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Journal articles on the topic 'Hyperbolic balance law'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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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 (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 (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 (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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Cimmelli, Vito Antonio. "Heat-Flux Relaxation and the Possibility of Spatial Interactions in Higher-Grade Materials." Mathematics 13, no. 4 (2025): 599. https://doi.org/10.3390/math13040599.

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We investigate the thermodynamic compatibility of weakly nonlocal materials with constitutive equations depending on the third spatial gradient of the deformation and the heat flux ruled by an independent balance law. In such materials, the molecules experience long-range interactions. Examples of biological systems undergoing nonlocal interactions are given. Under the hypothesis of weak nonlocality (constitutive equations depending on the gradients of the unknown fields), we exploit the second law of thermodynamics by considering the spatial differential consequences (gradients) of the balanc

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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 (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

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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 (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 Phy

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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, br

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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 (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 prese

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Cai, Yifan, Quanyi Wang, Meng Liu, et al. "Tensile Behavior, Constitutive Model, and Deformation Mechanisms of MarBN Steel at Various Temperatures and Strain Rates." Materials 15, no. 24 (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 dislocatio

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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 (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 m

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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 porou

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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 (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 neigh

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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 (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 play

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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 propo

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Lukianov, Pavlo, and Lin Song. "Compact analogs of the models of vortex flows generated by aircraft flight." Aerospace Technic and Technology, no. 5 (October 3, 2023): 4–20. http://dx.doi.org/10.32620/aktt.2023.5.01.

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The subject of this work is the development of compact analogs of vortex flows models, which are used in the modeling of vortex structures observed during the flight of an aircraft and the motion of a body in a fluid. In particular, two significant misunderstandings prevailing in this area of science are highlighted. The first misunderstanding is that the stationary motion of fluid parcels in a circle is treated as an inviscid vortex. Therefore, any vortex flow model that does not explicitly contain viscosity is considered to describe inviscid vortex motion. It has been proven that this is not

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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 (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 autho

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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 (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 param

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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

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Kang, Chuyan, Sijia Huo, Yingbo Yue, et al. "Analysis of MMC Circulation Phase Sequence Separation and Research on Flexible Sliding Mode Circulation Suppression Method." Energies 18, no. 4 (2025): 960. https://doi.org/10.3390/en18040960.

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Modular multilevel converter (MMC) circulating current suppression is an effective method in improving power conversion quality. However, due to the complex composition of circulation under a three-phase imbalanced state, as well as the limitations of existing sliding mode circulation suppression methods that can easily cause high-frequency oscillation in the system, the circulation suppression effectiveness still needs to be further improved. Firstly, this article clarifies the phase sequence law and key control factors of the circulation by separating the MMC circulation phase sequence and d

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Xia, Guofeng, Liwei Yang, and Fenghong Xiang. "Event-Triggered Neural Sliding Mode Guaranteed Performance Control." Processes 10, no. 9 (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 balan

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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 (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

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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 (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 combin

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Galashov, Nikolay N., Alexander A. Tubolev, Evgeny S. Boldushevsky, and Alexander A. Minor. "Impact of steam flow into a combustion chamber of a contact gas-steam installation on its energy characteristics." Bulletin of the Tomsk Polytechnic University Geo Assets Engineering 335, no. 2 (2024): 48–59. http://dx.doi.org/10.18799/24131830/2024/2/4436.

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Relevance. Reduction of natural gas consumption and emissions of harmful substances into the environment based on introduction of water vapor into a combustion chamber of a contact gas-steam installation. Aim. To carry out numerical studies on the influence of relative steam flow into the combustion chamber of the contact gas-steam installation on its energy characteristics. Objects. Contact gas-steam installations based on gas turbines with steam injection into the combustion chamber. Methods. Numerical methods based on material and energy balances of systems and elements of gas-steam install

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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 (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

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Abreu, Eduardo, Eduardo Pandini, and Wanderson Lambert. "An Enhanced Lagrangian‐Eulerian Method for a Class of Balance Laws: Numerical Analysis via a Weak Asymptotic Method With Applications." Numerical Methods for Partial Differential Equations 41, no. 1 (2024). https://doi.org/10.1002/num.23163.

