Artykuły w czasopismach: „Discrete Kinetic System”

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SCHIAVO, M. LO. "DISCRETE KINETIC CELLULAR MODELS OF TUMORS IMMUNE SYSTEM INTERACTIONS". Mathematical Models and Methods in Applied Sciences 06, nr 08 (grudzień 1996): 1187–209. http://dx.doi.org/10.1142/s021820259600050x.

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This paper deals with a kinetic modelling of the cellular dynamics of tumors interacting with an active immune defence system. The analysis starts from the model proposed in Refs. 4 and 5 where a kinetic (cellular) theory of the interactions and competition between tumor cells and immune system is developed in a framework similar to the one of nonlinear statistical mechanics. The class of models proposed in this paper replaces the system of integro-differential equations by a system of ordinary differential equations. This has several advantages. Firstly, it allows immediate interpretations of the control parameters and is characterized by a relatively lower computational complexity. Further, some interesting periodicity properties of the solutions are characterized.

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Papastavridis, J. G. "On the Boltzmann-Hamel Equations of Motion: A Vectorial Treatment". Journal of Applied Mechanics 61, nr 2 (1.06.1994): 453–59. http://dx.doi.org/10.1115/1.2901466.

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This paper presents a direct vectorial derivation of the famous Boltzmann-Hamel equations of motion of discrete mechanical systems, in general nonlinear nonholonomic coordinates and under general nonlinear (velocity) nonholonomic constraints. The connection between particle and system vectors is stressed throughout, in all relevant kinematic and kinetic quantities/principles/theorems. The specialization of these results to the common case of linear nonholonomic coordinates and linear nonholonomic (i.e., Pfaffian) constraints is carried out in the paper’s Appendix.

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STEFANOU, IOANNIS, i JEAN SULEM. "THREE-DIMENSIONAL COSSERAT CONTINUUM MODELING OF FRACTURED ROCK MASSES". Journal of Multiscale Modelling 02, nr 03n04 (wrzesień 2010): 217–34. http://dx.doi.org/10.1142/s1756973710000424.

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The behavior of rock masses is influenced by the existence of discontinuities, which divide the rock in joint blocks making it an inhomogeneous anisotropic material. From the mechanical point of view, the geometrical and mechanical properties of the rock discontinuities define the mechanical properties of the rock structure. In the present paper we consider a rock mass with three joint sets of different dip angle, dip direction, spacing and mechanical properties. The dynamic behavior of the discrete system is then described by a continuum model, which is derived by homogenization. The homogenization technique applied here is called generalized differential expansion homogenization technique and has its roots in Germain's (1973) formulation for micromorphic continua. The main advantage of the method is the avoidance of the averaging of the kinematic quotients and the derivation of a continuum that maps exactly the degrees of freedom of the discrete system through a one-to-one correspondence of the kinematic measures. The derivation of the equivalent continuum is based on the identification for any virtual kinematic field of the power of the internal forces and of the kinetic energy of the continuum with the corresponding quantities of the discrete system. The result is an anisotropic three-dimensional Cosserat continuum.

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Gan, Yanbiao, Aiguo Xu, Guangcai Zhang, Junqi Wang, Xijun Yu i Yang Yang. "Lattice Boltzmann kinetic modeling and simulation of thermal liquid–vapor system". International Journal of Modern Physics C 25, nr 12 (grudzień 2014): 1441002. http://dx.doi.org/10.1142/s0129183114410022.

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We present a highly efficient lattice Boltzmann (LB) kinetic model for thermal liquid–vapor system. Three key components are as below: (i) a discrete velocity model (DVM) by Kataoka et al. [Phys. Rev. E69, 035701(R) (2004)]; (ii) a forcing term Ii aiming to describe the interfacial stress and recover the van der Waals (VDW) equation of state (EOS) by Gonnella et al. [Phys. Rev. E76, 036703 (2007)] and (iii) a Windowed Fast Fourier Transform (WFFT) scheme and its inverse by our group [Phys. Rev. E84, 046715 (2011)] for solving the spatial derivatives, together with a second-order Runge–Kutta (RK) finite difference scheme for solving the temporal derivative in the LB equation. The model is verified and validated by well-known benchmark tests. The results recovered from the present model are well consistent with previous ones [Phys. Rev. E84, 046715 (2011)] or theoretical analysis. The usage of less discrete velocities, high-order RK algorithm and WFFT scheme with 16th-order in precision makes the model more efficient by about 10 times and more accurate than the original one.

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Aregba–Driollet, D., J. Breil, S. Brull, B. Dubroca i E. Estibals. "Modelling and numerical approximation for the nonconservative bitemperature Euler model". ESAIM: Mathematical Modelling and Numerical Analysis 52, nr 4 (lipiec 2018): 1353–83. http://dx.doi.org/10.1051/m2an/2017007.

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This paper is devoted to the study of the nonconservative bitemperature Euler system. We firstly introduce an underlying two species kinetic model coupled with the Poisson equation. The bitemperature Euler system is then established from this kinetic model according to an hydrodynamic limit. A dissipative entropy is proved to exist and a solution is defined to be admissible if it satisfies the related dissipation property. Next, four different numerical methods are presented. Firstly, the kinetic model gives rise to kinetic schemes for the fluid system. The second approach belongs to the family of the discrete BGK schemes introduced by Aregba–Driollet and Natalini. Finally, a quasi-linear relaxation approach and a Lagrange-remap scheme are considered.

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SAIKHANOV, MUSA. "QUANTIZATION OF NONEQUILIBRIUM NONSTATIONARY SYSTEM". International Journal of Modern Physics B 26, nr 12 (8.05.2012): 1241005. http://dx.doi.org/10.1142/s0217979212410056.

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The simultaneous description of nonequilibrium nonstationary system at local and global level is carried out thanks to layering of structure of its energy spectrum. It allows to carry out macroscopic quantization of total production of entropy and to formulate a variation principle. Nonuniformity of energy spectrum nonequilibrium system far from equilibrium state is due to the fact that energy levels in a layer are close to each other (a quasi-continuous spectrum), and the layers are divided by intervals comparable with their width (discrete spectrum). Kinetic processes in system are caused by carrying over of particles and energy between the layers. Quasi-equilibrium subsystems are formed through selective interactions of groups of particles which lead to rapprochement of their values of energies. It allows applying procedure of statistical averaging at local level. As a result, we observe a large-granular quantization at the level of all systems. This approach is applied to kinetic modeling of nonisothermal nonstationary systems.

