Journal articles: 'Discrete-time domain modelling'

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Kramar, V. "The Mathematical Models of Lattice Functions in Modelling of Control System." Journal of Physics: Conference Series 2096, no. 1 (November 1, 2021): 012149. http://dx.doi.org/10.1088/1742-6596/2096/1/012149.

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Abstract The paper proposes an approach to constructing a mathematical model of lattice functions, which are mainly used in the study of discrete control systems in the time and domain of the Laplace transform. The proposed approach is based on the assumption of the physical absence of an impulse element. An alternative to the classical approach to the description of discrete data acquisition - the process of quantization in time, is considered. As a result, models of the lattice function in the time domain and the domain of the discrete Laplace transform are obtained. Based on the obtained mathematical models of lattice functions, a mathematical model of the time quantization element of the system is obtained. This will allow in the future to proceed to the construction of mathematical models of various discrete control systems, incl. expanding the proposed approaches to the construction of mathematical models of multi-cycle continuous-discrete automatic control systems

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Imbaquingo, Carlos Enrique, Eduard Sarrà, Nicola Isernia, Alberto Tonellotto, Yu-Hsing Chen, Catalin Gabriel Dincan, Philip Kjær, Claus Leth Bak, and Xiongfei Wang. "Harmonic Susceptibility Study of DC Collection Network Based on Frequency Scan and Discrete Time-Domain Modelling Approach." Journal of Electrical and Computer Engineering 2018 (December 16, 2018): 1–25. http://dx.doi.org/10.1155/2018/1328736.

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The equivalent model of offshore DC power collection network for the harmonic susceptibility study is proposed based on the discrete time-domain modelling technique and frequency scan approach in the frequency domain. The proposed methodology for modelling a power converter and a DC collection system in the frequency domain can satisfy harmonic studies of any configuration of wind farm network and thereby find suitable design of power components and array network. The methodology is intended to allow studies on any configuration of the wind power collection, regardless of choice of converter topology, array cable configuration, and control design. To facilitate harmonic susceptibility study, modelling DC collection network includes creating the harmonic model of the DC turbine converter and modelling the array network. The current harmonics within the DC collection network are obtained in the frequency domain to identify the resonance frequency of the array network and potential voltage amplification issues, where the harmonic model of the turbine converter is verified by the comparison of the converter switching model in the PLECS™ circuit simulation tool and laboratory test bench, and show a good agreement.

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Fox, M., and D. Long. "Modelling Mixed Discrete-Continuous Domains for Planning." Journal of Artificial Intelligence Research 27 (October 31, 2006): 235–97. http://dx.doi.org/10.1613/jair.2044.

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In this paper we present pddl+, a planning domain description language for modelling mixed discrete-continuous planning domains. We describe the syntax and modelling style of pddl+, showing that the language makes convenient the modelling of complex time-dependent effects. We provide a formal semantics for pddl+ by mapping planning instances into constructs of hybrid automata. Using the syntax of HAs as our semantic model we construct a semantic mapping to labelled transition systems to complete the formal interpretation of pddl+ planning instances. An advantage of building a mapping from pddl+ to HA theory is that it forms a bridge between the Planning and Real Time Systems research communities. One consequence is that we can expect to make use of some of the theoretical properties of HAs. For example, for a restricted class of HAs the Reachability problem (which is equivalent to Plan Existence) is decidable. pddl+ provides an alternative to the continuous durative action model of pddl2.1, adding a more flexible and robust model of time-dependent behaviour.

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Felsen, Leopold B. "Modeling in the time domain: Discrete and discreet—a Poem." International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 5, no. 3 (August 1992): 143–44. http://dx.doi.org/10.1002/jnm.1660050303.

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Xu, Shuning, Lu Tang, and Junhao Yang. "Time-domain modelling and performance research of millimeter-wave all-digital phase-locked loop." Journal of Physics: Conference Series 2245, no. 1 (April 1, 2022): 012018. http://dx.doi.org/10.1088/1742-6596/2245/1/012018.

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Abstract In this paper, a modified time-domain model of millimeter-wave all-digital phase-locked loop (ADPLL) is implemented. In order to reflect the true behaviour of ADPLL, a quantified output digitally controlled-oscillator (DCO) with time domain jitter is proposed. In this ADPLL time-domain model, the DCO model can only output discrete frequency points to imitate the quantization effect of true DCO, and the overlap of different level tuning band is added into this model to imitate the true situation. In addition, the DCO time domain jitter and wander are also added into this model by using the Box-Muller method. Finally, a period estimation method is used to calculate the phase power spectrum density of the output signal, and then the phase noise is obtained through subsequent processing.

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Sun, Min, and Jing Liu. "General Six-Step Discrete-Time Zhang Neural Network for Time-Varying Tensor Absolute Value Equations." Discrete Dynamics in Nature and Society 2019 (December 29, 2019): 1–12. http://dx.doi.org/10.1155/2019/4861912.

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This article presents a general six-step discrete-time Zhang neural network (ZNN) for time-varying tensor absolute value equations. Firstly, based on the Taylor expansion theory, we derive a general Zhang et al. discretization (ZeaD) formula, i.e., a general Taylor-type 1-step-ahead numerical differentiation rule for the first-order derivative approximation, which contains two free parameters. Based on the bilinear transform and the Routh–Hurwitz stability criterion, the effective domain of the two free parameters is analyzed, which can ensure the convergence of the general ZeaD formula. Secondly, based on the general ZeaD formula, we design a general six-step discrete-time ZNN (DTZNN) for time-varying tensor absolute value equations (TVTAVEs), whose steady-state residual error changes in a higher order manner than those presented in the literature. Meanwhile, the feasible region of its step size, which determines its convergence, is also studied. Finally, experiment results corroborate that the general six-step DTZNN model is quite efficient for TVTAVE solving.

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Li, Yanpeng, Yaolin Jiang, and Ping Yang. "Time domain model order reduction of discrete-time bilinear systems with Charlier polynomials." Mathematics and Computers in Simulation 190 (December 2021): 905–20. http://dx.doi.org/10.1016/j.matcom.2021.06.021.

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Patchamatla, J. Rama Raju, and P. K. Emani. "Time Domain Implementation of Transmitting Boundaries in ABAQUS for Discrete Soil-structure Interaction Systems." International Journal of Mathematical, Engineering and Management Sciences 5, no. 3 (June 1, 2020): 447–62. http://dx.doi.org/10.33889/ijmems.2020.5.3.037.

