and discrete behavior. Often, computational approaches are employed to derive behaviors that approximate the analytic solution. An important part of this is the approximation of differential equation behavior by numerical integration. The accuracy and computational efficiency of the integration usually depend on the complexity of the method and its implicated approximation errors, especially...
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On the convergence of a finite-difference discretization à la Mickens of the generalized Burgers–Huxley equation
PublikacjaIn this note, we establish the property of convergence for a finite-difference discretization of a diffusive partial differential equation with generalized Burgers convective law and generalized Hodgkin–Huxley reaction. The numerical method was previously investigated in the literature and, amongst other features of interest, it is a fast and nonlinear technique that is capable of preserving positivity, boundedness and monotonicity....
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FDTD-Compatible Green's function based on scalar discrete Green's function and multidimensional Z-transform
PublikacjaIn this contribution, a new formulation of the discrete Green's function (DGF) is presented for the finitedifference time-domain (FDTD) grid. Recently, dyadic DGF has been derived from the impulse response of the discretized scalar wave equation (i.e., scalar DGF) with the use of the multidimensional Z-transform. Its software implementation is straightforward because only elementary functions are involved and a single function...
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Computationally Effcient Solution of a 2D Diffusive Wave Equation Used for Flood Inundation Problems
PublikacjaThis paper presents a study dealing with increasing the computational efficiency in modeling floodplain inundation using a two-dimensional diffusive wave equation. To this end, the domain decomposition technique was used. The resulting one-dimensional diffusion equations were approximated in space with the modified finite element scheme, whereas time integration was carried out using the implicit two-level scheme. The proposed...
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On possible applications of media described by fractional-order models in electromagnetic cloaking
PublikacjaThe purpose of this paper is to open a scientific discussion on possible applications of media described by fractional-order (FO) models (FOMs) in electromagnetic cloaking. A 2-D cloak based on active sources and the surface equivalence theorem is simulated. It employs a medium described by FOM in communication with sources cancelling the scattered field. A perfect electromagnetic active cloak is thereby demonstrated with the use...
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Sensitivity of entanglement decay of quantum-dot spin qubits to the external magnetic field
PublikacjaWe study the decay of entanglement of quantum-dot electron-spin qubits under hyperfine-interaction-mediated decoherence.We show that two-qubit entanglement of a single entangled initial state may exhibit decay characteristic of two disentanglement regimes in a single sample, when the externalmagnetic field is changed. The transition is manifested by the suppression of time-dependent entanglement oscillations which are superimposed...
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Factory Acceptance Test – Strain Gauge Measurement, Report no: WOiO /II/123/2014
PublikacjaTested object was 40 meters long jib and its foundation, placed in Gdansk Shiprepair Yard, manufactured by KMK. The contruction was dedicated to the passenger cruise vessel "Quantum of the Seas" The Strain Gauge measurement in different location and load situation was done in order to validate calculation finite element models used during strength analysis for project. The expertise contains: methodology of the measurements, description...
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Factory Acceptance Test – Strain Gauge Measurement - Report no: WOiO /II/88/2014
PublikacjaTested object was 40 meters long jib and its foundation, placed in Gdansk Shiprepair Yard, manufactured by KMK. The contruction was dedicated to the passenger cruise vessel "North Star" The Strain Gauge measurement in different location and load situation was done in order to validate calculation finite element models used during strength analysis for project. The expertise contains: methodology of the measurements, description...
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Parallel implementation of the DGF-FDTD method on GPU Using the CUDA technology
PublikacjaThe discrete Green's function (DGF) formulation of the finite-difference time-domain method (FDTD) is accelerated on a graphics processing unit (GPU) by means of the Compute Unified Device Architecture (CUDA) technology. In the developed implementation of the DGF-FDTD method, a new analytic expression for dyadic DGF derived based on scalar DGF is employed in computations. The DGF-FDTD method on GPU returns solutions that are compatible...