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Kuznetsov, Alexander A., Anna Yu Tsegelskaya, Pavel V. Buzin, Marina Yu Yablokova i Galina K. Semenova. "High Temperature Polyimide Synthesis in ‘Active’ Medium: Reactivity Leveling of the High and the Low Basic Diamines". High Performance Polymers 19, nr 5-6 (październik 2007): 711–21. http://dx.doi.org/10.1177/0954008307081214.

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The kinetics associated with the reaction of aromatic and aliphatic diamines with phthalic anhydride in glacial acetic acid was studied. This model system was intended to simulate the synthesis of polyimides from diamines and dianhydrides in molten benzoic acid. The reaction proceeds in two discrete steps, the first acylation occurs by the reaction of the diamine with phthalic anhydride followed by cy-clodehydration of the corresponding bis-(o-carboxyamides). The focus of the work was on the influence of chemical composition and basicity of the diamines on the kinetics. Kinetic and thermodynamic characteristics of model reactions were determined. It was established that acylation of aromatic and aliphatic diamines in acid medium proceeds as a reversible second-order reaction catalyzed by acid medium. On the basis of kinetic data obtained, an explanation is given for the observed phenomenon of reactivity leveling of diamines regardless of the basicity.

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DELITALA, MARCELLO, i ANDREA TOSIN. "MATHEMATICAL MODELING OF VEHICULAR TRAFFIC: A DISCRETE KINETIC THEORY APPROACH". Mathematical Models and Methods in Applied Sciences 17, nr 06 (czerwiec 2007): 901–32. http://dx.doi.org/10.1142/s0218202507002157.

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Following some general ideas on the discrete kinetic and stochastic game theory proposed by one of the authors in a previous work, this paper develops a discrete velocity mathematical model for vehicular traffic along a one-way road. The kinetic scale is chosen because, unlike the macroscopic one, it allows to capture the probabilistic essence of the interactions among the vehicles, and offers at the same time, unlike the microscopic one, the opportunity of a profitable analytical investigation of the relevant global features of the system. The discretization of the velocity variable, rather than being a pure mathematical technicality, plays a role in including the intrinsic granular nature of the flow of vehicles in the mathematical theory of traffic. Other important characteristics of the model concern the gain and loss terms of the kinetic equations, namely the construction of a density-dependent table of games to model velocity transitions and the introduction of a visibility length to account for nonlocal interactions among the vehicles.

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Liu, Sheng, Baoling Zhao i Ling Wu. "A Novel MPC with Actuator Dynamic Compensation for the Marine Steam Turbine Rotational Control with a Novel Energy Dynamic Model". Processes 7, nr 7 (3.07.2019): 423. http://dx.doi.org/10.3390/pr7070423.

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The conventional modeling method of the marine steam turbine rotational speed control system (MSTRSCS) is based on Newton’s second law, constructing the mechanical equations between the rotational acceleration and the resultant torque. The disadvantages of this are nonlinearity, a complex structure and an infinite point of discontinuity in the rotational acceleration when the rotational speed is close to 0. Taking the kinetic energy of MSTRSCS as the output variable by using the kinetic energy theorem in this paper, we convert the complex nonlinear model of MSTRSCS into a linear one, since kinetic energy and rotational speed are homeomorphic. Model predictive control (MPC) adopts a discrete-time model, whereas the real system is time-continuous. Hence, poor performance is obtained in the real system when the time-discrete control law is applied to the MSTRSCS through the actuator. In case of high requirements for system accuracy and control performance, conventional MPC (CMPC) cannot meet the engineering requirements. In order to lessen the impact of this phenomenon, this paper proposes a novel MPC with actuator dynamic compensation (ADCMPC), in which the dynamics of the actuator are quantified and the system performance is improved. Compared with other control techniques such as CMPC, the performance of the ADCMPC strategy in MSTRSCS is successfully validated.

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Lima, F. Welington S., i J. A. Plascak. "Kinetic Models of Discrete Opinion Dynamics on Directed Barabási–Albert Networks". Entropy 21, nr 10 (26.09.2019): 942. http://dx.doi.org/10.3390/e21100942.

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Kinetic models of discrete opinion dynamics are studied on directed Barabási–Albert networks by using extensive Monte Carlo simulations. A continuous phase transition has been found in this system. The critical values of the noise parameter are obtained for several values of the connectivity of these directed networks. In addition, the ratio of the critical exponents of the order parameter and the corresponding susceptibility to the correlation length have also been computed. It is noticed that the kinetic model and the majority-vote model on these directed Barabási–Albert networks are in the same universality class.

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Schreuders, P. D., K. R. Diller, J. J. Beaman i H. M. Paynter. "An Analysis of Coupled Multicomponent Diffusion in Interstitial Tissue". Journal of Biomechanical Engineering 116, nr 2 (1.05.1994): 164–71. http://dx.doi.org/10.1115/1.2895715.

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A one-dimensional multicomponent kinetic model was developed to simulate the interstitial diffusion of macromolecules in a three component system, consisting of water, the macromolecule and the interstitial matrix. Movement of the individual components was modeled as occurring in finite jumps between discrete low energy wells along paths defined in terms of species occupation. The flow rate was expressed as a function of the local species concentration, the jump distance, and a kinetic frequency parameter. The model, implemented in pseudo-bond graph form, was examined by fitting it to data obtained for the transport of fluorescein tagged dextran to determine the kinetic constants for that specific system.

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Aristov, V. V., i O. V. Ilyin. "Simulation of spatio-temporal turbulence on the basis of the discrete kinetic system". Procedia Computer Science 1, nr 1 (maj 2010): 725–34. http://dx.doi.org/10.1016/j.procs.2010.04.078.

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Adzhiev, S. Z., V. V. Vedenyapin i S. S. Filippov. "Н-Theorem for Continuous- and Discrete-Time Chemical Kinetic Systems and a System of Nucleosynthesis Equations". Computational Mathematics and Mathematical Physics 58, nr 9 (wrzesień 2018): 1462–76. http://dx.doi.org/10.1134/s0965542518090038.

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Sandu, A., i R. Sander. "Technical Note: Simulating chemical systems in Fortran90 and Matlab with the Kinetic PreProcessor KPP-2.1". Atmospheric Chemistry and Physics Discussions 5, nr 5 (13.09.2005): 8689–714. http://dx.doi.org/10.5194/acpd-5-8689-2005.

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Abstract. This paper presents the new version 2.1 of the Kinetic PreProcessor (KPP). Taking a set of chemical reactions and their rate coefficients as input, KPP generates Fortran90, Fortran77, Matlab, or C code for the temporal integration of the kinetic system. Efficiency is obtained by carefully exploiting the sparsity structures of the Jacobian and of the Hessian. A comprehensive suite of stiff numerical integrators is also provided. Moreover, KPP can be used to generate the tangent linear model, as well as the continuous and discrete adjoint models of the chemical system.