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Soil-structure-interaction (SSI) analyses are essential to evaluate the seismic performance of important structures before finalizing their structural design. SSI under seismic condition involves much more complex interaction with soil compared to the dynamic loads having source on the structure. Seismic SSI analysis requires due consideration of site-specific and structure-specific properties to estimate the actual ground motion (scattered motion) experienced at the base of the structure, and subsequently the effects of the scattered motion on the structure. Most challenging aspect of seismic SSI analysis is to implement transmitting boundaries that absorb the artificial reflections of stress waves at the truncated interface of the finite and infinite domains, while allowing the seismic waves to enter the finite domain. In this paper, the time domain implementation of seismic analysis of a soil-structure system is presented using classical discrete models of structure and interactive force boundary conditions for soil. These models represent typical SSI systems- a single Degree of Freedom (DOF) of a spherical cavity with mass attached to its wall, a two DOF system consisting of a mass attached by a nonlinear spring to a semi-infinite rod on elastic foundation, and a three DOF system with additional DOFs for modelling the structural stiffness and damping. The convolution integral representing the force boundary condition on the truncated interface, is evaluated interactively using UAMP user-subroutine in ABAQUS and applied as concentrated forces at the interface (truncated interface) nodes of the bounded domain or generalized-structure domain. The verification problems presented in the paper show the satisfactory performance of the developed MATLAB code and ABAQUS implementation with FORTRAN user-subroutines. The classical phenomena associated with the dynamic soil-structure systems are discussed through the present work.

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Chen, Yu-Hsing, Catalin Gabriel Dincan, Philip Kjær, Claus Leth Bak, Xiongfei Wang, Carlos Enrique Imbaquingo, Eduard Sarrà, Nicola Isernia, and Alberto Tonellotto. "Model-Based Control Design of Series Resonant Converter Based on the Discrete Time Domain Modelling Approach for DC Wind Turbine." Journal of Renewable Energy 2018 (December 2, 2018): 1–18. http://dx.doi.org/10.1155/2018/7898679.

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This paper focuses on the modelling of the series resonant converter proposed as a DC/DC converter for DC wind turbines. The closed-loop control design based on the discrete time domain modelling technique for the converter (named SRC#) operated in continuous-conduction mode (CCM) is investigated. To facilitate dynamic analysis and design of control structure, the design process includes derivation of linearized state-space equations, design of closed-loop control structure, and design of gain scheduling controller. The analytical results of system are verified in z-domain by comparison of circuit simulator response (in PLECS™) to changes in pulse frequency and disturbances in input and output voltages and show a good agreement. Furthermore, the test results also give enough supporting arguments to proposed control design.

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Cialenco, Igor, and Yicong Huang. "A note on parameter estimation for discretely sampled SPDEs." Stochastics and Dynamics 20, no. 03 (August 27, 2019): 2050016. http://dx.doi.org/10.1142/s0219493720500161.

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We consider a parameter estimation problem for one-dimensional stochastic heat equations, when data is sampled discretely in time or spatial component. We prove that, the real valued parameter next to the Laplacian (the drift), and the constant parameter in front of the noise (the volatility) can be consistently estimated under somewhat surprisingly minimal information. Namely, it is enough to observe the solution at a fixed time and on a discrete spatial grid, or at a fixed space point and at discrete time instances of a finite interval, assuming that the mesh-size goes to zero. The proposed estimators have the same form and asymptotic properties regardless of the nature of the domain –bounded domain or whole space. The derivation of the estimators and the proofs of their asymptotic properties are based on computations of power variations of some relevant stochastic processes. We use elements of Malliavin calculus to establish the asymptotic normality properties in the case of bounded domain. We also discuss the joint estimation problem of the drift and volatility coefficient. We conclude with some numerical experiments that illustrate the obtained theoretical results.

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ZENG, LI, and YI ZHAO. "CHARACTERIZATION OF STATIC BIFURCATIONS FOR MAPS IN THE FREQUENCY DOMAIN." International Journal of Bifurcation and Chaos 17, no. 03 (March 2007): 975–83. http://dx.doi.org/10.1142/s0218127407017690.

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In this paper n-dimensional discrete-time systems with static bifurcations are considered from the viewpoint of control theory. This paper presents an adaption of available formulas for bifurcation analysis in two-dimensional continuous-time systems to the case of smooth maps using a frequency domain approach. The analyzed bifurcations are the building blocks to understand other more complex singularities and to propose certain methods for controlling the bifurcation behavior in nonlinear maps in the future.

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Klonk, Steffen, and Francois Bay. "Induction Heat Treatment for an Automotive Crankshaft: Large Scale Modelling with Moving Inductors." Key Engineering Materials 554-557 (June 2013): 1539–44. http://dx.doi.org/10.4028/www.scientific.net/kem.554-557.1539.

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A numerical model for a multiphysics problem is presented. It includes the movement of subdomains, which are embedded in a global air domain. The description of the movement is based on a discrete level set representation of the moving boundaries. It is based on the original geometry of the moving tools, such that the mesh quality is not reduced in subsequent time steps.

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D'Oca, Simona, H. Burak Gunay, Sara Gilani, and William O'Brien. "Critical review and illustrative examples of office occupant modelling formalisms." Building Services Engineering Research and Technology 40, no. 6 (February 6, 2019): 732–57. http://dx.doi.org/10.1177/0143624419827468.

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It is widely understood that occupants can have a significant impact on building performance. Accordingly, the field has benefited extensively from research efforts in the past decade. However, the methods and terminology involved in modelling occupants in buildings remains fragmented across a large number of studies. This fragmentation represents a major obstacle to those who intend to join in this research endeavor as well as for the convergence and standardization of methods. To address this issue, this paper investigates occupant modelling methods for the key domains of electric lighting, blinds, operable windows, thermostats, plug loads, and occupancy. In the reviewed literature, five broad categories of occupant model formalisms were identified: schedules, Bernoulli models, discrete-time Markov models, discrete-event Markov models, and survival models. Illustrative examples were provided from two independent datasets to demonstrate the strengths and weaknesses of these model forms. It was shown that Markov models are suitable to represent occupants' adaptive behaviors, while survival models are suitable to represent occupancy, non-adaptive behaviors, and infrequently executed adaptive behaviors, such as the blinds opening behavior. Practical application: The engineering application of the occupant modelling formalisms that are critically reviewed in this paper is that these models are highly beneficial for incorporating occupants' presence and behaviors into building design and control. Building design can be improved significantly regarding energy use and occupant comfort when the most suitable occupant models are implemented in simulation-aided building design process. Ultimately, like for any modelling domain, the most suitable model is dependent on the modelling objective (e.g. optimizing passive design, equipment sizing), building type and size, occupant-related domain (e.g. occupancy, window-opening behavior), and climate zones. Furthermore, there is great potential in improving occupant comfort and energy savings of existing buildings when occupants' presence and interactions with buildings' systems and components are predicted accurately using occupant models.

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KAWASHIMA, SHUICHI. "EXPONENTIAL STABILITY OF STATIONARY SOLUTIONS TO THE DISCRETE BOLTZMANN EQUATION IN A BOUNDED DOMAIN." Mathematical Models and Methods in Applied Sciences 02, no. 02 (June 1992): 239–48. http://dx.doi.org/10.1142/s0218202592000156.

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Large-time behavior of solutions of the discrete Boltzmann equation in a bounded domain is studied. The boundary conditions considered are pure diffuse relection and general reflection. Under suitable assumptions it is proved that a unique solution exists globally in time and converges to the corresponding unique stationary solution exponentially as time goes to infinity. The crucial point of the proof is in the derivation of desired boundary estimates of the solution subordinate to the general reflection.

