Journal articles on the topic 'Hyperbolic balance law'
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1
Mascia, C. "Travelling wave solutions for a balance law." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 127, no. 3 (1997): 567–93. http://dx.doi.org/10.1017/s0308210500029917.
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We study entropy travelling wave solutions for first-order hyperbolic balance laws. Results concerning existence, regularity and asymptotic stability of such solutions are proved for convex fluxes and source terms with simple isolated zeros.
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COLOMBO, RINALDO M., and ANDREA CORLI. "ON A CLASS OF HYPERBOLIC BALANCE LAWS." Journal of Hyperbolic Differential Equations 01, no. 04 (December 2004): 725–45. http://dx.doi.org/10.1142/s0219891604000317.
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Consider an n×n system of hyperbolic balance laws with coinciding shock and rarefaction curves. This note proves the well-posedness in the large of this system, provided there exists a domain that is invariant both with respect to the homogeneous conservation law and to the ordinary differential system generated by the right-hand side. No "non-resonance" hypothesis is assumed.
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Barlow, Douglas A., Emilie LaVoie-Ingram, and Jahan Bayat. "Population-balance study of protein crystal growth from solution using a hyperbolic rate law." Journal of Crystal Growth 578 (January 2022): 126417. http://dx.doi.org/10.1016/j.jcrysgro.2021.126417.
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HBID, MY LHASSAN, EVA SÁNCHEZ, and RAFAEL BRAVO DE LA PARRA. "STATE-DEPENDENT DELAYS ASSOCIATED TO THRESHOLD PHENOMENA IN STRUCTURED POPULATION DYNAMICS." Mathematical Models and Methods in Applied Sciences 17, no. 06 (June 2007): 877–900. http://dx.doi.org/10.1142/s0218202507002145.
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The aim of this paper is to put in evidence the onset of state-dependent delays in threshold models for structured population dynamics. A unified approach to these models is provided, based on solving the corresponding balance law (hyperbolic P.D.E.) along the characteristic lines and showing the common underlying ideas. Size and age-structured models in different fields are presented: insect populations, cell proliferation and epidemics.
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Durur, Hülya. "Different types analytic solutions of the (1+1)-dimensional resonant nonlinear Schrödinger’s equation using (G′/G)-expansion method." Modern Physics Letters B 34, no. 03 (December 18, 2019): 2050036. http://dx.doi.org/10.1142/s0217984920500360.
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In this paper, an alternative method has been studied for traveling wave solutions of mathematical models which have an important place in applied sciences and balance term is not integer. With this method, the trigonometric, hyperbolic, complex and rational type traveling wave solutions of the (1[Formula: see text]+[Formula: see text]1)-dimensional resonant nonlinear Schrödinger’s (RNLS) equation with the parabolic law have constructed. This method can be applied reliably and effectively in many differential equations.
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Boyaval, Sébastien, and Mark Dostalík. "Non-isothermal viscoelastic flows with conservation laws and relaxation." Journal of Hyperbolic Differential Equations 19, no. 02 (June 2022): 337–64. http://dx.doi.org/10.1142/s0219891622500096.
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We propose a system of conservation laws with relaxation source terms (i.e. balance laws) for non-isothermal viscoelastic flows of Maxwell fluids. The system is an extension of the polyconvex elastodynamics of hyperelastic bodies using additional structure variables. It is obtained by writing the Helmholtz free energy as the sum of a volumetric energy density (function of the determinant of the deformation gradient det F and the temperature [Formula: see text] like the standard perfect-gas law or Noble–Abel stiffened-gas law) plus a polyconvex strain energy density function of F, [Formula: see text] and of symmetric positive-definite structure tensors that relax at a characteristic time scale. One feature of our model is that it unifies various ideal materials ranging from hyperelastic solids to perfect fluids, encompassing fluids with memory like Maxwell fluids. We establish a strictly convex mathematical entropy to show that the system is symmetric-hyperbolic. Another feature of the proposed model is therefore the short-time existence and uniqueness of smooth solutions, which define genuinely causal viscoelastic flows with waves propagating at finite speed. In heat-conductors, we complement the system by a Maxwell–Cattaneo equation for an energy-flux variable. The system is still symmetric-hyperbolic, and smooth evolutions with finite-speed waves remain well-defined.
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Said, Hamid. "An analytical mechanics approach to the first law of thermodynamics and construction of a variational hierarchy." Theoretical and Applied Mechanics, no. 00 (2020): 11. http://dx.doi.org/10.2298/tam200315011s.