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Alternative convolution approach to friction in unsteady pipe flow
PublikacjaIn the paper some aspects of the unsteady friction in pipe flow expressed by the convolution are analyzed. This additional term introduced into the motion equation involves the accelerations of fluid occurring in the past and a weighting function. The essence of such approach is to assume the appropriate form of weighting function. However, until now no fully reliable formula for this function has been found. To avoid some inconveniences...
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Determination of t8/5 cooling times for underwater local dry welding of steel
PublikacjaKnowledge of thermal history is the basic condition for studying the structure - properties of welded joints. The determinant of thermal history is the thermal cycle, whose in-situ measurements are still a big challenge. Water as the welding environment complicates this issue even more. The article presents a method to determine an equation for calculating t8/5 cooling times for underwater gas metal arc welding of unalloyed steels...
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Rhamnolipid CMC Prediction
PublikacjaRelationships between the purity, pH, hydrophobicity (log Kow) of the carbon substrate, and the critical micelle concentration (CMC) of rhamnolipid type biosurfactants (RL) were investigated using a quantitative structure–property relationship (QSPR) approach and are presented here for the first time. Measured and literature CMC values of 97 RLs, representing biosurfactants at different stages of purification, were considered....
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Influence of Protonation State on the Excited State Dynamics of a Photobiologically Active Ru(II) Dyad
PublikacjaThe influence of ligand protonation on the photophysics of a ruthenium (Ru) dyad bearing the 2-(1-pyrenyl)-1H-imidazo[4,5-f][1,10]-phenanthroline (ippy) ligand was investigated by time-resolved transient absorption spectroscopy. It was found that changes in the protonation state of the imidazole group led to changes in the electronic configuration of the lowest lying excited state. Formation of the fully deprotonated imidazole...
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Pregnane X receptor dependent up-regulation of CYP2C9 and CYP3A4 in tumor cells by antitumor acridine agents, C-1748 and C-1305, selectively diminished under hypoxia
PublikacjaInduction of proteins involved in drug metabolism and in drug delivery has a significant impact on drug-drug interactions and on the final therapeutic effects. Two antitumor acridine derivatives selected for present studies, C-1748 (9-(2’-hydroxyethylamino)-4-methyl-1-nitroacridine) and C-1305 (5-dimethylaminopropylamino-8-hydroxy-triazoloacridinone), expressed high and low susceptibility to metabolic transformations with liver...
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THIRD-ORDER EXPONENTIAL INTEGRATOR FOR LINEAR KLEIN–GORDON EQUATIONS WITH TIME AND SPACE-DEPENDANT MASS
PublikacjaAllowing for space- and time-dependance of mass in Klein–Gordon equations re- solves the problem of negative probability density and of violation of Lorenz covariance of interaction in quantum mechanics. Moreover it extends their applicability to the domain of quantum cosmology, where the variation in mass may be accompanied by high oscillations....
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THIRD-ORDER EXPONENTIAL INTEGRATOR FOR LINEAR KLEIN–GORDON EQUATIONS WITH TIME AND SPACE-DEPENDANT MASS
PublikacjaAllowing for space- and time-dependance of mass in Klein–Gordon equations re- solves the problem of negative probability density and of violation of Lorenz covariance of interaction in quantum mechanics. Moreover it extends their applicability to the domain of quantum cosmology, where the variation in mass may be accompanied by high oscillations....
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Numerical modeling of quantum dynamical processes
PublikacjaIn this dissertation I present a high-precision (15, 18 or 33 decimal places) C++ implementation of quantum dynamics time propagation algorithms for both time-independent and time-dependent Hamiltonian with an inhomogeneous source term. Moreover I present an extension of both algorithms for time propagation to handle arbitrary number of coupled electronic levels. I have performed a careful validation of these implementations comparing...
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A Model-Order Reduction Approach for Electromagnetic Problems With Nonaffine Frequency Dependence
PublikacjaThe aim of this paper is to present a novel model-order reduction (MOR) technique for the efcient frequency-domain nite-element method (FEM) simulation of microwave components. It is based on the standard reduced-basis method, but the subsequent expansion frequency points are selected following the so-called sparsied greedy strategy. This feature makes it especially useful to perform a fast-frequency sweep of problems that lead...