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Sandu, A., i R. Sander. "Technical note: Simulating chemical systems in Fortran90 and Matlab with the Kinetic PreProcessor KPP-2.1". Atmospheric Chemistry and Physics 6, nr 1 (26.01.2006): 187–95. http://dx.doi.org/10.5194/acp-6-187-2006.

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Abstract. This paper presents the new version 2.1 of the Kinetic PreProcessor (KPP). Taking a set of chemical reactions and their rate coefficients as input, KPP generates Fortran90, Fortran77, Matlab, or C code for the temporal integration of the kinetic system. Efficiency is obtained by carefully exploiting the sparsity structures of the Jacobian and of the Hessian. A comprehensive suite of stiff numerical integrators is also provided. Moreover, KPP can be used to generate the tangent linear model, as well as the continuous and discrete adjoint models of the chemical system.

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BERTOTTI, MARIA LETIZIA, i MARCELLO DELITALA. "FROM DISCRETE KINETIC AND STOCHASTIC GAME THEORY TO MODELLING COMPLEX SYSTEMS IN APPLIED SCIENCES". Mathematical Models and Methods in Applied Sciences 14, nr 07 (lipiec 2004): 1061–84. http://dx.doi.org/10.1142/s0218202504003544.

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This paper deals with some methodological aspects related to the discretization of a class of integro-differential equations modelling the evolution of the probability distribution over the microscopic state of a large system of interacting individuals. The microscopic state includes both mechanical and socio-biological variables. The discretization of the microscopic state generates a class of dynamical systems defining the evolution of the densities of the discretized state. In general, this yields a system of partial differential equations replacing the continuous integro-differential equation. As an example, a specific application is discussed, which refers to modelling in the field of social dynamics. The derivation of the evolution equation needs the development of a stochastic game theory.

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Burini, D., S. De Lillo i G. Fioriti. "Influence of drivers ability in a discrete vehicular traffic model". International Journal of Modern Physics C 28, nr 03 (marzec 2017): 1750030. http://dx.doi.org/10.1142/s0129183117500309.

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A vehicular traffic model is presented, based on the so-called Kinetic Theory of Active Particles. Vehicles are characterized by a lattice of discrete speeds and by the driving ability of the drivers. The evolution of the system is modeled through nonlinear interactions, whose output is described by stochastic games. The results of numerical simulations are consistent with experimental measurements of traffic flow.

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Civelek, Cem. "Analysis of a coupled physical discrete time system by means of extended Euler-Lagrange difference equation and discrete dissipative canonical equation". COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 38, nr 6 (24.10.2019): 1810–27. http://dx.doi.org/10.1108/compel-04-2019-0163.

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Purpose The purpose of this study is the application of the following concepts to the time discrete form. Variational Calculus, potential and kinetic energies, velocity proportional Rayleigh dissipation function, the Lagrange and Hamilton formalisms, extended Hamiltonians and Poisson brackets are all defined and applied for time-continuous physical processes. Such processes are not always time-continuously observable; they are also sometimes time-discrete. Design/methodology/approach The classical approach is developed with the benefit of giving only a short table on charge and flux formulation, as they are similar to the classical case just like all other formulation types. Moreover, an electromechanical example is represented as well. Findings Lagrange and Hamilton formalisms together with the velocity proportional (Rayleigh) dissipation function can also be used in the discrete time case, and as a result, dissipative equations of generalized motion and dissipative canonical equations in the discrete time case are obtained. The discrete formalisms are optimal approaches especially to analyze a coupled physical system which cannot be observed continuously. In addition, the method makes it unnecessary to convert the quantities to the other. The numerical solutions of equations of dissipative generalized motion of an electromechanical (coupled) system in continuous and discrete time cases are presented. Originality/value The formalisms and the velocity proportional (Rayleigh) dissipation function aforementioned are used and applied to a coupled physical system in time-discrete case for the first time to the best of the author’s knowledge, and systems of difference equations are obtained depending on formulation type.

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Bianca, Carlo, Bruno Carbonaro i Marco Menale. "On the Cauchy Problem of Vectorial Thermostatted Kinetic Frameworks". Symmetry 12, nr 4 (2.04.2020): 517. http://dx.doi.org/10.3390/sym12040517.

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This paper is devoted to the derivation and mathematical analysis of new thermostatted kinetic theory frameworks for the modeling of nonequilibrium complex systems composed by particles whose microscopic state includes a vectorial state variable. The mathematical analysis refers to the global existence and uniqueness of the solution of the related Cauchy problem. Specifically, the paper is divided in two parts. In the first part the thermostatted framework with a continuous vectorial variable is proposed and analyzed. The framework consists of a system of partial integro-differential equations with quadratic type nonlinearities. In the second part the thermostatted framework with a discrete vectorial variable is investigated. Real world applications, such as social systems and crowd dynamics, and future research directions are outlined in the paper.

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Mallet, Jessy, Stéphane Brull i Bruno Dubroca. "An Entropic Scheme for an Angular Moment Model for the Classical Fokker-Planck-Landau Equation of Electrons". Communications in Computational Physics 15, nr 2 (luty 2014): 422–50. http://dx.doi.org/10.4208/cicp.050612.030513a.

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AbstractIn plasma physics domain, the electron transport is described with the Fokker-Planck-Landau equation. The direct numerical solution of the kinetic equation is usually intractable due to the large number of independent variables. That is why we propose in this paper a new model whose derivation is based on an angular closure in the phase space and retains only the energy of particles as kinetic dimension. To find a solution compatible with physics conditions, the closure of the moment system is obtained under a minimum entropy principle. This model is proved to satisfy the fundamental properties like a H theorem. Moreover an entropic discretization in the velocity variable is proposed on the semi-discrete model. Finally, we validate on numerical test cases the fundamental properties of the full discrete model.

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Dimarco, G., i L. Pareschi. "Numerical methods for kinetic equations". Acta Numerica 23 (maj 2014): 369–520. http://dx.doi.org/10.1017/s0962492914000063.

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In this survey we consider the development and mathematical analysis of numerical methods for kinetic partial differential equations. Kinetic equations represent a way of describing the time evolution of a system consisting of a large number of particles. Due to the high number of dimensions and their intrinsic physical properties, the construction of numerical methods represents a challenge and requires a careful balance between accuracy and computational complexity. Here we review the basic numerical techniques for dealing with such equations, including the case of semi-Lagrangian methods, discrete-velocity models and spectral methods. In addition we give an overview of the current state of the art of numerical methods for kinetic equations. This covers the derivation of fast algorithms, the notion of asymptotic-preserving methods and the construction of hybrid schemes.