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A simple procedure is presented for the study of the conservation of energy equation with dissipation in continuum mechanics in 1D. This procedure is used to transform this nonlinear evolution-diffusion equation into a hyperbolic PDE; specifically, a second-order quasi-linear wave equation. An immediate implication of this procedure is the formation of a least action principle for the balance of energy with dissipation. The corresponding action functional enables us to establish a complete analytic mechanics for thermomechanical systems: a Lagrangian-Hamiltonian theory, integrals of motion, bracket formalism, and Noether?s theorem. Furthermore, we apply our procedure iteratively and produce an infinite sequence of interlocked variational principles, a variational hierarchy, where at each level or iteration the full implication of the least action principle can be shown again.
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Meyer, Fabian, Christian Rohde, and Jan Giesselmann. "A posteriori error analysis for random scalar conservation laws using the stochastic Galerkin method." IMA Journal of Numerical Analysis 40, no. 2 (February 15, 2019): 1094–121. http://dx.doi.org/10.1093/imanum/drz004.
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Abstract In this article we present an a posteriori error estimator for the spatial–stochastic error of a Galerkin-type discretization of an initial value problem for a random hyperbolic conservation law. For the stochastic discretization we use the stochastic Galerkin method and for the spatial–temporal discretization of the stochastic Galerkin system a Runge–Kutta discontinuous Galerkin method. The estimator is obtained using smooth reconstructions of the discrete solution. Combined with the relative entropy stability framework of Dafermos (2016, Hyperbolic Conservation Laws in Continuum Physics, 4th edn., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 325, Berlin, Springer, pp. xxxviii+826), this leads to computable error bounds for the space–stochastic discretization error. Moreover, it turns out that the error estimator admits a splitting into one part representing the spatial error, and a remaining term, which can be interpreted as the stochastic error. This decomposition allows us to balance the errors arising from spatial and stochastic discretization. We conclude with some numerical examples confirming the theoretical findings.
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Wang, Yanli, and Shudao Zhang. "Solving Vlasov-Poisson-Fokker-Planck Equations using NRxx method." Communications in Computational Physics 21, no. 3 (February 7, 2017): 782–807. http://dx.doi.org/10.4208/cicp.220415.080816a.
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AbstractWe present a numerical method to solve the Vlasov-Poisson-Fokker-Planck (VPFP) system using the NRxx method proposed in [4, 7, 9]. A globally hyperbolic moment system similar to that in [23] is derived. In this system, the Fokker-Planck (FP) operator term is reduced into the linear combination of the moment coefficients, which can be solved analytically under proper truncation. The non-splitting method, which can keep mass conservation and the balance law of the total momentum, is used to solve the whole system. A numerical problem for the VPFP system with an analytic solution is presented to indicate the spectral convergence with the moment number and the linear convergence with the grid size. Two more numerical experiments are tested to demonstrate the stability and accuracy of the NRxx method when applied to the VPFP system.
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Cai, Yifan, Quanyi Wang, Meng Liu, Yunqing Jiang, Tongfei Zou, Yunru Wang, Qingsong Li, et al. "Tensile Behavior, Constitutive Model, and Deformation Mechanisms of MarBN Steel at Various Temperatures and Strain Rates." Materials 15, no. 24 (December 7, 2022): 8745. http://dx.doi.org/10.3390/ma15248745.
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To reduce harmful gas emission and improve the operational efficiency, advanced ultra-supercritical power plants put forward higher requirements on the high temperature mechanical properties of applied materials. In this paper, the tensile behavior and deformation mechanisms of MarBN steel are discussed at different strain rates (5 × 10−3 s−1, 5 × 10−4 s−1, and 5 × 10−5 s−1) under room temperature and 630 °C. The results show that the tensile behavior of the alloy is dependent on temperature and strain rate, which derived from the balance between the average dislocation velocity and dislocation density. Furthermore, observed dynamic recrystallized grains under severe deformation reveal the existence of dynamic recovery at 630 °C, which increases the elongation compared to room temperature. Finally, three typical constitutive equations are used to quantitatively describe the tensile deformation behavior of MarBN steel under different strain rates and temperatures. Meanwhile, the constitutive model of flow stress for MarBN steel is developed based on the hyperbolic sine law.
