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1
Després, Bruno, and Frédéric Lagoutière. "Un schéma non linéaire anti-dissipatif pour l'équation d'advection linéaire." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 328, no. 10 (May 1999): 939–43. http://dx.doi.org/10.1016/s0764-4442(99)80301-2.
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2
Mamouri, Saïd, and Adnan Ibrahimbegovic. "Schéma dissipatif HHT d'intégration temporelle pour un modèle de poutre en grandes rotations." Revue Européenne des Éléments Finis 10, no. 5 (January 2001): 607–23. http://dx.doi.org/10.1080/12506559.2001.9737562.
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3
Huang, Shiyi, and Zhixue Li. "Optimization and Application of Coal Pillar in Fully Mechanized Mining Face based on Energy Analysis." International Journal of Energy 3, no. 3 (December 1, 2023): 47–51. http://dx.doi.org/10.54097/ije.v3i3.011.
Повний текст джерелаАнотація:
Based on the theory of energy dissipation, a numerical model of goaf excavation was established by FLAC3D based on the backflow channel of Heilong Coal Industry 2202. The dissipative energy distribution characteristics of coal pillars with different widths were studied, and the dissipative energy evolution law of surrounding rock of goaf roadway was analyzed. With the increase of the width of coal pillar, the width of elastic core zone is positively correlated with the bearing capacity. The peak value of dissipated energy density decreases with the increase of the width of coal pillar, and the concentration degree and region of dissipated energy density on the side of coal pillar are greater than that on the side of solid coal pillar. The project is applied to Heilong 2201 working face, and the optimum width of coal pillar and its supporting scheme are given. The practice results show that when the width of coal pillar is 5m, the deformation of surrounding rock can be effectively controlled and the demand for safe and efficient production can be met.
4
Chen, Xiaowei, Mingzhan Song, and Songhe Song. "A Fourth Order Energy Dissipative Scheme for a Traffic Flow Model." Mathematics 8, no. 8 (July 28, 2020): 1238. http://dx.doi.org/10.3390/math8081238.
Повний текст джерелаАнотація:
We propose, analyze and numerically validate a new energy dissipative scheme for the Ginzburg–Landau equation by using the invariant energy quadratization approach. First, the Ginzburg–Landau equation is transformed into an equivalent formulation which possesses the quadratic energy dissipation law. After the space-discretization of the Fourier pseudo-spectral method, the semi-discrete system is proved to be energy dissipative. Using diagonally implicit Runge–Kutta scheme, the semi-discrete system is integrated in the time direction. Then the presented full-discrete scheme preserves the energy dissipation, which is beneficial to the numerical stability in long-time simulations. Several numerical experiments are provided to illustrate the effectiveness of the proposed scheme and verify the theoretical analysis.
5
Burkhardt, Ulrike, and Erich Becker. "A Consistent Diffusion–Dissipation Parameterization in the ECHAM Climate Model." Monthly Weather Review 134, no. 4 (April 1, 2006): 1194–204. http://dx.doi.org/10.1175/mwr3112.1.
Повний текст джерелаАнотація:
Abstract The diffusion–dissipation parameterizations usually adopted in GCMs are not physically consistent. Horizontal momentum diffusion, applied in the form of a hyperdiffusion, does not conserve angular momentum and the associated dissipative heating is commonly ignored. Dissipative heating associated with vertical momentum diffusion is often included, but in a way that is inconsistent with the second law of thermodynamics. New, physically consistent, dissipative heating schemes due to horizontal diffusion (Becker) and vertical diffusion (Becker, and Boville and Bretherton) have been developed and tested. These schemes have now been implemented in 19- and 39-level versions of the ECHAM4 climate model. The new horizontal scheme requires the replacement of the hyperdiffusion with a ∇2 scheme. Dissipation due to horizontal momentum diffusion is found to have maximum values in the upper troposphere/lower stratosphere in midlatitudes and in the winter hemispheric sponge layer, resulting in a warming of the area around the tropopause and of the polar vortex in Northern Hemispheric winter. Dissipation associated with vertical momentum diffusion is largest in the boundary layer. The change in parameterization acts to strengthen the vertical diffusion and therefore the associated dissipative heating. Dissipation due to vertical momentum diffusion has an indirect effect on the upper-tropospheric/stratospheric temperature field in northern winter, which is to cool and strengthen the northern polar vortex. The warming in the area of the tropopause resulting from the change in both dissipation parameterizations is quite similar in both model versions, whereas the response in the temperature of the northern polar vortex depends on the model version.