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BACCOU, JEAN, and JACQUES LIANDRAT. "DEFINITION AND ANALYSIS OF A WAVELET/FICTITIOUS DOMAIN SOLVER FOR THE 2D-HEAT EQUATION ON A GENERAL DOMAIN." Mathematical Models and Methods in Applied Sciences 16, no. 06 (June 2006): 819–45. http://dx.doi.org/10.1142/s0218202506001364.

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This paper is devoted to the setting and analysis of a Petrov–Galerkin wavelet-fictitious domain numerical method for the approximation of the solution of multi-dimensional parabolic equations on a general domain. In this method, the original parabolic equation, set on a domain ω, is first discretized in time using a finite difference scheme. At each time step, the corresponding elliptic equation on ω is transformed into a saddle point problem on a functional space defined on a bigger but simply shaped domain Ω where the initial boundary conditions on ω are enforced using surface Lagrange multipliers (Ref. 2). The solution of this problem is then approximated, thanks to a Petrov–Galerkin formulation, using wavelets and time scheme associated "vaguelettes" (Ref. 8). Existence, uniqueness and convergence of the approximated solution, when finite dimension spaces are used, are established and the efficiency as well as the stability of the numerical algorithm (namely the Uzawa algorithm) used in the resolution are analyzed. The constraint of a discrete inf-sup condition as well as ill-conditioning associated to the trace operator are investigated in the wavelet framework. Numerical results related to the 2D heat equation are presented.

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Birajdar, Gunvant A. "Numerical Solution of Time Fractional Navier-Stokes Equation by Discrete Adomian decomposition method." Nonlinear Engineering 3, no. 1 (March 1, 2014): 21–26. http://dx.doi.org/10.1515/nleng-2012-0004.

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AbstractIn this paper we find the solution of time fractional discrete Navier-Stokes equation using Adomian decomposition method. Here we discretize the space domain. The graphical representation of solution given by using Matlab software, and it compared with exact solution for alpha = 1.

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Lemos, José V. "Modelling the Dynamics of Masonry Structures with Discrete Elements." Open Construction and Building Technology Journal 10, no. 1 (May 31, 2016): 210–19. http://dx.doi.org/10.2174/1874836801610010210.

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Block models have been shown to provide a realistic representation of the behavior of many types of masonry structures under static and dynamic loads. When the strength of the units is such that movements along the joints govern the behavior, it is acceptable to make the simplifying assumption that blocks act as rigid bodies. This assumption is particularly useful when dealing with seismic problems, for which the computational times for time domain analysis may be substantial. In this paper, the application of discrete element models for dynamic analysis of masonry structures is addressed. The emphasis is on the seismic behavior of block stone masonry, but the treatment is general to cover other types of masonry. First, the assumptions involved in the choice of a block representation are discussed, stressing in particular the case of rigid block models. Numerical issues are examined, including contact models, calculation of natural frequencies, time stepping algorithms, damping and boundary conditions. A review is presented of modeling examples published in the literature for various types of masonry structures. The choice of numerical representation and its main features are discussed for each case.

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Hoefer, Wolfgang J. R. "The discrete time domain Green's function or Johns matrix — A new powerful concept in transmission line modelling (TLM)." International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 2, no. 4 (December 1989): 215–25. http://dx.doi.org/10.1002/jnm.1660020405.

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Erbay, H. A., S. Erbay, and A. Erkip. "Convergence of a semi-discrete numerical method for a class of nonlocal nonlinear wave equations." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 3 (May 2018): 803–26. http://dx.doi.org/10.1051/m2an/2018035.

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In this article, we prove the convergence of a semi-discrete numerical method applied to a general class of nonlocal nonlinear wave equations where the nonlocality is introduced through the convolution operator in space. The most important characteristic of the numerical method is that it is directly applied to the nonlocal equation by introducing the discrete convolution operator. Starting from the continuous Cauchy problem defined on the real line, we first construct the discrete Cauchy problem on a uniform grid of the real line. Thus the semi-discretization in space of the continuous problem gives rise to an infinite system of ordinary differential equations in time. We show that the initial-value problem for this system is well-posed. We prove that solutions of the discrete problem converge uniformly to those of the continuous one as the mesh size goes to zero and that they are second-order convergent in space. We then consider a truncation of the infinite domain to a finite one. We prove that the solution of the truncated problem approximates the solution of the continuous problem when the truncated domain is sufficiently large. Finally, we present some numerical experiments that confirm numerically both the expected convergence rate of the semi-discrete scheme and the ability of the method to capture finite-time blow-up of solutions for various convolution kernels.

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Lamba, Harbir, Pavel Krejčí, and Dmitrii Rachinskii. "The global stability of a class of history-dependent macroeconomic models." Mathematical Modelling of Natural Phenomena 15 (2020): 49. http://dx.doi.org/10.1051/mmnp/2019061.

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We consider piecewise-linear, discrete-time, macroeconomic models that have a continuum of feasible equilibrium states. The non-trivial equilibrium set and resulting path-dependence are induced by stickiness in either expectations or the response of the Central Bank. For a low-dimensional variant of the model with one representative agent, and also for a multi-agent model, we show that when exogenous noise is absent from the system the continuum of equilibrium states is the global attractor and each solution trajectory converges exponentially to one of the equilibria. Further, when a uniformly bounded noise is present, or the equilibrium states are destabilized by an imperfect Central Bank policy (or both), we estimate the size of the domain that attracts all the trajectories. The proofs are based on introducing a family of Lyapunov functions and, for the multi-agent model, deriving a formula for the inverse of the Prandtl-Ishlinskii operator acting in the space of discrete-time inputs and outputs.

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WU, HAI-SHAN, ANDREW J. EINSTEIN, LIANE DELIGDISCH, TAMARA KALIR, and JOAN GIL. "CHARACTERIZATION OF NUCLEAR IMAGES BASED ON ANALYSIS OF FRACTIONAL SUMMATION SYSTEMS." Fractals 12, no. 02 (June 2004): 157–69. http://dx.doi.org/10.1142/s0218348x04002483.

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While frequency-based methods for the characterization of fractals are popular and effective in many applications, they have limitations when applied to irregularly shaped images, such as nuclear images. The irregularity renders texture characterization by frequency domain methods, based upon Fourier transform, problematic. To address this situation, this paper presents an algorithm based upon the signal analysis in the spatial domain. An autocovariance function can be estimated regardless of the shape and size of regions where the image is defined. As in the continuous fractional Brownian motion (FBM) that results from inputting white noise into a specific fractional integral system, a discrete FBM can be related to white noise by a specific fractional summation system (FSS) that is linear, causal and shift-invariant. Although the method of direct sampling is not valid for converting a continuous fractional integral to a discrete fractional summation, discrete fractional summations similar to the sampled system functions can be obtained through an iterative process. While the continuous system function of a fractional integral is linear in the frequency domain when plotted in log-log scales, unfortunately, it is not true for the comparable discrete system function. The discrete system function is actually approximately linear in the log-log scales over a very limited range. The slope of the straight line that approximates the function curve in the mean-square-error (MSE) sense in a specific time range provides a description of the autocovariance function that reveals the statistical relations among the local textures. Applications to characterization of ovary nuclear images in groups of normal, atypical and cancer cases are studied and presented.