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De Marchis, Mauro, Gabriele Freni, and Barbara Milici. "Experimental analysis of pressure-discharge relationship in a private water supply tank." Journal of Hydroinformatics 20, no. 3 (March 21, 2018): 608–21. http://dx.doi.org/10.2166/hydro.2018.135.
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Abstract In Mediterranean countries, users are often equipped with private tanks, which provide a temporary water storage capacity, able to compensate service interruptions due to either scarcity or irregularity of water supply. In the presence of private water storage, water supply is no longer linked to users' consumption and network-operating conditions can be off-design, therefore specific models have to be introduced in simulation models of water distribution networks. Here, a new mathematical model is proposed that is able to reproduce a tank's emptying/filling cycles. Specifically, by means of experimental analysis, a hyperbolic tangent law was tested to reproduce the filling process for private tanks. The flow rate is calculated by means of the classical Torricelli law, in which the float valve emitter coefficient and the valve area are calculated using a function that takes into account the water level within the private tank. The comparison obtained through the mathematical model and those observed from experiments confirmed the ability of the model to predict the flow rate balance within private tanks. The results show that the model is suitable for any length of float valve branch. The mathematical system can be easily used in a transient model to correctly estimate the supplied demand.
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Trapeznikova, Marina, Natalia Churbanova, and Antonina Chechina. "Different-Scale Simulation of Flows in Porous Media." EPJ Web of Conferences 248 (2021): 01016. http://dx.doi.org/10.1051/epjconf/202124801016.
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The paper considers the development of algorithms for an adequate description of processes of different scales in porous media. The choice of a computational technique is determined by the reference size of the problem being solved. Models of porous medium flow under Darcy’s law, neglecting the medium microstructure, are used for the simulation at macro-scale. While at micro-scale, a direct description of fluid flow in porous channels with complex geometry by means of gas dynamic equations is used. In the first case the proposed model of non-isothermal multiphase multicomponent flow in a porous medium includes the mass balance and total energy conservation equations modified by analogy to the known quasi-gas dynamic equations. The model features are the introduction of minimal reference scales in space and in time and the change of the system type from parabolic to hyperbolic to increase the stability of explicit difference schemes applied for approximation. In the second case the dimensionless form of the quasi-gas dynamic system with pressure decomposition, developed by the authors earlier, is adapted to the simulation of flows in the pore space. The fictitious domain method is proposed to reproduce the core microstructure. The developed approaches have been verified by test predictions.
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BANACH, ZBIGNIEW, and WIESLAW LARECKI. "EVOLUTION OF CENTRAL MOMENTS FOR A GENERAL-RELATIVISTIC BOLTZMANN EQUATION: THE CLOSURE BY ENTROPY MAXIMIZATION." Reviews in Mathematical Physics 14, no. 05 (May 2002): 469–510. http://dx.doi.org/10.1142/s0129055x02001223.
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Beginning from the relativistic Boltzmann equation in a curved space-time, and assuming that there exists a fiducial congruence of timelike world lines with four-velocity vector field u, it is the aim of this paper to present a systematic derivation of a hierarchy of closed systems of moment equations. These systems are found by using the closure by entropy maximization. Our concepts are primarily applied to the formalism of central moments because if an alternative and more familiar theory of covariant moments is taken into account, then the method of maximum entropy is ill-defined in a neighborhood of equilibrium states. The central moments are not covariant in the following sense: two observers looking at the same relativistic gas will, in general, extract two different sets of central moments, not related to each other by a tensorial linear transformation. After a brief review of the formalism of trace-free symmetric spacelike tensors, the differential equations for irreducible central moments are obtained and compared with those of Ellis et al. [Ann. Phys. (NY)150 (1983) 455]. We derive some auxiliary algebraic identities which involve the set of central moments and the corresponding set of Lagrange multipliers; these identities enable us to show that there is an additional balance law interpreted as the equation of balance of entropy. The above results are valid for an arbitrary choice of the Lorentzian metric g and the four-velocity vector field u. Later, the definition of u as in the well-known theory of Arnowitt, Deser, and Misner is proposed in order to construct a hierarchy of symmetric hyperbolic systems of field equations. Also, the Eckart and Landau–Lifshitz definitions of u are discussed. Specifically, it is demonstrated that they lead, in general, to the systems of nonconservative equations.
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Webb, G. M., M. Brio, and G. P. Zank. "Steady MHD flows with an ignorable co-ordinate and the potential transonic flow equation." Journal of Plasma Physics 52, no. 1 (August 1994): 141–88. http://dx.doi.org/10.1017/s0022377800017827.