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Optimization of the femtosecond laser impulse for excitation and the Spin-Orbit mediated dissociation in the NaRb Dimer
PublikacjaWe study the dynamics of multiple coupled states under the influence of an arbitrary time-dependent external field to investigate the femtosecond laser-driven excitation and the spin-orbit mediated dissociation in the NaRb dimer. In this process, the dimer is excited from the ground triplet state 1^3Sigma+ to the 1^3Pi state using the femtosecond laser impulse and the spin-orbit coupling between the 1^3Pi and 2^1Sigma+ states results...
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Efficiency Evaluation of High Performance Computing Systems Using Data Envelopment Analysis
PublikacjaThe paper presents an evaluation method of high performance computing (HPC) systems using multicriteria efficiency analysis. The Data Envelopment Analysis approach was applied and adapted to the specifics of HPC, which enabled us to compare relative efficiency of systems considering simultaneously multiple parameters. The analysis is based on the TOP500 list of world largest supercomputers and their parameters such as: the number...
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Simplified Map-based Selection of Optimal Spindle Speeds When Milling Complex Structures
PublikacjaIn the paper a method for selecting optimal spindle speeds for complex structures during milling operations is presented. It is based on the selection of the spindle speed in accordance with a simple equation resulting from the minimisation of vibration energy, which leads to the minimisation of the work of cut-ting forces presented in previous elaborations by the authors [1]. Optimal spindle speeds are obtained for many points...
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Absorbing Boundary Conditions Derived Based on Pauli Matrices Algebra
PublikacjaIn this letter, we demonstrate that a set of absorbing boundary conditions (ABCs) for numerical simulations of waves, proposed originally by Engquist and Majda and later generalized by Trefethen and Halpern, can alternatively be derived with the use of Pauli matrices algebra. Hence a novel approach to the derivation of one-way wave equations in electromagnetics is proposed. That is, the classical wave equation can be factorized...
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Crank–Nicolson FDTD Method in Media Described by Time-Fractional Constitutive Relations
PublikacjaIn this contribution, we present the Crank-Nicolson finite-difference time-domain (CN-FDTD) method, implemented for simulations of wave propagation in media described by time-fractional (TF) constitutive relations. That is, the considered constitutive relations involve fractional-order (FO) derivatives based on the Grünwald-Letnikov definition, allowing for description of hereditary properties and memory effects of media and processes....
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Comparative Study of Integer and Non-Integer Order Models of Synchronous Generator
PublikacjaThis article presents a comparison between integer and non-integer order modelling of a synchronous generator, in the frequency domain as well as in the time domain. The classical integer order model was compared to one containing half -order systems. The half-order systems are represented in a Park d-q axis equivalent circuit as impedances modelled by half-order transmittances. Using a direct method based on the approximation...
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Mg2+ Doping Effects on the Structural and Dielectric Properties of CaCu3Ti4O12 Ceramics Obtained by Mechanochemical Synthesis
PublikacjaIn this study, ceramic CaCu3Ti4O12 (CCTO) and CaCu3−xMgxTi4O12 solid solutions in which 0.1 ≤ x ≤ 0.5 were prepared by the mechanochemical method, realized by a high‐energy ball milling technique. The effects of the Mg2+ ion concentration and sintering time on the dielectric response in the prepared ceramics were investigated and discussed. It was demonstrated that, by the use of a sufficiently high energy of mechanochemical treatment,...
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Comparative analysis of numerical with optical soliton solutions of stochastic Gross–Pitaevskii equation in dispersive media
PublikacjaThis article deals with the stochastic Gross–Pitaevskii equation (SGPE) perturbed with multiplicative time noise. The numerical solutions of the governing model are carried out with the proposed stochastic non-standard finite difference (SNSFD) scheme. The stability of the scheme is proved by using the Von-Neumann criteria and the consistency is shown in the mean square sense. To seek exact solutions, we applied the Sardar subequation...