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POP, IULIU SORIN, and BEN SCHWEIZER. "REGULARIZATION SCHEMES FOR DEGENERATE RICHARDS EQUATIONS AND OUTFLOW CONDITIONS." Mathematical Models and Methods in Applied Sciences 21, no. 08 (August 2011): 1685–712. http://dx.doi.org/10.1142/s0218202511005532.

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We analyze regularization schemes for the Richards equation and a time discrete numerical approximation. The original equations can be doubly degenerate, therefore they may exhibit fast and slow diffusion. In addition, we treat outflow conditions that model an interface separating the porous medium from a free flow domain. In both situations we provide a regularization with a non-degenerate equation and standard boundary conditions, and discuss the convergence rates of the approximations.

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D'AMICO, MARÍA BELÉN, JORGE L. MOIOLA, and EDUARDO E. PAOLINI. "STUDY OF DEGENERATE BIFURCATIONS IN MAPS: A FEEDBACK SYSTEMS APPROACH." International Journal of Bifurcation and Chaos 14, no. 05 (May 2004): 1625–41. http://dx.doi.org/10.1142/s0218127404010266.

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The dynamical behavior of nonlinear maps undergoing degenerate period doubling or degenerate Hopf bifurcations is studied via a frequency-domain approach. The technique is based on a discrete-time feedback representation of the system and the application of the well-known engineering tools of harmonic balance to approximate the emerging solutions. More specifically, the results are a higher-order extension of the previous developments obtained by the authors for nondegenerate bifurcations. Two examples are included for illustration.

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DRANGA, OCTAVIAN, CHI K. TSE, HERBERT H. C. IU, and ISTVÁN NAGY. "BIFURCATION BEHAVIOR OF A POWER-FACTOR-CORRECTION BOOST CONVERTER." International Journal of Bifurcation and Chaos 13, no. 10 (October 2003): 3107–14. http://dx.doi.org/10.1142/s0218127403008478.

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The aim of the paper is to investigate the bifurcation behavior of the power-factor-correction (PFC) boost converter under a conventional peak current-mode control. The converter is operated in continuous-conduction mode. The bifurcation analysis performed by computer simulations reveals interesting effects of variation of some chosen parameters on the stability of the converter. The results are illustrated by time-domain waveforms, discrete-time maps and parameter plots. An analytical investigation confirms the results obtained by computer simulations. Such an analysis allows convenient prediction of stability boundaries and facilitates the selection of parameter values to guarantee stable operation.

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Norton, J. P. "Translation of bounds on time-domain behaviour of dynamical systems into parameter bounds for discrete-time rational transfer-function models." Mathematics and Computers in Simulation 48, no. 4-6 (June 1999): 469–78. http://dx.doi.org/10.1016/s0378-4754(99)00026-9.

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Wang, Y., J. Grimaldi, L. Landier, E. Chavanon, and J. P. Gastellu-Etchegorry. "INTRODUCTION OF CLOUDS IN DART MODEL." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLIII-B3-2020 (August 21, 2020): 843–48. http://dx.doi.org/10.5194/isprs-archives-xliii-b3-2020-843-2020.

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Abstract. Clouds cover around two thirds of the Earth’s surface. Most of them are thick enough to influence the radiative budget of our planet: they increase the top of atmosphere (TOA) exitance and they alter the bottom of atmosphere (BOA) direct and diffuse irradiance. However, most radiative transfer models dedicated to Earth surfaces, such as DART (Discrete Anisotropic Radiative Transfer), simulate only cloudless atmospheres. We recently introduced clouds in DART in order to improve the modelling of weather for remote sensing simulations. In this implementation, clouds were characterized with user specified optical properties and vertical distribution. They were modelled as layered one-dimensional medium that coexists with gases and aerosols. The atmospheric radiative transfer modelling relies on the discrete ordinate method already in DART. In addition, an iterative inversion procedure was designed to test this improvement with field measurements during two cloudy days at Lamasquère meteorological station (France). Specifically, it derives time-series of atmosphere parameters from time-series of BOA solar irradiance measurements. These inversed atmospheric parameters were used to simulate total and diffuse BOA irradiance in PAR (Photosynthetically Active Radiation) domain. The comparison of time-series of measured and DART simulated PAR irradiance lead to very encouraging results (mean relative error ∼8% for total irradiance and ∼20% for diffuse irradiance). It stresses the potential of DART to accurately simulate irradiance in cloudy days.

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Goldstein, Rhys, Azam Khan, Olivier Dalle, and Gabriel Wainer. "Multiscale representation of simulated time." SIMULATION 94, no. 6 (September 28, 2017): 519–58. http://dx.doi.org/10.1177/0037549717726868.

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To better support multiscale modeling and simulation, we present a multiscale time representation consisting of data types, data structures, and algorithms that collectively support the recording of past events and scheduling of future events in a discrete event simulation. Our approach addresses the drawbacks of conventional time representations: limited range in the case of 32- or 64-bit fixed-point time values; problematic rounding errors in the case of floating-point numbers; and the lack of a universally acceptable precision level in the case of brute force approaches. The proposed representation provides both extensive range and fine resolution in the timing of events, yet it stores and manipulates the majority of event times as standard 64-bit numbers. When adopted for simulation purposes, the representation allows a domain expert to choose a precision level for his/her model. This time precision is honored by the simulator even when the model is integrated with other models of vastly different time scales. Making use of C++11 programming language features and the Discrete Event System Specification formalism, we implemented a simulator to test the time representation and inform a discussion on its implications for collaborative multiscale modeling efforts.

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Yan, Yan, Bingqian Wang, Quan Z. Sheng, Adnan Mahmood, Tao Feng, and Pengshou Xie. "Modelling the Publishing Process of Big Location Data Using Deep Learning Prediction Methods." Electronics 9, no. 3 (March 1, 2020): 420. http://dx.doi.org/10.3390/electronics9030420.

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Centralized publishing of big location data can provide accurate and timely information to assist in traffic management and for facilitating people to decide travel time and route, mitigate traffic congestion, and reduce unnecessary waste. However, the spatio-temporal correlation, non-linearity, randomness, and uncertainty of big location data make it impossible to decide an optimal data publishing instance through traditional methods. This paper, accordingly, proposes a publishing interval predicting method for centralized publication of big location data based on the promising paradigm of deep learning. First, the adaptive adjusted sampling method is designed to address the challenge of finding a reasonable release time via a prediction mechanism. Second, the Maximal Overlap Discrete Wavelet Transform (MODWT) is introduced for the decomposition of time series in order to separate different features of big location data. Finally, different deep learning models are selected to construct the entire framework according to various time-domain features. Experimental analysis suggests that the proposed prediction scheme is not only feasible, but also improves the prediction accuracy in contrast to the traditional deep learning mechanisms.