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Lapshin, Oleg, Olga Shkoda, Oksana Ivanova i Sergey Zelepugin. "Discrete One-Stage Mechanochemical Synthesis of Titanium-Nitride in a High-Energy Mill". Metals 11, nr 11 (30.10.2021): 1743. http://dx.doi.org/10.3390/met11111743.

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Discrete (discontinuous) mechanochemical synthesis of titanium nitride was experimentally investigated. The experimental results show that mechanical activation intensifies the chemical conversion in the Ti-N system, and the discrete synthesis of the final product is conducted under “soft” controlled conditions without high heat release. The new theory of mechanochemical synthesis and the mathematical model based on it were used for theoretical evaluation of the dynamics of titanium activation in the nitrogen medium. It was found that the discrete mode of synthesis includes two factors accelerating mechanochemical reactions in the Ti-N synthesis: structural (grinding of metallic reagent and formation of interfacial areas) and kinetic (accumulation of excess energy stored in the formed structural defects in metallic reagent). The kinetic constants of the process were found using experimental data and the inverse problem method. The diagrams defining the controlled modes of obtaining titanium nitride particles with the given characteristics were constructed. A mathematical model for theoretical estimation of the dynamics of activation of titanium powder in the nitrogen medium was developed using a new macrokinetic theory of mechanochemical synthesis.

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BELLOUQUID, A., E. DE ANGELIS i L. FERMO. "TOWARDS THE MODELING OF VEHICULAR TRAFFIC AS A COMPLEX SYSTEM: A KINETIC THEORY APPROACH". Mathematical Models and Methods in Applied Sciences 22, supp01 (kwiecień 2012): 1140003. http://dx.doi.org/10.1142/s0218202511400033.

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Kinetic theory methods are applied in this paper to model the dynamics of vehicular traffic. The basic idea is to consider each vehicular-driver system as a single part, or micro-system, of a large complex system, in order to capture the heterogeneous behavior of all the micro-systems that compose the overall system. The evolution of the system is ruled by nonlinearly additive interactions described by stochastic games. A qualitative analysis for the proposed model with discrete states is developed, showing well-posedness of the related Cauchy problem for the spatially homogeneous case and for the spatially nonhomogeneous case, the latter with periodic boundary conditions. Numerical simulations are also performed, with the aim to show how the model proposed is able to reproduce empirical data and to show emerging behavior as the formation of clusters.

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Fermo, Luisa, i Andrea Tosin. "A fully-discrete-state kinetic theory approach to traffic flow on road networks". Mathematical Models and Methods in Applied Sciences 25, nr 03 (8.12.2014): 423–61. http://dx.doi.org/10.1142/s0218202515400023.

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This paper presents a new approach to the modeling of vehicular traffic flows on road networks based on kinetic equations. While in the literature the problem has been extensively studied by means of macroscopic hydrodynamic models, to date there are still not, to the authors' knowledge, contributions tackling it from a genuine statistical mechanics point of view. Probably one of the reasons is the higher technical complexity of kinetic traffic models, further increased in case of several interconnected roads. Here such difficulties of the theory are overcome by taking advantage of a discrete structure of the space of microscopic states of the vehicles, which is also significant in view of including the intrinsic microscopic granularity of the system in the mesoscopic representation.

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Ali Eshtewy, Neveen, i Lena Scholz. "Model Reduction for Kinetic Models of Biological Systems". Symmetry 12, nr 5 (25.05.2020): 863. http://dx.doi.org/10.3390/sym12050863.

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High dimensionality continues to be a challenge in computational systems biology. The kinetic models of many phenomena of interest are high-dimensional and complex, resulting in large computational effort in the simulation. Model order reduction (MOR) is a mathematical technique that is used to reduce the computational complexity of high-dimensional systems by approximation with lower dimensional systems, while retaining the important information and properties of the full order system. Proper orthogonal decomposition (POD) is a method based on Galerkin projection that can be used for reducing the model order. POD is considered an optimal linear approach since it obtains the minimum squared distance between the original model and its reduced representation. However, POD may represent a restriction for nonlinear systems. By applying the POD method for nonlinear systems, the complexity to solve the nonlinear term still remains that of the full order model. To overcome the complexity for nonlinear terms in the dynamical system, an approach called the discrete empirical interpolation method (DEIM) can be used. In this paper, we discuss model reduction by POD and DEIM to reduce the order of kinetic models of biological systems and illustrate the approaches on some examples. Additional computational costs for setting up the reduced order system pay off for large-scale systems. In general, a reduced model should not be expected to yield good approximations if different initial conditions are used from that used to produce the reduced order model. We used the POD method of a kinetic model with different initial conditions to compute the reduced model. This reduced order model is able to predict the full order model for a variety of different initial conditions.

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Yang, Jing Fang, Xian Ying Feng, Hong Jun Fu i Shi Gang Mu. "Model Parameter Identification of Tire Dynamic Balance Detection System". Applied Mechanics and Materials 157-158 (luty 2012): 731–36. http://dx.doi.org/10.4028/www.scientific.net/amm.157-158.731.

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Tire dynamic balance detection plays an important part in tire quality detection area. An accurate model structure and precise model parameters are the basis of the right test results. This paper builds a kinetic model based on engineering practice. To acquire parameters presents a method following identification theory. According to the need of actual production, a validation experiment is put forward. In the parameter identification process, data acquisition is completed by the PCI card. For data processing, this paper designs the fitting filter and then it also fetches the signal amplitude and phase with discrete Fourier transform. The results are proven to be right and practicable.

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Ruppe, Alex, Kathryn Mains i Jerome M. Fox. "A kinetic rationale for functional redundancy in fatty acid biosynthesis". Proceedings of the National Academy of Sciences 117, nr 38 (3.09.2020): 23557–64. http://dx.doi.org/10.1073/pnas.2013924117.