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HANSEN, JAKOB, ALEXEI KHOKHLOV, and IGOR NOVIKOV. "PROPERTIES OF FOUR NUMERICAL SCHEMES APPLIED TO A NONLINEAR SCALAR WAVE EQUATION WITH A GR-TYPE NONLINEARITY." International Journal of Modern Physics D 13, no. 05 (May 2004): 961–82. http://dx.doi.org/10.1142/s021827180400502x.
Повний текст джерелаАнотація:
We study stability, dispersion and dissipation properties of four numerical schemes (Itera-tive Crank–Nicolson, 3rd and 4th order Runge–Kutta and Courant–Fredrichs–Levy Nonlinear). By use of a Von Neumann analysis we study the schemes applied to a scalar linear wave equation as well as a scalar nonlinear wave equation with a type of nonlinearity present in GR-equations. Numerical testing is done to verify analytic results. We find that the method of lines (MOL) schemes are the most dispersive and dissipative schemes. The Courant–Fredrichs–Levy Nonlinear (CFLN) scheme is most accurate and least dispersive and dissipative, but the absence of dissipation at Nyquist frequency, if fact, puts it at a disadvantage in numerical simulation. Overall, the 4th order Runge–Kutta scheme, which has the least amount of dissipation among the MOL schemes, seems to be the most suitable compromise between the overall accuracy and damping at short wavelengths.
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Li, Guodong, Haifeng Zhang, Xingnan Li, Lihao Guo, Yanyan Gao, and Dandan Cai. "Numerical Simulation of Stepped Spillways with Front Step Deformation." Mathematical Problems in Engineering 2021 (March 29, 2021): 1–15. http://dx.doi.org/10.1155/2021/7079606.
Повний текст джерелаАнотація:
In order to solve the flood discharge problem of both small- and medium-sized warping dams in the Loess Plateau, a stepped spillway scheme, based on an ecological bag, to achieve full-section water flow and energy dissipation has been proposed in this paper. The hydraulic and energy dissipation characteristics of a stepped spillway layout scheme were studied using 3D numerical simulation. As the height of the dams is low and the spillways are short, the research has shown that the traditional single-step layout scheme leads to a low overall energy dissipation rate due to the small amount of energy dissipated in the initial steps. As a result of this, this paper has put forward two kinds of step layout schemes such as the shunt type and the staggered type for the initial steps. Through analysis of the flow state, the pressure distribution, and the total energy dissipation rate, the results have shown that shunt type and staggered type with front step deformation produced an obvious mixing of the water flow, fewer negative pressure areas, and a higher energy dissipation rate. The optimal energy dissipation rate of the staggered type reached 87.75%, and the maximum energy dissipation rate was increased by 27.97%.
8
Lin, F. B., and F. Sotiropoulos. "Assessment of Artificial Dissipation Models for Three-Dimensional Incompressible Flow Solutions." Journal of Fluids Engineering 119, no. 2 (June 1, 1997): 331–40. http://dx.doi.org/10.1115/1.2819138.
Повний текст джерелаАнотація:
Various approaches for constructing artificial dissipation terms for three-dimensional artificial compressibility algorithms are presented and evaluated. Two, second-order accurate, central-differencing schemes, with explicitly added scalar and matrix-valued fourth-difference artificial dissipation, respectively, and a third-order accurate flux-difference splitting upwind scheme are implemented in a multigrid time-stepping procedure and applied to calculate laminar flow through a strongly curved duct. Extensive grid-refinement studies are carried out to investigate the grid sensitivity of each discretization approach. The calculations indicate that even the finest mesh employed, consisting of over 700,000 grid nodes, is not sufficient to establish grid independent solutions. However, all three schemes appear to converge toward the same solution as the grid spacing approaches zero. The matrix-valued dissipation scheme introduces the least amount of artificial dissipation and should be expected to yield the most accurate solutions on a given mesh. The flux-difference splitting upwind scheme, on the other hand, is more dissipative and, thus, particularly sensitive to grid resolution, but exhibits the best overall convergence characteristics on grids with large aspect ratios.
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Zhang, Yang, Laiping Zhang, Xin He, and Xiaogang Deng. "An Improved Second-Order Finite-Volume Algorithm for Detached-Eddy Simulation Based on Hybrid Grids." Communications in Computational Physics 20, no. 2 (July 21, 2016): 459–85. http://dx.doi.org/10.4208/cicp.190915.240216a.