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Burman, Erik, Jonathan Ish-Horowicz, and Lauri Oksanen. "Fully discrete finite element data assimilation method for the heat equation." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 5 (September 2018): 2065–82. http://dx.doi.org/10.1051/m2an/2018030.

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We consider a finite element discretization for the reconstruction of the final state of the heat equation, when the initial data is unknown, but additional data is given in a sub domain in the space time. For the discretization in space we consider standard continuous affine finite element approximation, and the time derivative is discretized using a backward differentiation. We regularize the discrete system by adding a penalty on the H2-semi-norm of the initial data, scaled with the mesh-parameter. The analysis of the method uses techniques developed in E. Burman and L. Oksanen [Numer. Math. 139 (2018) 505–528], combining discrete stability of the numerical method with sharp Carleman estimates for the physical problem, to derive optimal error estimates for the approximate solution. For the natural space time energy norm, away from t = 0, the convergence is the same as for the classical problem with known initial data, but contrary to the classical case, we do not obtain faster convergence for the L2-norm at the final time.

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El Bhih, Amine, Youssef Benfatah, Soukaina Ben Rhila, Mostafa Rachik, and Adil El Alami Laaroussi. "A Spatiotemporal Prey-Predator Discrete Model and Optimal Controls for Environmental Sustainability in the Multifishing Areas of Morocco." Discrete Dynamics in Nature and Society 2020 (April 23, 2020): 1–18. http://dx.doi.org/10.1155/2020/2780651.

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In this work, we propose a multifishing area prey-predator discrete-time model which describes the interaction between the prey and middle and top predators in various areas, which are connected by their movements to their neighbors, to provide realistic description prey effects of two predators. A grid of colored cells is presented to illustrate the entire domain; each cell may represent a subdomain or area. Next, we propose two harvesting control strategies that focus on maximizing the biomass of prey, in the targeted area, and minimizing the biomass of middle and top predators coming from the neighborhood of this targeted area to ensure sustainability and maintain a differential chain system. Theoretically, we have proved the existence of optimal controls, and we have given a characterization of controls in terms of states and adjoint functions based on a discrete version of Pontryagin’s maximum principle. To illustrate the theoretical results obtained, we propose numerical simulations for several scenarios applying the forward-backward sweep method (FBSM) to solve our optimality system in an iterative process.

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Teixeira, Rafael Luís, Francisco Paulo Lépore Neto, and José Francisco Ribeiro. "Modelling and Experimental Investigation of an Active Damper." Shock and Vibration 13, no. 4-5 (2006): 343–54. http://dx.doi.org/10.1155/2006/486719.

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This paper presents a validation methodology of the dynamic behavior of an active viscous damper. The damper has two flexible metallic bellows connected to a rigid reservoir filled with fluid. When one of the bellows is connected to a vibrating structure a periodic flow passes through a variable internal orifice and the damping effect is produced. The size of the orifice is adjusted by a controlled linear piezoelectric actuator that positions the conical core into a conical cavity. The device finite element structural model consists of the valve body and its conical core that are assumed rigid and the flexible bellows are represented by two pistons with elastic suspensions. The flow developed inside the damper is modeled considering the fluid-structure interation, using the Lagrangean-Eulerian formulation. To validate the proposed model a prototype was constructed and experimental tests and numerical simulations are accomplished in the time domain, applying harmonic excitations. The results are compared using curves that relate the damping coefficient with the orifice size and with the input velocity applied at the bellows face. However, for the proper control design and system operation, the direct use of the finite element model becomes unviable due to its high computational time. Then, a reduced second order discrete dynamic model for the damper was developed. The model parameters are identified by analysis in the frequency domain, using impulsive excitation force, for constant and variable orifice sizes. At low excitation frequencies, the damper prototype behaves like a single degree of freedom system which damping factor changes with the orifice size A fuzzy controller was designed and it generates the orifice reference size associated to the desired damping factor. The active system presented better performance when compared to the passive one.

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Hara, Shinji, Toni Bakhtiar, and Masaaki Kanno. "The Best Achievableℋ2Tracking Performances for SIMO Feedback Control Systems." Journal of Control Science and Engineering 2007 (2007): 1–12. http://dx.doi.org/10.1155/2007/93904.

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This paper is concerned with the inherentℋ2tracking performance limitation of single-input and multiple-output (SIMO) linear time-invariant (LTI) feedback control systems. The performance is measured by the tracking error between a step reference input and the plant output with additional penalty on control input. We employ the plant augmentation strategy, which enables us to derive analytical closed-form expressions of the best achievable performance not only for discrete-time system, but also for continuous-time system by exploiting the delta domain version of the expressions.

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Hiltebrand, Andreas, Siddhartha Mishra, and Carlos Parés. "Entropy-stable space–time DG schemes for non-conservative hyperbolic systems." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 3 (May 2018): 995–1022. http://dx.doi.org/10.1051/m2an/2017056.

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We propose a space–time discontinuous Galerkin (DG) method to approximate multi-dimensional non-conservative hyperbolic systems. The scheme is based on a particular choice of interface fluctuations. The key difference with existing space–time DG methods lies in the fact that our scheme is formulated in entropy variables, allowing us to prove entropy stability for the method. Additional numerical stabilization in the form of streamline diffusion and shock-capturing terms are added. The resulting method is entropy stable, arbitrary high-order accurate, fully discrete, and able to handle complex domain geometries discretized with unstructured grids. We illustrate the method with representative numerical examples.

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Wu, Yuexiu, Quansheng Liu, Andrew H. C. Chan, and Hongyuan Liu. "Implementation of a Time-Domain Random-Walk Method into a Discrete Element Method to Simulate Nuclide Transport in Fractured Rock Masses." Geofluids 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/5940380.

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It is essential to study nuclide transport with underground water in fractured rock masses in order to evaluate potential radionuclide leakage in nuclear waste disposal. A time-domain random-walk (TDRW) method was firstly implemented into a discrete element method (DEM), that is, UDEC, in this paper to address the pressing challenges of modelling the nuclide transport in fractured rock masses such as massive fractures and coupled hydromechanical effect. The implementation was then validated against analytical solutions for nuclide transport in a single fracture and a simple fracture network. After that, the proposed implementation was applied to model the nuclide transport in a complex fracture network investigated in the DECOVALEX 2011 project to analyze the effect of matrix diffusion and stress on the nuclide transport in the fractured rock masses. It was concluded that the implementation of the TDRW method into UDEC provided a valuable tool to study the nuclide transport in the fractured rock masses. Moreover, it was found that the total travel time of the nuclide particles in the fractured rock masses with the matrix diffusion and external stress modelled was much longer than that without the matrix diffusion and external stress modelled.