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Cells build fatty acids with biocatalytic assembly lines in which a subset of enzymes often exhibit overlapping activities (e.g., two enzymes catalyze one or more identical reactions). Although the discrete enzymes that make up fatty acid pathways are well characterized, the importance of catalytic overlap between them is poorly understood. We developed a detailed kinetic model of the fatty acid synthase (FAS) ofEscherichia coliand paired that model with a fully reconstituted in vitro system to examine the capabilities afforded by functional redundancy in fatty acid synthesis. The model captures—and helps explain—the effects of experimental perturbations to FAS systems and provides a powerful tool for guiding experimental investigations of fatty acid assembly. Compositional analyses carried out in silico and in vitro indicate that FASs with multiple partially redundant enzymes enable tighter (i.e., more independent and/or broader range) control of distinct biochemical objectives—the total production, unsaturated fraction, and average length of fatty acids—than FASs with only a single multifunctional version of each enzyme (i.e., one enzyme with the catalytic capabilities of two partially redundant enzymes). Maximal production of unsaturated fatty acids, for example, requires a second dehydratase that is not essential for their synthesis. This work provides a kinetic, control-theoretic rationale for the inclusion of partially redundant enzymes in fatty acid pathways and supplies a valuable framework for carrying out detailed studies of FAS kinetics.

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Bliokh, Yu P., M. G. Lyubarsky i V. O. Podobinsky. "About chaotization mechanisms of the distributed dynamical systems which are close to discrete". Discrete Dynamics in Nature and Society 1, nr 3 (1997): 233–41. http://dx.doi.org/10.1155/s102602269700023x.

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The investigations of stochastization mechanisms of distributed dynamical systems (DDS) are developed not so complete as stochastization of dynamical systems with concentrated parameters (CDS). Therefore the corresponding DDS which is close (in one or other sense) to the CDS under consideration is used. Such substitution means some roughening of an initial problem. However, there are such important stochastization mechanisms understanding properties, which are connected with system “distributivity” on principle. In this paper the conception of a proximity to the CDS is introduced for one particular class of the DDS. It is shown that such kind of systems has two stochastization mechanisms, one of which is common to the DDS and the corresponding CDS. Another stochastization mechanism inherent in DDS disappears under transition from DDS to CDS.Distributed dynamical system considered below is not abstract but describes the set of concrete physical devices, for example, microwave oscillators. It may be devices in which kinetic energy of an accelerated electron beam is transformed into electromagnetic radiation energy, or oscillators with delayed feedback.

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Allgeyer, Sebastien, Marie-Odile Bristeau, David Froger, Raouf Hamouda, V. Jauzein, Anne Mangeney, Jacques Sainte-Marie, Fabien Souillé i Martin Vallée. "Numerical approximation of the 3D hydrostatic Navier–Stokes system with free surface". ESAIM: Mathematical Modelling and Numerical Analysis 53, nr 6 (listopad 2019): 1981–2024. http://dx.doi.org/10.1051/m2an/2019044.

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In this paper we propose a stable and robust strategy to approximate the 3D incompressible hydrostatic Euler and Navier–Stokes systems with free surface. Compared to shallow water approximation of the Navier–Stokes system, the idea is to use a Galerkin type approximation of the velocity field with piecewise constant basis functions in order to obtain an accurate description of the vertical profile of the horizontal velocity. Such a strategy has several advantages. It allows to rewrite the Navier–Stokes equations under the form of a system of conservation laws with source terms,the easy handling of the free surface, which does not require moving meshes,the possibility to take advantage of robust and accurate numerical techniques developed in extensive amount for Shallow Water type systems. Compared to previous works of some of the authors, the three dimensional case is studied in this paper. We show that the model admits a kinetic interpretation including the vertical exchanges terms, and we use this result to formulate a robust finite volume scheme for its numerical approximation. All the aspects of the discrete scheme (fluxes, boundary conditions, ...) are completely described and the stability properties of the proposed numerical scheme (well-balancing, positivity of the water depth, ...) are discussed. We validate the model and the discrete scheme with some numerical academic examples (3D non stationary analytical solutions) and illustrate the capability of the discrete model to reproduce realistic tsunami waves propagation, tsunami runup and complex 3D hydrodynamics in a raceway.

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30

Zhao, Bin, i Yongqiang Guan. "Data-sampling controllability of multi-agent systems". IMA Journal of Mathematical Control and Information 37, nr 3 (15.10.2019): 794–813. http://dx.doi.org/10.1093/imamci/dnz026.

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Abstract In this paper, we consider data-sampling controllability of multi-agent systems (MASs), where the interconnection topology is directed and weighted and the nodes have generic linear kinetic dynamics. First, the asynchronous data sampling protocols and synchronous data sampling protocols are proposed, respectively. Then the discussions focus on deriving the necessary and sufficient conditions for data-sampling controllability of MASs with a single leader and multiple leaders. The criteria for data-sampling controllability are derived in terms of recursions of matrix multiplication. For the single-leader situation, the asynchronous data-sampling controllability is equivalently transformed to be the output controllability of a discrete linear system. For the multiple-leader situation, the asynchronous data-sampling controllability is equivalently transformed to be the output controllability of a discrete time-delayed linear system. Finally, the synchronous data-sampling controllability is discussed as a special case of asynchronous data-sampling controllability. Two numerical examples are given to illustrate the effectiveness of the theoretical results.

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31

Craifaleanu, Andrei, i Nicolaie Orăşanu. "Reduction of Arbitrary Rigid Bodies to Inertially Equivalent Discrete Systems of Material Points". Applied Mechanics and Materials 762 (maj 2015): 33–40. http://dx.doi.org/10.4028/www.scientific.net/amm.762.33.

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In a previous paper of the authors, a general method was presented for the reduction of a rigid plane plate to a discrete system of material points, with equivalent inertial properties (mass, center of mass, tensor of inertia). The present paper generalizes the method for rigid bodies of arbitrary shape, i.e. for material volumes, as well as for curved shells. It is shown that a homogenous ellipsoid can be reduced to a system of seven material points placed in significant geometrical points of the body. Next, starting from the concept of ellipsoid of inertia, an equivalent homogenous ellipsoid is determined for an arbitrary body. The method simplifies considerably the calculation of various mechanical quantities, such as moments and products of inertia with respect to rotated Cartesian coordinate systems, angular momentum and kinetic energy, of rigid bodies part of all types of mechanical devices or structures.

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Li, Chengbo, Qianqian Gao i Xianchang Li. "A Study of Contact Detection between Noncircular Particles in Discrete Element Method". Advances in Materials Science and Engineering 2022 (31.08.2022): 1–15. http://dx.doi.org/10.1155/2022/2514023.

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One of the key points of modeling noncircular particles in the discrete element method is the contact detection of particles. In this study, a general contact detection algorithm of two-dimensional particles with analytic shape functions is provided. The contact detection of particles with strictly convex shape function, such as ellipses and superellipses, is solved by Newton–Raphson method, and a grid method is provided to deal with heart-shaped particles. The grid method can be generalized into a particle system, in which the shape function is not convex. The accuracy and stability of the algorithm are verified by a series of tests. For the collision of a pair of ellipses with an aspect ratio of α = a / b = 1000, the efficiency is not worse than the Newton–Raphson method. For random packing under gravity, no residual kinetic energy is observed, and the force that acts on the bottom is equal to the gravity, that is, the system reaches a mechanical equilibrium state. After equilibrium, the process of hopper discharge is also simulated. The present method is suitable for arbitrarily shaped particles with analytic shape functions in two-dimensional cases. In addition to superellipses, the method can also be applied to other particle systems as long as the shape functions are given.