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The paper explores the interrelationship between the generalized Grad-Shafranov equation, or trans-field force balance equation, for steady MHD flows with an ingnorable co-ordinate, and work by Imai on field-aligned MHD flows. The development of Imai, assumes at the outset that the fluid velocity V is parallel to the magnetic field B, and exploits an analogy with steady compressible irrotational flow in ordinary fluid dynamics. In Imai's analysis the magnetic induction B is written in the form B = σb, where , and MA is the appropriate Alfvén Mach number. Gauss' law Δ. B = Δ. (σb) = 0 then plays a role analogous to the mass continuity equation in ordinary fluid dynamics, where σ corresponds to the density of the pseudo-fluid. Imai's analysis leads to a transonic equation for the field potential φ defined by b = Δφ. For a restricted class of flows the trans-field force balance equation formulation also leads to the transonic potential flow equation, but the assumption of an ignorable co-ordinate allows for the possibility of non-field-aligned flows with non-zero electric field potential ΦE The characteristics of the generalized Grad—Shafranov equation are related to the Mach cone and the group velocity surface for linear magnetosonic waves. The corresponding forms of the characteristics for the potential transonic flow equation in the (x, y) plane and in the (bx, by) hodograph plane are discussed. Sample solutions of the potential transonic flow equation for radial, helical and spiral flows are obtained by means of the hodograph transformation, and are used to illustrate the differences between hyperbolic and elliptic flows. The potential transonic flow equation is obtained for the case of an ignorable co-ordinate z of a rectangular Cartesian co-ordinate system (x, y, z), and also for the case of flows with an ignorable co-ordinate of a spherical polar co-ordinate system (r, θ, ω). Astrophysical applications are briefly discussed.
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Zhao, Ningyu, Hongjun Wu, Yi Song, and Shun Xiang. "Calculation of Negative Frictional Resistance of Foundation Pile in Deep Fill Foundation." Mathematical Problems in Engineering 2021 (February 27, 2021): 1–8. http://dx.doi.org/10.1155/2021/6640777.
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In deep fill foundations, the pile foundation might suffer from negative frictional resistance (NFR) due to the consolidation and settlement of the soil. The NFR will cause the pile to settle excessively and reduce its bearing capacity. However, there are not yet many accurate methods to calculate the NFR of foundation piles in deep fill foundations. To make up for the gap, this paper carries out shear tests on the pile-soil interface and discusses the mechanism of pile-side frictional resistance. Considering the distribution law of pile-side frictional resistance with depth, the authors proposed a piecewise calculation model for pile-side frictional resistance, which couples the hyperbolic model and effective stress method. Then, the energy balance equation of the pile when the NFR occurs was established in the light of the energy transfer of the pile-soil system during the settlement of the soil around the pile. Furthermore, the calculation formulas of the axial force and displacement of the pile at different depths were derived, considering the pile-soil displacement and the potential energy change of the pile-soil system. The proposed method was applied to calculate the NFR of the foundation pile in a construction site, and the calculated results were compared with the measured data. The results show that the axial force-depth curve of the pile obtained through theoretical calculation agrees well with the measured data. Hence, our method can accurately reveal the mechanical features of the pile foundation in deep fill foundations.
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Rzayev, A. H., G. A. Guluyev, F. H. Pashayev, As H. Rzayev, and R. Sh Asadova. "Mathematical Models for Determining the Distribution of Fluid Flow Temperature along the Wellbore and Horizontal Pipeline." Mekhatronika, Avtomatizatsiya, Upravlenie 21, no. 6 (June 4, 2020): 337–47. http://dx.doi.org/10.17587/mau.21.337-347.