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Sharma, Anuj, Wolfgang Mueller-Hirsch, Sven Herold, and Tobias Melz. "Localized Discrete Modelling of Contact Interfaces to Predict the Dynamic Behaviour of Assembled Structures under Random Excitation." Applied Mechanics and Materials 807 (November 2015): 13–22. http://dx.doi.org/10.4028/www.scientific.net/amm.807.13.

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Joints used to fasten different parts are the source of local non-linearity with predominance of contact damping in comparison to inherent material damping. The conventional numerical models can predict the dynamic behaviour to a good accuracy, but their implementation for the large system under real time dynamic excitations - like random vibration are encountered with problems of numerical convergence and high computational cost. This paper proposes an approach to model the contact interfaces using discrete elements, with a non-homogeneous definition for the equivalent contact stiffness and damping over the contact interface. The non-homogeneous definition captures the non-linear effects and the local linearisation provides the capability to perform the frequency domain analysis for non-deterministic excitations. The proposed model is validated with experimental results for a test structure excited with random white noise base excitation.

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BARUCQ, HÉLÈNE, JULIEN DIAZ, and VÉRONIQUE DUPRAT. "LONG-TERM STABILITY ANALYSIS OF ACOUSTIC ABSORBING BOUNDARY CONDITIONS." Mathematical Models and Methods in Applied Sciences 23, no. 11 (July 23, 2013): 2129–54. http://dx.doi.org/10.1142/s0218202513500280.

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This work deals with the stability analysis of a one-parameter family of Absorbing Boundary Conditions (ABC) that have been derived for the acoustic wave equation. We tackle the problem of long-term stability of the wave field both at the continuous and the numerical levels. We first define a function of energy and show that it is decreasing in time. Its discrete form is also decreasing under a Courant–Friedrichs–Lewy (CFL) condition that does not depend on the ABC. Moreover, the decay rate of the continuous energy can be determined: it is exponential if the computational domain is star-shaped and this property can be illustrated numerically.

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Garibaldi, L., E. Giorcelli, and B. A. D. Piombo. "ARMAV Techniques for Traffic Excited Bridges." Journal of Vibration and Acoustics 120, no. 3 (July 1, 1998): 713–18. http://dx.doi.org/10.1115/1.2893888.

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In this paper ARMAV (Auto Regressive Moving Average Vector) models are used for system identification and modal analysis purposes. This time domain technique allows to estimate a discrete time system response function without performing any domain change (i.e. it doesn’t use FFT and IFFT to evaluate the model parameters) and without applying any time window (also when sampled data are non periodic): this leads to well-estimated system parameters, also for short data records. These models are useful to perform system identification for multiple input-output cases also when the excitation is just statistically known. The present analysis is dedicated to a scaled bridge, designed according to the theory of models, whose static and dynamic characteristics are compatible to those of real bridges. The aim of the tests is to collect a series of supervised measurements in a controlled environment, with statistically defined traffic conditions; the comparison of the model results with those acquired on the real bridge is the compulsory step towards a correct modelling of bridges for their identification and monitoring. The paper reports encouraging results obtained with experimental simulations on the model.

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DUTTA, DEBASHREE, S. N. GANGULY, P. BARAT, P. MUKHERJEE, S. K. BANDYOPADHYAY, and PINTU SEN. "FRACTAL CHARACTERIZATION OF ULTRASONIC SIGNALS FROM POLYCRYSTALLINE MATERIALS." Fractals 03, no. 01 (March 1995): 1–8. http://dx.doi.org/10.1142/s0218348x95000023.

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For the first time the concept of fractal geometry is introduced to characterize discrete time domain ultrasonic signals scattered from polycrystalline materials aluminium and brass using the pulse echo method. The fractal dimension of these scattered signals was evaluated using the box counting method and power spectral method. These signals possess unique fractal dimension which remains invariant with the change in sampling rate of signal capturing. The fractal dimension evaluated by the above two methods remains constant in case of aluminium but gives remarkably different values for brass. This observation is interpreted on the basis of the variation of scattering mechanism in these two materials.

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Balázsová, Monika, Miloslav Feistauer, and Miloslav Vlasák. "Stability of the ale space-time discontinuous Galerkin method for nonlinear convection-diffusion problems in time-dependent domains." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 6 (November 2018): 2327–56. http://dx.doi.org/10.1051/m2an/2018062.

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The paper is concerned with the analysis of the space-time discontinuous Galerkin method (STDGM) applied to the numerical solution of nonstationary nonlinear convection-diffusion initial- boundary value problem in a time-dependent domain. The problem is reformulated using the arbitrary Lagrangian-Eulerian (ALE) method, which replaces the classical partial time derivative by the so-called ALE derivative and an additional convective term. The problem is discretized with the use of the ALE- space time discontinuous Galerkin method (ALE-STDGM). In the formulation of the numerical scheme we use the nonsymmetric, symmetric and incomplete versions of the space discretization of diffusion terms and interior and boundary penalty. The nonlinear convection terms are discretized with the aid of a numerical flux. The main attention is paid to the proof of the unconditional stability of the method. An important step is the generalization of a discrete characteristic function associated with the approximate solution and the derivation of its properties.

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Swarnakar, Jaydeep, Prasanta Sarkar, and Lairenlakpam Joyprakash Singh. "A unified direct approach for discretizing fractional-order differentiator in delta-domain." International Journal of Modeling, Simulation, and Scientific Computing 09, no. 06 (December 2018): 1850055. http://dx.doi.org/10.1142/s1793962318500551.

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Fractional-order differentiator is a principal component of the fractional-order controller. Discretization of fractional-order differentiator is essential to implement the fractional-order controller digitally. Discretization methods generally include indirect approach and direct approach to find the discrete-time approximation of fractional-order differentiator in the [Formula: see text]-domain as evident from the existing literature. In this paper, a direct approach is proposed for discretization of fractional-order differentiator in delta-domain instead of the conventional [Formula: see text]-domain as the delta operator unifies both analog system and digital system together at a high sampling frequency. The discretization of fractional-order differentiator is accomplished in two stages. In the first stage, the generating function is framed by reformulating delta operator using trapezoidal rule or Tustin approximation and in the next stage, the fractional-order differentiator has been approximated by expanding the generating function using continued fraction expansion method. The proposed method has been compared with two well-known direct discretization methods taken from the existing literature. Two examples are presented in this context to show the efficacy of the proposed discretization method using simulation results obtained from MATLAB.

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Farooq, Umar, Abubakr Taha Bakheit Taha, Fuchang Tian, Ximin Yuan, Muhammad Ajmal, Irfan Ullah, and Mahmood Ahmad. "Flood Modelling and Risk Analysis of Cinan Feizuo Flood Protection Area, Huaihe River Basin." Atmosphere 14, no. 4 (April 3, 2023): 678. http://dx.doi.org/10.3390/atmos14040678.