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33

Luding, Stefan. "How does static granular matter re-arrange for different isotropic strain rate?" EPJ Web of Conferences 249 (2021): 10001. http://dx.doi.org/10.1051/epjconf/202124910001.

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The question of how soft granular matter, or dense amorphous systems, re-arrange their microstructure under isotropic compression and de-compression, at different strain rates, will be answered by particle simulations of frictionless model systems in a periodic three-dimensional cuboid. Starting compression below jamming, the systems experience the well known jamming transition, with characteristic evolutions of the state variables elastic energy, elastic stress, coordination number, and elastic moduli. For large strain rates, kinetic energy comes into play and the evolution is more dynamic. In contrast, at extremely slow deformation, the system relaxes to hyper-elastic states, with well-defined elastic moduli, in static equilibrium between irreversible (plastic) re-arrangement events, discrete in time. Small, finite strains explore those reversible (elastic) states, before larger strains push the system into new states, by irreversible, sudden re-arrangements of the micro-structure.

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34

Din, Qamar, i Umer Saeed. "Stability, Discretization, and Bifurcation Analysis for a Chemical Reaction System". Match Communications in Mathematical and in Computer Chemistry 90, nr 1 (2023): 151–74. http://dx.doi.org/10.46793/match.90-1.151d.

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Chemical reactions reveal all types of exotic behavior, that is, multistability, oscillation, chaos, or multistationarity. The mathematical framework of rate equations enables us to discuss steadystates, stability and oscillatory behavior of a chemical reaction. A planar cubic dynamical system governed by nonlinear differential equations induced by kinetic differential equations for a two-species chemical reaction is studied. It is investigated that system has unique positive steady state. Moreover, local dynamics of system is studied around its positive steady state. Existence and direction of Hopf bifurcation about positive equilibrium are carried out. In order to modify the bifurcating behavior, bifurcation control is investigated. Keeping in mind, a consistency preserving discretization for continuous chemical reaction system, a discrete counterpart is proposed, and its qualitative behavior is investigated. Numerical simulation along with bifurcation diagrams are provided to illustrate the mathematical investigations.

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35

Vasil’eva, Ol’ga Aleksandrovna. "Numerical investigation of the Carleman system". Vestnik MGSU, nr 6 (czerwiec 2015): 7–15. http://dx.doi.org/10.22227/1997-0935.2015.6.7-15.

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In the article the Cauchy problem of the Carleman equation is considered. The Carleman system of equations is a model problem of the kinetic theory of gases. It is a discrete kinetic model of one-dimensional gas consisting of identical monatomic molecules. The molecules can have one of two speeds, which have equal values and opposite directions. This system of the equations is quasi-linear hyperbolic system of partial differential equations. There is no analytic solution for this problem in general case. So, the numerical investigation of the Cauchy problem of the Carleman system solution is very important.The paper presents and discusses the results of the numerical investigation of the Cauchy problem for the studied system solution with periodic initial conditions. The dependence of the stabilization time of the solution and the time dependence of energy exchange from small parameter are obtained.The second point of the paper is numerical investigation of the solution of the Cauchy problem with non-periodic initial conditions. The solution stabilization to the equilibrium state is obtained. The solution stabilization time is compared with stabilization time in periodic case.The final point of the paper is numerical investigation of the Cauchy problem with stationary normal processes as initial conditions. The solution to this problem is two stationary stochastic processes for any fixed value of time variable. As a rule, the practical interest is not a stochastic solution but its statistical characteristics. The stochastic solution realization is presented and discussed. The dependence of the mathematical expectation of the solution deviation modulus from equilibrium state is obtained. It demonstrates the process of the solution stabilization.

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36

Vasseur, Alexis. "Convergence of a semi-discrete kinetic scheme for the system of isentropic gas dynamics with \gamma=3". Indiana University Mathematics Journal 48, nr 1 (1999): 0. http://dx.doi.org/10.1512/iumj.1999.48.1572.

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37

Liu, Hongtao, Feng Shi, Jie Wan, Xiaoming He i Yong Cao. "Discrete unified gas kinetic scheme for a reformulated BGK–Vlasov–Poisson system in all electrostatic plasma regimes". Computer Physics Communications 255 (październik 2020): 107400. http://dx.doi.org/10.1016/j.cpc.2020.107400.

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38

Dabnoun, Najat M. Omar, i Maria Stella Mongiovì. "A contribution to the mathematical modeling of immune-cancer competition". Communications in Applied and Industrial Mathematics 9, nr 2 (1.12.2018): 76–90. http://dx.doi.org/10.2478/caim-2018-0012.

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Abstract This paper deals with the modeling of interactions between the immune system and cancer cells, in the framework of the mathematical kinetic theory for active particles. The work deepens a previous paper of Belloquid et al. that assumes spatial homogeneity and discrete values of the activity of cancer and immune cells. A number of simulations are made with the aim to investigate how the state of the various cell populations evolves in time depending on the choice of the free parameters.

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39

Khachatryan, Kh A., i H. S. Petrosyan. "Existence and Uniqueness Theorems for One Infinite System of Nonlinear Algebraic Equations". Bulletin of Irkutsk State University. Series Mathematics 44 (2023): 44–54. http://dx.doi.org/10.26516/1997-7670.2023.44.44.

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We study a infinite system of algebraic equations with monotone nonlinearities and with an infinite Toeplitz type matrix. This system has applications in discrete problems of the dynamical theory of 𝑝-adic open-closed strings, the kinetic theory of gases, and mathematical biology. Under certain restrictions on the nonlinearities and on the corresponding Toeplitz matrix, it is possible to prove existence and uniqueness theorems for a nontrivial solution in the class of bounded sequences. The main tool for proving the uniqueness theorem for a nontrivial solution is an auxiliary independent theorem on the asymptotic behavior of a nonnegative nontrivial and bounded solution on ±∞. At the end of the paper, specific applied examples of nonlinearities and the corresponding matrix are given to illustrate the importance of the results obtained.