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This paper presents a proposed new indirect method determining instantly oil well debit using developed mathematical models. As a result integrated analysis using the models it has been revealed correlation between oil well debit and well throw out flow temperature. Therefore putting purpose was obtained. Mathematical models are developed for the distribution of fluid flow temperature along the length of the tubing from the well bottom to the wellhead and along the length of the oil pipeline from the collector of oil wells to the oil treatment unit. On the basis of experimental data, the authors propose formulas in the form of the relationship between oil emulsion (OE) viscosity, the flow temperature and concentration of water globule in OE and the coefficient of heat transfer from the fluid flow in the wellbore (WB) to the rock, and heat capacity and thermal conductivity of gas, water, rock and steel of the WB walls. This effect is demonstrated in the constructed diagrams. It is shown bottom temperature jump as a result of the Joule Thomson drosseling effect then connective transmitted up at flow rate v. In such case well-head or well outlet oil mixture (OM) flow temperature depend more of volume of stream flow than of bottom hole temperature. Thought in the paper, do not taking into consideration great casing annulus areas influence to the well outlet flow temperature. As shown from supporting paper the relative values og the thermal conductivity of the liquid column and gas column present in the casing annulus order less than well bore (WB) wall thermal conductivity. Consequently well outlet OM flow temperature will depends not only of the volume of stream flow, also of the bottom hole temperature and of the gas column and liquid column.A new method for determining the oil well flow rate by measuring the downstream temperature is developed. A mathematical model is proposed that allows calculating the thermal profile of the fluid along the wellbore for determining the oil well flow rate with account of the geothermal gradient in the rock surrounding the wellbore. It is shown, that unlike the existing methods the new proposed method allows determining the instantaneous discharge of a well very easily. One of the actual challenges in fluid (oil, water and gas) transportation from wells to oil treatment installation is determination of a law of temperature distribution along the length of a pipeline at low ambient temperature. That temperature leads to increase in viscosity and deposition of wax on inner surface of a pipe. To overcome that challenge it is needed to consider several defining characteristics of formation fluid (FF) flow. Complexity of a solution is caused by two factors. From the one hand, in most cases (especially on a late stage of field development) FF is an oil emulsion (OE) that contains gas bubbles. From the other hand, temperature gradient between fluid flow and the environment has significant value (especially in the winter period of the year). At the same time, the higher content of emulsified water droplets (EWD) in OE and lower flow temperature, the higher FF viscosity, and consequently productivity (efficiency) of oil pumping system is reduced. Performed research and analysis of field experimental data showed that a function of oil viscosity versus temperature has a hyperbolic law; a function of OE viscosity versus concentration of EWD has a parabolic one. A heat balance for a certain section of a pipeline in steady state of fluid motion using a method of separation of variables was established taking into account above mentioned factors, Fourier’s empirical laws on heat conductivity and Newton’s law on heat transfer. As a result, unlike existing works, an exponential law of distribution of temperature along the length of a pipeline is obtained. A law takes into account nonlinear nature of change in viscosity of OE from change in temperature of flow and concentration of water in an emulsion. As a result, in contrast to the existing works, the proposed exponential law of temperature distribution along the length of the pipeline is obtained, taking into account the nonlinear nature of variation of OE viscosity with the change in the flow temperature and the concentration of water in the emulsion. The results of the calculation are presented in the form of a table and graphs.
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Murillo, J., S. Martinez-Aranda, A. Navas-Montilla, and P. García-Navarro. "Adaptation of flux-based solvers to 2D two-layer shallow flows with variable density including numerical treatment of the loss of hyperbolicity and drying/wetting fronts." Journal of Hydroinformatics 22, no. 5 (July 17, 2020): 972–1014. http://dx.doi.org/10.2166/hydro.2020.207.
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Abstract An important feature of the two-layer shallow flow model is that the resulting system of equations cannot be expressed in conservation-law form. Here, the HLLS and ARoe solvers, derived initially for systems of conservation laws, are reformulated and applied to the two-layer shallow flows in a great variety of problems. Their resulting extension and combination allows us to overcome the loss of the hyperbolic character, ensuring energy or exactly balanced property, guarantees positivity of the solution, and provides a correct drying/wetting advance front without requiring tuning parameters. As a result, in those cases where the rich description of internal and external waves cannot be provided by the ARoe solver, HLLS is applied. Variable density is considered in each layer as a result of a bulk density driven by the mixture of different constituents. A wide variety of test cases is presented confirming the properties of this combination, including exactly balanced scenarios in subcritical and subcritical-transcritical scenarios, dam-break problems over bed variations and wet/dry fronts, non-hyperbolic conditions, transcritical exchange flow with loss of hyperbolicity. Despite the complexity of the test cases presented here, accurate and stable simulations are guaranteed, ensuring positivity of the solution without decreasing the time step.
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Ngatcha Ndengna, Arno Roland, Yves Mimbeu, Raphael Onguene, Sévérin Nguiya, and Abdou Njifenjou. "A Novel Sediment Transport Model (STM) Accounting Phase Lag Effect. A Resonance Condition." WSEAS TRANSACTIONS ON FLUID MECHANICS 17 (December 16, 2022): 189–211. http://dx.doi.org/10.37394/232013.2022.17.19.