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This study evaluated multiple aspects of flood risks and effects on the Cinan Feizuo flood protection area in the Huaihe River basin. Flooding remains a leading problem for infrastructure, especially in urban, residential areas of the region. Effective flood modeling for urbanized floodplains is challenging, but MIKE (ID-2D) is paramount for analyzing and quantifying the risk in the vulnerable region. The Saint-Venant equation and a one-dimensional (1D) MIKE 11 model were used to understand the flood dynamics in the Huaihe River, and a two-dimensional (2D) MIKE 21 model was applied to assess the risk in the Cinan Feizuo flood protection area. The finite volume method (FVM) was used for discrete grid problems, and the models were coupled through the weir equation to find the flow volume from the 1D domain to the 2D domain to investigate water level changes. Flood inundation maps were generated for the flood protection area. The maximum discharge, velocity, and submerged depth for 50- and 100-year flood events were assessed with flood risk. Chenbei indicated a high flood risk level in 50 to 100 years in which the water level exceeds a high level and inundates the maximum area with minimum time. Conversely, the 100-year flood inundation in the flood protection area was comparatively higher than the 50-year flood, with a lower time step. The risk analysis identified significant damage caused by the flood over the target regions. The findings of this study provide technical support for flood risk analysis and loss assessment within the flood protection area and have important reference values for regional flood control, disaster reduction decision making, and constructive planning.

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Bergamaschi, Peter, Arjo Segers, Dominik Brunner, Jean-Matthieu Haussaire, Stephan Henne, Michel Ramonet, Tim Arnold, et al. "High-resolution inverse modelling of European CH₄ emissions using the novel FLEXPART-COSMO TM5 4DVAR inverse modelling system." Atmospheric Chemistry and Physics 22, no. 20 (October 17, 2022): 13243–68. http://dx.doi.org/10.5194/acp-22-13243-2022.

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Abstract. We present a novel high-resolution inverse modelling system (“FLEXVAR”) based on FLEXPART-COSMO back trajectories driven by COSMO meteorological fields at 7 km×7 km resolution over the European COSMO-7 domain and the four-dimensional variational (4DVAR) data assimilation technique. FLEXVAR is coupled offline with the global inverse modelling system TM5-4DVAR to provide background mole fractions (“baselines”) consistent with the global observations assimilated in TM5-4DVAR. We have applied the FLEXVAR system for the inverse modelling of European CH4 emissions in 2018 using 24 stations with in situ measurements, complemented with data from five stations with discrete air sampling (and additional stations outside the European COSMO-7 domain used for the global TM5-4DVAR inversions). The sensitivity of the FLEXVAR inversions to different approaches to calculate the baselines, different parameterizations of the model representation error, different settings of the prior error covariance parameters, different prior inventories, and different observation data sets are investigated in detail. Furthermore, the FLEXVAR inversions are compared to inversions with the FLEXPART extended Kalman filter (“FLExKF”) system and with TM5-4DVAR inversions at 1∘×1∘ resolution over Europe. The three inverse modelling systems show overall good consistency of the major spatial patterns of the derived inversion increments and in general only relatively small differences in the derived annual total emissions of larger country regions. At the same time, the FLEXVAR inversions at 7 km×7 km resolution allow the observations to be better reproduced than the TM5-4DVAR simulations at 1∘×1∘. The three inverse models derive higher annual total CH4 emissions in 2018 for Germany, France, and BENELUX compared to the sum of anthropogenic emissions reported to UNFCCC and natural emissions estimated from the Global Carbon Project CH4 inventory, but the uncertainty ranges of top-down and bottom-up total emission estimates overlap for all three country regions. In contrast, the top-down estimates for the sum of emissions from the UK and Ireland agree relatively well with the total of anthropogenic and natural bottom-up inventories.

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BILOTTA, ELEONORA, and PIETRO PANTANO. "DISCRETE CHAOTIC DYNAMICS FROM CHUA'S OSCILLATOR: CHUA MACHINES." International Journal of Bifurcation and Chaos 19, no. 01 (January 2009): 1–115. http://dx.doi.org/10.1142/s0218127409022774.

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In previous work, the authors explored the parameter space for Chua's circuit and its generalizations, discovering new routes to chaos, and nearly a thousand new attractors. These were obtained by varying the parameters of the physical circuit and of systems derived from it. Here, we present a novel class of computational system that does not respect the classical constraints in Chua's circuit, and that generates chaotic dynamics via an iterative process based on discrete versions of the equations for Chua's circuit and its variants. We call these systems Chua Machines. After presenting the chaotic dynamics, we provide a formal description of Chua Machines and a Gallery of 222 3D images, illustrating their dynamics. We discuss the method used to discover these systems and the metrics applied in the exploration of their parameter space and offer examples of highly complex bifurcation maps, together with images showing how patterns can evolve with time, or vary significantly changing the values of one of the parameters. Finally, we present a detailed analysis of qualitative changes in a Chua Machine as it traverses the parameter space of the bifurcation map. The evidence suggests that these dynamics are even richer and more complex than their counterpart in the continuous domain.

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Lozia, Zbigniew. "Application of Modelling and Simulation in Durability Tests of Vehicles and Their Components." Energies 15, no. 24 (December 12, 2022): 9398. http://dx.doi.org/10.3390/en15249398.

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The use of simulation and modelling has been proposed for determining the excitations to be applied in the procedures of laboratory testing of a car’s structural components, without the need to test the complete vehicle. The paper presents the general concept as well as an example of the procedure. It covers determining the spectrum and time-domain realization of a load on a selected node of the vehicle structure under durability tests. The author used both the mathematical and physical model of the tractor-semitrailer unit, where the input was considered as a random process resulting from the road profile. He calculated the transmittance modules and the power spectral densities of the vertical force on the joint between the tractor’s fifth wheel and the kingpin of the semitrailer and the extreme values of the dynamic components of this force. The inverse discrete Fourier transform makes it possible to generate the realization of the said force. It can be used in durability studies. The limitation of the work to the testing of a specific structural node reduces the scope and, in consequence, the cost of the process. The method presented may also be used for various types of vehicle models, including hybrid and electric vehicles.

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ELSCHNER, JOHANNES, and GUANGHUI HU. "SCATTERING OF PLANE ELASTIC WAVES BY THREE-DIMENSIONAL DIFFRACTION GRATINGS." Mathematical Models and Methods in Applied Sciences 22, no. 04 (April 2012): 1150019. http://dx.doi.org/10.1142/s0218202511500199.

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The reflection and transmission of a time-harmonic plane wave in an isotropic elastic medium by a three-dimensional diffraction grating is investigated. If the diffractive structure involves an impenetrable surface, we study the first, second, third and fourth kind boundary value problems for the Navier equation in an unbounded domain by the variational approach. A radiation condition based on the Rayleigh expansion of the quasi-periodic solutions is presented. Existence of solutions in Sobolev spaces is established if the grating profile is a two-dimensional Lipschitz surface, while uniqueness is proved only for small frequencies or for all frequencies excluding a discrete set. Similar solvability results are obtained for multilayered transmission gratings in the case of an incident pressure wave. Moreover, by a periodic Rellich identity, uniqueness of the solution to the first kind (Dirichlet) boundary value problem is established for all frequencies under the assumption that the impenetrable surface is given by the graph of a Lipschitz function.