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40

DELITALA, M., P. PUCCI i M. C. SALVATORI. "FROM METHODS OF THE MATHEMATICAL KINETIC THEORY FOR ACTIVE PARTICLES TO MODELING VIRUS MUTATIONS". Mathematical Models and Methods in Applied Sciences 21, supp01 (kwiecień 2011): 843–70. http://dx.doi.org/10.1142/s0218202511005398.

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The paper presents a model of virus mutations and evolution of epidemics in a system of interacting individuals, where the intensity of the pathology, described by a real discrete positive variable, is heterogeneously distributed, and the virus is in competition with the immune system or therapeutical actions. The model is developed within the framework of the Kinetic Theory of Active Particles. The paper also presents a qualitative analysis developed to study the well-posedness of the mathematical problem associated to the general framework. Finally, simulations show the ability of the model to predict some interesting emerging phenomena, such as the mutation to a subsequent virus stage, the heterogeneous evolution of the pathology with the co-presence of individual carriers of the virus at different levels of progression, and the presence of oscillating time phases with either virus prevalence or immune system control.

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41

Mirahmadi, Marjan-S., Amir H. Fatollahi i Mohammad Khorrami. "The similarity of attractive and repulsive forces on a lattice". Modern Physics Letters A 30, nr 23 (20.07.2015): 1550112. http://dx.doi.org/10.1142/s0217732315501126.

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On a lattice, as the momentum space is compact, the kinetic energy is bounded not only from below but also from above. It is shown that this somehow removes the distinction between repulsive and attractive forces. In particular, it is seen that a region with attractive force would appear forbidden for states with energies higher than a certain value, while repulsive forces could develop bound-states. An explicit transformation is introduced which transforms the spectrum of a system corresponding to a repulsive force, to that of a similar system corresponding to an attractive force. Explicit numerical examples are presented for discrete energies of bound-states of a particle experiencing repulsive force by a piecewise constant potential. Finally, the parameters of a specific one-dimensional (1D) translationally invariant system on continuum are tuned so that the energy of the system resembles the kinetic energy of a system on a 1D lattice. In particular, the parameters are tuned so that while the width of the first energy band and its position are kept finite, the gap between the first energy band and the next energy band goes to infinity, so that effectively only the first energy band is relevant.

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42

Godinez-Garrido, Gildardo, Omar-Jacobo Santos-Sánchez, Hugo Romero-Trejo i Orlando García-Pérez. "Discrete Integral Optimal Controller for Quadrotor Attitude Stabilization: Experimental Results". Applied Sciences 13, nr 16 (16.08.2023): 9293. http://dx.doi.org/10.3390/app13169293.

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The Unmanned Aerial Vehicle (UAV) attitude stabilization problem has been dealt with in many previous works through applying a vast range of philosophies of control strategies. In this paper, a discrete controller based on a Linear Quadratic Regulator (LQR) plus integral action is synthesized to stabilize the attitude and altitude of a quadrotor helicopter. This kind of control strategy allows us to reduce the energy consumption rate, and the desired UAV behavior is properly achieved. Experimental tests are conducted with external disturbances such as crosswinds deliberately added to affect the performance of the aerial vehicle. This provides experimental evidence that the integral part considered in the proposed control strategy contributes to improving the performance of the vehicle under external disturbances. In fact, a comparative analysis of potential and kinetic energy consumption is developed between the Optimal Integral Controller (OIC) and a Proportional Integral Derivative Controller (PID), allowing us to determine the level of improvement of the closed-loop system when the discrete Integral Optimal Controller is applied.

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43

Kazura, Evan, Ray Mernaugh i Franz Baudenbacher. "A Capillary-Perfused, Nanocalorimeter Platform for Thermometric Enzyme-Linked Immunosorbent Assay with Femtomole Sensitivity". Biosensors 10, nr 6 (24.06.2020): 71. http://dx.doi.org/10.3390/bios10060071.

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Enzyme-catalyzed chemical reactions produce heat. We developed an enclosed, capillary-perfused nanocalorimeter platform for thermometric enzyme-linked immunosorbent assay (TELISA). We used catalase as enzymes to model the thermal characteristics of the micromachined calorimeter. Model-assisted signal analysis was used to calibrate the nanocalorimeter and to determine reagent diffusion, enzyme kinetics, and enzyme concentration. The model-simulated signal closely followed the experimental signal after selecting for the enzyme turnover rate (kcat) and the inactivation factor (InF), using a known label enzyme amount (Ea). Over four discrete runs (n = 4), the minimized model root mean square error (RMSE) returned 1.80 ± 0.54 fmol for the 1.5 fmol experiments, and 1.04 ± 0.37 fmol for the 1 fmol experiments. Determination of enzyme parameters through calibration is a necessary step to track changing enzyme kinetic characteristics and improves on previous methods to determine label enzyme amounts on the calorimeter platform. The results obtained using model-system signal analysis for calibration led to significantly improved nanocalorimeter platform performance.

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44

Leary, N. O., A. Pembroke i P. F. Duggan. "Improving Accuracy of Glucose Oxidase Procedure for Glucose Determinations on Discrete Analyzers". Clinical Chemistry 38, nr 2 (1.02.1992): 298–302. http://dx.doi.org/10.1093/clinchem/38.2.298.

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Abstract We describe a rapid kinetic glucose oxidase (EC 1.1.3.4) procedure for quantifying glucose. Glucose oxidase concentration was reduced from the more usual 20 kU/L to 4 kU/L, and pH was reduced from 7.0 to 6.6. Potassium ferrocyanide (20 mumol/L) and ascorbate oxidase (1 kU/L) were incorporated in the procedure. The assay results vary linearly with glucose concentration from 0 to 50 mmol/L and are unaffected by bilirubin concentrations less than or equal to 600 mumol/L, hemoglobin less than or equal to 12 g/L, Intralipid less than or equal to 4 g/L, urate less than or equal to 1 mmol/L, and ascorbate less than or equal to 2.0 mmol/L. The assay is readily adaptable to most open-system analyzers.

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45

Zammit, V. A., N. T. Price, F. Fraser i V. N. Jackson. "Structure-function relationships of the liver and muscle isoforms of carnitine palmitoyltransferase I". Biochemical Society Transactions 29, nr 2 (1.05.2001): 287–91. http://dx.doi.org/10.1042/bst0290287.