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The classical Exner model coupled with a bed-load sediment flux formula is widely used to describe the morphodynamics of coastal environments. However, the main drawbacks of this model are (i) Lack of robustness, (ii) Lack of differentiation between sediment and fluid velocities, and (iii) Generation of instabilities when the interactions between sediment and fluid flow become more important. Moreover, Exner's model does not allow us to know with which characteristic velocity the bottom is moving. This set of drawbacks weakens the effectiveness of most sediment transport models proposed in the literature, particularly the Exner model. In this work, we reformulate the bed-load equation and we propose a new averaged sediment transport model for application in coastal or estuarine environments. The proposed model incorporates phase shift effects into the bed-load equation. The bedform's characteristic velocity, sediment, and fluid velocity are differentiated. We developed a new first-order, well-balanced, positivity-preserving, path-preserving, and central wind (WBPP-PCCU) scheme to solve the proposed hyperbolic sediment transport model (HSTM). We used the Averaging Essentially Non-Oscillatory (AENO) reconstruction coupled with the third-order Runge-Kutta Semi-Implicit (SI-RK3) method to achieve second-order accuracy. The balance and positivity of the water depth properties were proven. In this work, a resonance condition is proposed. The model facilitates the application of several other schemes such as Roe, HLLC, HLLEM, PVM (polynomial viscosity matrix), RVM (rational viscosity matrix), which require the diagonalization of the Jacobian matrix. The accuracy, robustness, positivity preservation, and equilibrium properties of the resulting model are evaluated using a series of carefully selected test cases. The proposed model provides an excellent ability to simulate sediment transport in a wide range of coastal environments.
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Xia, Guofeng, Liwei Yang, and Fenghong Xiang. "Event-Triggered Neural Sliding Mode Guaranteed Performance Control." Processes 10, no. 9 (September 1, 2022): 1742. http://dx.doi.org/10.3390/pr10091742.
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To solve the trajectory tracking control problem for a class of nonlinear systems with time-varying parameter uncertainties and unknown control directions, this paper proposed a neural sliding mode control strategy with prescribed performance against event-triggered disturbance. First, an enhanced finite-time prescribed performance function and a compensation term containing the Hyperbolic Tangent function are introduced to design a non-singular fast terminal sliding mode (NFTSM) surface to eliminate the singularity in the terminal sliding mode control and speed up the convergence in the balanced unit-loop neighborhood. This sliding surface guarantees arbitrarily small overshoot and fast convergence speed even when triggering mistakes. Meanwhile, we utilize the Nussbaum gain function to solve the problem of unknown control directions and unknown time-varying parameters and design a self-recurrent wavelet neural network (SRWNN) to handle the uncertainty terms in the system. In addition, we use a non-periodic relative threshold event-triggered mechanism to design a new trajectory tracking control law so that the conventional time-triggered mechanism has overcome a significant resource consumption problem. Finally, we proved that all the closed-loop signals are eventually uniformly bounded according to the stability analysis theory, and the Zeno phenomenon can be eliminated. The method in this paper has a better tracking effect and faster response and can obtain better control performance with lower control energy than the traditional NFTSM method, which is verified in inverted pendulum and ball and plate system.
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DARMANI KUHI, H., E. KEBREAB, S. LOPEZ, and J. FRANCE. "A comparative evaluation of functions for the analysis of growth in male broilers." Journal of Agricultural Science 140, no. 4 (June 2003): 451–59. http://dx.doi.org/10.1017/s0021859603003149.
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Data from six studies with male broilers fed diets covering a wide range of energy and protein were used in the current two analyses. In the first analysis, five models, specifically re-parameterized for analysing energy balance data, were evaluated for their ability to determine metabolizable energy intake at maintenance and efficiency of utilization of metabolizable energy intake for producing gain. In addition to the straight line, two types of functional form were used. They were forms describing (i) diminishing returns behaviour (monomolecular and rectangular hyperbola) and (ii) sigmoidal behaviour with a fixed point of inflection (Gompertz and logistic). These models determined metabolizable energy requirement for maintenance to be in the range 437–573 kJ/kg of body weight/day depending on the model. The values determined for average net energy requirement for body weight gain varied from 7·9 to 11·2 kJ/g of body weight. These values show good agreement with previous studies. In the second analysis, three types of function were assessed as candidates for describing the relationship between body weight and cumulative metabolizable energy intake. The functions used were: (a) monomolecular (diminishing returns behaviour), (b) Gompertz (smooth sigmoidal behaviour with a fixed point of inflection) and (c) Lopez, France and Richards (diminishing returns and sigmoidal behaviour with a variable point of inflection). The results of this analysis demonstrated that equations capable of mimicking the law of diminishing returns describe accurately the relationship between body weight and cumulative metabolizable energy intake in broilers.