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ABSTRACTIn this work, we designed and implemented an enhanced Lagrangian‐Eulerian numerical method for solving a wide range of nonlinear balance laws, including systems of hyperbolic equations with source terms. We developed both fully discrete and semi‐discrete formulations, and extended the concept of No‐Flow curves to this general class of nonlinear balance laws. We conducted a numerical convergence study using weak asymptotic analysis, which involved investigating the existence, uniqueness, and regularity of entropy‐weak solutions computed with our scheme. The proposed method is Riemann‐so

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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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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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Thein, Ferdinand. "Stabilization of a Multi‐Dimensional System of Hyperbolic Balance Laws – A Case Study." PAMM 22, no. 1 (2023). http://dx.doi.org/10.1002/pamm.202200056.

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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 genera

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Patten, Michael A., and Jutta C. Burger. "Hyperbolic discounting underpins response curves of mammalian avoidance behaviour." Biology Letters 20, no. 7 (2024). http://dx.doi.org/10.1098/rsbl.2024.0054.

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As humans clear natural habitat, they are brought into increased conflict with wild animals. Some conflict is direct (e.g. elevated exposure of people to predators), some indirect (e.g. abandoning suitable habitat because of human activity). The magnitude of avoidance is expected to track frequency of human activity, but the type of response is an open question. We postulated that animals do not respond passively to increased disturbance nor does response follow a power law; instead, their ability to estimate magnitude leads to ‘discounting’ behaviour, as in classic time-to-reward economic mod

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Rukolaine, Sergey A. "Integral Representation of Solutions to Initial‐Boundary Value Problems on a Finite Interval in the Framework of the Hyperbolic Heat Equation." Mathematical Methods in the Applied Sciences, June 11, 2025. https://doi.org/10.1002/mma.11140.

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ABSTRACTWe consider initial‐boundary value problems on a finite interval for the system of the energy balance equation and modified Fourier's law (constitutive equation, commonly called the Cattaneo equation) describing temperature (or internal energy) and heat flux. This hyperbolic system of first‐order partial differential equations is the simplest model of non‐Fourier heat conduction. Boundary conditions include various models of behavior of a physical system at the boundaries, including boundary conditions describing Newton's law, which states that the heat flux at the boundary is directly

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Ханхасаев, В. Н., and Э. В. Дармахеев. "ON SOME APPLICATIONS OF THE HYPERBOLIC HEAT EQUATION AND THE METHODS FOR SOLVING IT." Журнал «Математические заметки СВФУ», no. 1 (May 21, 2018). http://dx.doi.org/10.25587/svfu.2018.1.12772.

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Создание новых технологических процессов, основанных на использовании высокоинтенсивных потоков энергии, вынуждает при определении температурного состояния учитывать конечную скорость распространения тепла. Этот учет может быть осуществлен при помощи гиперболического уравнения теплопроводности, полученного А. В. Лыковым в рамках неравновесной феноменологической термодинамики как следствие обобщения закона Фурье для потоков и уравнения теплового баланса. В прежних работах В. Н. Ханхасаева моделировался процесс коммутационного отключения электрической дуги в спутном потоке газа с использованием

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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 (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 nonl

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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 vortici

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Emmerson, Parker. "INFINITY TENSORS, THE STRANGE ATTRACTOR, AND THE RIEMANN HYPOTHESIS: AN ACCURATE REWORDING OF THE RIEMANN HYPOTHESIS YIELDS FORMAL PROOF." March 1, 2023. https://doi.org/10.5281/zenodo.7686996.

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Abstract:

Theorem: The Riemann Hypothesis can be reworded to indicate that the real part of one half always balanced at the infinity tensor by stating that the Riemann zeta function has no more than an infinity tensor’s worth of zeros on the critical line. For something to be true in proof, it often requires an outside perspective. In other words, there must be some exterior, alternate perspective or system on or applied to the hypothesis from which the proof can be derived. Two perspectives, essentially must agree. Here, a fractal web with infinitesimal 3D strange attractor is theorized as presen

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