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Elucidation of the membrane topology of carnitine palmitoyltransferase (CPT) I showed that the extreme N-terminus is involved in determining the sensitivity of the liver (L) isoform to malonyl-CoA and suggested that interaction between the two cytosolic segments of the CPT I molecule determines the kinetic characteristics of the enzyme. Work with chimaeric liver/muscle-isoform (L/M) proteins constructed from all six possible combinations of three domains [N-terminus plus transmembrane domain 1 (TM1), loop plus TM2 and C-domain] expressed in Pichia pastoris showed that the precise N-C and TM1-TM2 pairings determine the overall kinetic parameters of the protein. Discrete short sequences within the respective N-terminal regions have negative or positive effects on malonyl-CoA sensitivity (L-isoform) or the Km for carnitine (M-isoform) in the full-length proteins, thus imparting to them their distinctive kinetic characteristics. Interactions within N-terminal domains also seem to be important in the targeting of the protein to microsomes in the P. pastoris expression system.

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46

Krivovichev, Gerasim V., i Sergey A. Mikheev. "On the Stability of Multi-Step Finite-Difference-Based Lattice Boltzmann Schemes". International Journal of Computational Methods 16, nr 01 (21.11.2018): 1850087. http://dx.doi.org/10.1142/s0219876218500871.

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Stability of finite-difference-based off-lattice Boltzmann schemes is analyzed. The time derivative in system of discrete Boltzmann equations is approximated by two-step modified central difference. Advective term is approximated by finite differences from first- to fourth-orders of accuracy. Characteristics-based (CB) schemes and schemes with traditional separate approximations of space derivatives are considered. A special class of high-order CB schemes with approximation in the internal nodes of grid patterns is constructed. It is demonstrated that apparent viscosity for the schemes of high-order is equal to kinematic viscosity of the system of Bhatnaghar–Gross–Krook kinetic equations. Stability of the schemes is analyzed by the von Neumann method for the cases of two flow regimes in unbounded domain. Stability is analyzed by the investigation of the stability domains in parameter space. The area of the domain is considered as the main numerical characteristic of the stability. As the main result of the analysis, it must be mentioned that the areas of CB schemes are greater than areas for the schemes with separate approximations.

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47

Květoň, Josef, i Jan Eliáš. "Discrete Modeling of Strain Rate Effect in Concrete Fracture". Key Engineering Materials 754 (wrzesień 2017): 345–48. http://dx.doi.org/10.4028/www.scientific.net/kem.754.345.

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Concrete fracture can be simulated in static regime, however, it is a dynamical process. For very slow loading rates, the kinetic energy is negligible compared to the energy dissipated by fracturing, and the influence of inertia can be neglected. In all other cases, neglecting the influence of inertia forces can lead to improper results. With increasing loading rate, increase in strength and energy dissipation as well as changes in crack pattern can be observed. The contribution presents dynamical simulations of experiments on concrete specimens under various displacement rates, from very slow, quasi-static, to high displacement rates. The simulations are calculated using discrete particle model, the material is represented by a system of interconnected ideally rigid polyhedral particles. The solution of equations of motion is calculated using implicit time integration Newmark scheme. The constitutive behavior of the material is strain rate independent. For high strain rates the influence of inertia forces dominates and is mainly responsible for increase in loading forces as well as for change in the crack pattern and crack branching. The results obtained with the model are compared to experimental data from literature.

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Tepavitcharova, Stefka, Antonina Kovacheva i Christo Balarew. "Crystallization and Thermal Behavior of 2MX·CuX₂·2H₂O (M⁺ = K, NH₄, Rb, Cs; X^- = Cl, Br)". Solid State Phenomena 194 (listopad 2012): 222–25. http://dx.doi.org/10.4028/www.scientific.net/ssp.194.222.

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The crystallization in the MX – CuX2 – H2O system (M+ = K, NH4, Rb, Cs; X- = Cl, Br) was studied and 2MX.CuX2.2H2O was found to be the predominant type of double salts. All of them are isostructural (tetragonal crystal system, sp. gr. P42/mnm) and the structure consists of discrete [Me(H2O)2X4] octahedra and separate M+ ions. The thermal behavior of 2MX.CuX2.2H2O was studied in the range 20-780°C. Ammonium salts showed analogous behavior but higher thermal stability (up to 100-120°C) than the other salts (up to 50-60°C). The first step of 2MX.CuX2.2H2O decomposition was dehydration to anhydrous double salts that occurred up to 100-210°C. The second step was the decomposition of the anhydrous double salts followed by CuX2 decomposition. Formal kinetic parameters (E*deh and A) were calculated and kinetic equations of the dehydration processes were derived from the TG curves using the differential method of non-isothermal decomposition. The results pointed to a diffusion-controlled dehydration process in all cases.

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49

Muminov, Zahriddin, Fudziah Ismail, Zainidin Eshkuvatov i Jamshid Rasulov. "On the Discrete Spectrum of a Model Operator in Fermionic Fock Space". Abstract and Applied Analysis 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/875194.

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We consider a model operatorHassociated with a system describing three particles in interaction, without conservation of the number of particles. The operatorHacts in the direct sum of zero-, one-, and two-particle subspaces of thefermionic Fock space ℱa(L2(𝕋3))overL2(𝕋3). We admit a general form for the "kinetic" part of the HamiltonianH, which contains a parameterγto distinguish the two identical particles from the third one. (i) We find a critical valueγ*for the parameterγthat allows or forbids the Efimov effect (infinite number of bound states if the associated generalized Friedrichs model has a threshold resonance) and we prove that only forγ<γ*the Efimov effect is absent, while this effect exists for anyγ>γ*. (ii) In the caseγ>γ*, we also establish the following asymptotics for the numberN(z)of eigenvalues ofHbelowz<Emin=infσessH:limz→EminNz/logEmin-z=𝒰0γ 𝒰0γ>0, for allγ>γ*.

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50

Mayer, Bernd, i Steen Rasmussen. "The Lattice Molecular Automaton(LMA): A Simulation System for Constructive Molecular Dynamics". International Journal of Modern Physics C 09, nr 01 (luty 1998): 157–77. http://dx.doi.org/10.1142/s0129183198000133.

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Molecular self-assembly is frequently encountered in biochemical systems generating higher order structures with well-defined functionalities. However, the driving forces underlying these processes are not well understood. The Lattice Molecular Automaton (LMA) is a deterministic computational tool suitable for simulation of self-organization processes in large scale, molecular systems. This paper introduces the basic computational concepts needed to formulate molecular dynamics and self-assembly in a discrete field, cellular automaton environment: Molecular objects are encoded as data structures on a 2D triangular lattice. Propagating force particles together with kinetic and potential energy terms define simulation objects that specify molecular dynamics and force field properties. As an example, the simulation of polymer dynamics in an aqueous environment is shown. In this paper we focus on the mathematical and algorithmic formulation of a variety of intra- and intermolecular interactions. Thermodynamical characteristics together with a variety of other physico-chemical properties of the LMA are discussed in detail in Ref. 1.

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