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KUHI, H. DARMANI, F. REZAEE, A. FARIDI, J. FRANCE, M. MOTTAGHITALAB, and E. KEBREAB. "Application of the law of diminishing returns for partitioning metabolizable energy and crude protein intake between maintenance and growth in growing male and female broiler breeder pullets." Journal of Agricultural Science 149, no. 3 (February 2, 2011): 385–94. http://dx.doi.org/10.1017/s0021859611000062.
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SUMMARYThe suitability of diminishing return functions such as the monomolecular and rectangular hyperbola equations, specifically re-parameterized for analysing energy balance data, has been investigated in ruminants, pigs, broilers and turkeys. In the current study, these equations were applied to a total of six time course profiles with male and female broiler breeder pullets (Ross 308 between 1 and 21 weeks of age, n=63 for each sex) in order to provide estimates for energy and protein requirements for maintenance and growth. Non-linear regression was used to estimate parameters and combine them to determine other biological indicators. All statistical computations were implemented in SAS (SAS 2000) by means of the NLMIXED procedure. The best-performing model was identified based on model behaviour when fitting the data, biologically meaningful parameter estimates and statistical performance. In spite of similarity between the biological indicators calculated for each sex using parameter estimates of the two models, quantitative examination of their predictive ability by error measurement indices showed the monomolecular model was superior. The metabolizable energy (ME) and crude protein (CP) requirements for maintenance ranged from 365 to 432 kJ/kg live weight (LW)/d and from 4·3 to 4·9 g/kg LW/d, respectively. The average ME and CP utilization ranged from 11·30 to 12·10 kJ/g body weight (BW) gain and from 0·61 to 0·64 g/g CP intake, respectively. The results obtained using the models were within the range reported by different researchers. Utilization of ME and CP for gain was more efficient at low levels of energy and protein intake, and gradually decreased as the level of energy and protein intakes increased. In conclusion, the models described herein were considered advantageous because they could predict the magnitude and direction of the responses of growing broiler breeder pullets to dietary ME and CP intake, which can be used in choosing and developing special feeding programs to decrease production costs.
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Mantri, Yogiraj, and Sebastian Noelle. "Well-balanced discontinuous Galerkin scheme for 2 × 2 hyperbolic balance law." Journal of Computational Physics, November 2020, 110011. http://dx.doi.org/10.1016/j.jcp.2020.110011.
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Xu, Tianyuan, Chunhua Jin, and Shanming Ji. "Discontinuous traveling waves for scalar hyperbolic-parabolic balance law." Boundary Value Problems 2016, no. 1 (February 5, 2016). http://dx.doi.org/10.1186/s13661-016-0540-8.
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Hernandez-Duenas, Gerardo, and Jorge Balbás. "A central-upwind scheme for two-layer shallow-water flows with friction and entrainment along channels." ESAIM: Mathematical Modelling and Numerical Analysis, September 3, 2021. http://dx.doi.org/10.1051/m2an/2021052.
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We present a new high-resolution, non-oscillatory semi-discrete central-upwind scheme for one-dimensional two-layer shallow-water flows with friction and entrainment along channels with arbitrary cross sections and bottom topography. These flows are described by a conditionally hyperbolic balance law with non-conservative products. A detailed description of the properties of the model is provided, including entropy inequalities and asymptotic approximations of the eigenvalues of the corresponding coefficient matrix. The scheme extends existing central-upwind semi-discrete numerical methods for hyperbolic conservation and balance laws and it satisfies two properties crucial for the accurate simulation of shallow-water flows: it {\it preserves the positivity} of the water depth for each layer, and it is {\it well balanced}, {\it i.e.}, the source terms arising from the geometry of the channel are discretized so as to balance the non-linear hyperbolic flux gradients. Along with the description of the scheme and proofs of these two properties, we present several numerical experiments that demonstrate the robustness of the numerical algorithm.
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Barker, Blake, Mathew Johnson, Pascal Noble, L. Miguel Rodrigues, and Kevin Zumbrun. "Whitham averaged equations and modulational stability of periodic traveling waves of a hyperbolic-parabolic balance law." Journées Équations aux dérivées partielles, 2010, 1–24. http://dx.doi.org/10.5802/jedp.60.