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Artina, Marco, Filippo Cagnetti, Massimo Fornasier, and Francesco Solombrino. "Linearly constrained evolutions of critical points and an application to cohesive fractures." Mathematical Models and Methods in Applied Sciences 27, no. 02 (February 2017): 231–90. http://dx.doi.org/10.1142/s0218202517500014.

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We introduce a novel constructive approach to define time evolution of critical points of an energy functional. Our procedure, which is different from other more established approaches based on viscosity approximations in infinite-dimension, is prone to efficient and consistent numerical implementations, and allows for an existence proof under very general assumptions. We consider in particular rather nonsmooth and nonconvex energy functionals, provided the domain of the energy is finite-dimensional. Nevertheless, in the infinite-dimensional case study of a cohesive fracture model, we prove a consistency theorem of a discrete-to-continuum limit. We show that a quasistatic evolution can be indeed recovered as a limit of evolutions of critical points of finite-dimensional discretizations of the energy, constructed according to our scheme. To illustrate the results, we provide several numerical experiments both in one- and two-dimensions. These agree with the crack initiation criterion, which states that a fracture appears only when the stress overcomes a certain threshold, depending on the material.

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Field, Timothy R., and Robert J. A. Tough. "Coupled dynamics of populations supported by discrete sites and their continuum limit." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2121 (April 29, 2010): 2561–86. http://dx.doi.org/10.1098/rspa.2010.0049.

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The illumination of single population behaviour subject to the processes of birth, death and immigration has provided a basis for the discussion of the non-Gaussian statistical and temporal correlation properties of scattered radiation. As a first step towards the modelling of its spatial correlations, we consider the populations supported by an infinite chain of discrete sites, each subject to birth, death and immigration and coupled by migration between adjacent sites. To provide some motivation, and illustrate the techniques we will use, the migration process for a single particle on an infinite chain of sites is introduced and its diffusion dynamics derived. A certain continuum limit is identified and its properties studied via asymptotic analysis. This forms the basis of the multi-particle model of a coupled population subject to single site birth, death and immigration processes, in addition to inter-site migration. A discrete rate equation is formulated and its generating function dynamics derived. This facilitates derivation of the equations of motion for the first- and second-order cumulants, thus generalizing the earlier results of Bailey through the incorporation of immigration at each site. We present a novel matrix formalism operating in the time domain that enables solution of these equations yielding the mean occupancy and inter-site variances in the closed form. The results for the first two moments at a single time are used to derive expressions for the asymptotic time-delayed correlation functions, which relates to Glauber’s analysis of an Ising model. The paper concludes with an analysis of the continuum limit of the birth–death–immigration–migration process in terms of a path integral formalism. The continuum rate equation and evolution equation for the generating function are developed, from which the evolution equation of the mean occupancy is derived, in this limit. Its solution is provided in closed form.

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Huang, Xin, Yazhou Chen, and Yuming Wang. "Simulation of Interference Effects of UWB Pulse Signal to the GPS Receiver." Discrete Dynamics in Nature and Society 2021 (July 17, 2021): 1–8. http://dx.doi.org/10.1155/2021/9935543.

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Ultra-wideband (UWB) pulse signal has an extremely narrow pulse width and wide frequency bandwidth, which overlaps with the operating frequency band of Global Position System (GPS) receivers, posing a potential threat to their performance. In response to this problem, through mathematical analysis and software simulation, the effects of UWB pulse signal under time-hopping-pulse position modulation (TH-PPM) on the performance of GPS receivers were studied. First, the expression and waveform of the UWB pulse signal were analyzed in the time-frequency domain, and it is concluded that the pulse repetition frequency (PRF) mainly affects the discrete spectrum of the UWB signal and the TH code period mainly affects the continuous spectrum. On this basis, the simulation on the power spectral density (PSD) of GPS signal and UWB signal under different pulse parameters was represented, from which a conclusion can be drawn that the PRF is the main factor impacting the PSD of the GPS signal. Furthermore, this paper analyzed the degradation of GPS receiver equivalent carrier-to-noise ratio (C/N0) and C/A code demodulation bit error rate (BER) under UWB interference, which are the crucial evaluating indicators of GPS signal quality. Eventually, we theoretically calculated the minimum interference level of the UWB interference signal to the GPS receiver, providing a theoretical reference for reducing the interference effects of UWB pulse signal on the performance of GPS receivers.

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Krause, Andrew L., Dmitry Beliaev, Robert A. Van Gorder, and Sarah L. Waters. "Bifurcations and Dynamics Emergent From Lattice and Continuum Models of Bioactive Porous Media." International Journal of Bifurcation and Chaos 28, no. 11 (October 2018): 1830037. http://dx.doi.org/10.1142/s0218127418300379.

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We study the dynamics emergent from a two-dimensional reaction–diffusion process modeled via a finite lattice dynamical system, as well as an analogous PDE system, involving spatially nonlocal interactions. These models govern the evolution of cells in a bioactive porous medium, with the evolution of the local cell density depending on a coupled quasi-static fluid flow problem. We demonstrate differences emergent from the choice of a discrete lattice or a continuum for the spatial domain of such a process. We find long-time oscillations and steady states in cell density in both lattice and continuum models, but that the continuum model only exhibits solutions with vertical symmetry, independent of initial data, whereas the finite lattice admits asymmetric oscillations and steady states arising from symmetry-breaking bifurcations. We conjecture that it is the structure of the finite lattice which allows for more complicated asymmetric dynamics. Our analysis suggests that the origin of both types of oscillations is a nonlocal reaction–diffusion mechanism mediated by quasi-static fluid flow.

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Kumar, Anshuman, Chandramani Upadhyay, and Vivekananda Kukkala. "Study of Surface Characterization and Parametric Optimization during Wire Electric Discharge Machining for Inconel 625." Materials Science Forum 978 (February 2020): 97–105. http://dx.doi.org/10.4028/www.scientific.net/msf.978.97.

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This presented article focuses on surface characterization and assessing the satisfactory machining condition of WEDMed Inconel 625. This work material has been received remarkable attention to the industrial and academic organization for its end use applications. WEDM is well-known machining process for intricate shape cutting and machining hard materials. The experimental design was planned according to L27 orthogonal array (OA), by varying controllable process parameter (i.e. Wire-Tension, Wire-speed, Flushing-Pressure, Discharge-Current and Spark-on Time), each parameter varied at four discrete levels, within the selected parametric domain. WEDMed surfaces have been investigated with a focus to the surface characterization of selected machined surface through captured images from scanning electron microscope (SEM). Eventually, multi-response optimization of process parameters was sought by using a combination of nonlinear regression modelling, fuzzy inference system (FIS) with Teaching Learning-Based Optimization (TLBO) algorithm. The obtained TLBO result was compared with the Genetic algorithm (GA). The results show that optimization algorithms are effective tools for getting satisfactory optimal machining conditions during WEDM process of Inconel 625.

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Journal articles on the topic 'Discrete-time domain modelling'

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