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Ibrahim, Israa A., Raad A. Hameed, Wafaa M. Taha, and Maan A. Rasheed. "New Path of Popularized Homogeneous Balance Method and Travelling Wave Solutions of a Nonlinear Klein-Gordon Equation." Iraqi Journal of Science, June 30, 2022, 2656–66. http://dx.doi.org/10.24996/ijs.2022.63.6.31.
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The aim of this paper is to obtain a set of traveling wave solutions for klein –Gorden equation with kerr law non-linearity. More precisely, we apply a new path of popularized homogeneous balance (HB) method in terms of using linear auxiliary equations to find the results of non-linear klein-Gorden equation, which is a fundamental approach to determine competent solutions. The solutions are achieved as the integration of exponential, hyperbolic, trigonometric and rational functions. Besides, some of the solutions are demonstrated by the3D graphics.
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Chejne, Farid, Whady F. Florez, Juan C. Maya, Javier Ordonez-Loza, and Manuel Garcia-Perez. "Physical Mathematical Modeling and Simulation Based on Hyperbolic Heat Transfer for High Heating Rate Processes in Biomass Pyrolysis." Journal of Non-Equilibrium Thermodynamics, September 10, 2022. http://dx.doi.org/10.1515/jnet-2022-0028.
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Abstract This paper explores the hyperbolic heat transfer effects in processes involving high heating rates. The behavior of the model is analyzed in detail under different boundary conditions and the circumstances under which a non-Fourier law could be used to describe thermal conduction processes established from physical mathematical analysis. Finally, the model developed here is coupled to a previous population balance framework to predict the bubbling phenomenon that occurs during the fast pyrolysis of biomass. We found that a transient overheating occurs in the central zone of the generated liquid phase due to the high heating rates that take place during that process.
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Aguilar-López, Ricardo. "Outlet Temperature Regulation for a Class of Plug Flow Chemical Reactor via Nonlinear Feedback." International Journal of Chemical Reactor Engineering 5, no. 1 (June 14, 2007). http://dx.doi.org/10.2202/1542-6580.1389.
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The aim of this paper is the regulation of the temperature, at outlet conditions, for a class of plug flow chemical reactors. The considered reactor is modeled by a set of hyperbolic partial differential equations, as related to mass and energy balances, with consideration that the measured output for this kind of systems is the outlet temperature, as is usual with industrial practice. It is proposed that in nonlinear feedback which contains a proportional contribution of the named regulation error plus a high order sliding-mode term-to-tray to compensate for the convective transport, the nonlinear terms and disturbances employing the stabilizing effects of the sliding modes have a satisfactory performance. A theoretical frame for the stabilization properties of the proposed controller is provided and numerical simulations illustrate the corresponding performance, which is compared with a well tuned PI control law.
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Maitland-Davies, Cai, and Oliver Bühler. "Two-way wave–vortex interactions in a Lagrangian-mean shallow water model." Journal of Fluid Mechanics 954 (December 20, 2022). http://dx.doi.org/10.1017/jfm.2022.889.
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We derive and investigate numerically a reduced model for wave–vortex interactions involving non-dispersive waves, which we study in a two-dimensional shallow water system with an eye towards applications in atmosphere–ocean fluid dynamics. The model consists of a coupled set of nonlinear partial differential equations for the Lagrangian-mean velocity and the wave-related pseudomomentum vector field defined in generalized Lagrangian-mean theory. It allows for two-way interactions between the waves and the balanced flow that is controlled by the distribution of Lagrangian-mean potential vorticity, and for strong solutions it features a desirable exact energy conservation law for the sum of wave energy and mean flow energy. Our model goes beyond standard ray tracing as we can derive weak solutions that contain discontinuities in the pseudomomentum field, using the theory of weakly hyperbolic systems. This allows caustics to form without predicting infinite wave amplitudes, as would be the case in the standard ray-tracing theory. Suitable wave forcing and dissipation terms are added to the model and a numerical scheme for the model is implemented as a coupled set of pseudo-spectral and finite-volume integrators. Idealized examples of interactions between wavepackets and simple vortex structures are presented to illustrate the model dynamics. The unforced and non-dissipative simulations suggest a heuristic rule of ‘greedy’ waves, i.e. in the long run the wave field always extracts energy from the mean flow.