Повний текст джерелаАнотація:
AbstractA hybrid grid based second-order finite volume algorithm has been developed for Detached-Eddy Simulation (DES) of turbulent flows. To alleviate the effect caused by the numerical dissipation of the commonly used second order upwind schemes in implementing DES with unstructured computational fluid dynamics (CFD) algorithms, an improved second-order hybrid scheme is established through modifying the dissipation term of the standard Roe's flux-difference splitting scheme and the numerical dissipation of the scheme can be self-adapted according to the DES flow field information. By Fourier analysis, the dissipative and dispersive features of the new scheme are discussed. To validate the numerical method, DES formulations based on the two most popular background turbulence models, namely, the one equation Spalart-Allmaras (SA) turbulence model and the two equationk–ωShear Stress Transport model (SST), have been calibrated and tested with three typical numerical examples (decay of isotropic turbulence, NACA0021 airfoil at 60° incidence and 65° swept delta wing). Computational results indicate that the issue of numerical dissipation in implementing DES can be alleviated with the hybrid scheme, the resolution for turbulence structures is significantly improved and the corresponding solutions match the experimental data better. The results demonstrate the potentiality of the present DES solver for complex geometries.
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Zhao, Peng, and Yu Chuan Bai. "Study on Hydraulic Characteristics and Optimization of Siphon Channel with Two Inlets in Drydock." Applied Mechanics and Materials 638-640 (September 2014): 1285–92. http://dx.doi.org/10.4028/www.scientific.net/amm.638-640.1285.
Повний текст джерелаАнотація:
Compared with the siphon channel with one inlet, the siphon channel with two inlets has some problems such as low efficiency of flooding. Combining with the model test of siphon channel with two inlets in a drydock, three-dimensional numerical model was built to study the hydraulic characteristics of siphon channel system. The reliability of numerical model was confirmed by comparing the calculated value and measured value of hump pressure and flooding rate. Results of turbulent kinetic energy and dissipation rate indicate that flow kinetic energy is mainly dissipated by the friction and its impacting the wall behind partition and the effect of energy dissipation pillars are not obvious. By comparing flow state in front of energy dissipation section and flooding rate between design scheme and modified scheme, it is suggested that the guide wall should be dismantled to ameliorate flow state.
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Kish, Laszlo B. "Comments on “Sub-kBT Micro-Electromechanical Irreversible Logic Gate”." Fluctuation and Noise Letters 15, no. 04 (September 29, 2016): 1620001. http://dx.doi.org/10.1142/s0219477516200017.
Повний текст джерелаАнотація:
In a recent paper, [M. López-Suárez, I. Neri and L. Gammaitoni, Sub-[Formula: see text] micro-electromechanical irreversible logic gate, Nat. Commun. 7 (2016) 12068] the authors claimed that they demonstrated sub-[Formula: see text] energy dissipation at elementary logic operations. However, the argumentation is invalid because it neglects the dominant source of energy dissipation, namely, the charging energy of the capacitance of the input electrode, which totally dissipates during the full (0-1-0) cycle of logic values. The neglected dissipation phenomenon is identical with the mechanism that leads to the lower physical limit of dissipation (70–100 [Formula: see text] in today’s microprocessors (CMOS logic) and in any other system with thermally activated errors thus the same limit holds for the new scheme, too.
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Gingrich, Todd R., Grant M. Rotskoff, Gavin E. Crooks, and Phillip L. Geissler. "Near-optimal protocols in complex nonequilibrium transformations." Proceedings of the National Academy of Sciences 113, no. 37 (August 29, 2016): 10263–68. http://dx.doi.org/10.1073/pnas.1606273113.
Повний текст джерелаАнотація:
The development of sophisticated experimental means to control nanoscale systems has motivated efforts to design driving protocols that minimize the energy dissipated to the environment. Computational models are a crucial tool in this practical challenge. We describe a general method for sampling an ensemble of finite-time, nonequilibrium protocols biased toward a low average dissipation. We show that this scheme can be carried out very efficiently in several limiting cases. As an application, we sample the ensemble of low-dissipation protocols that invert the magnetization of a 2D Ising model and explore how the diversity of the protocols varies in response to constraints on the average dissipation. In this example, we find that there is a large set of protocols with average dissipation close to the optimal value, which we argue is a general phenomenon.
13
Lu, Changna, Qianqian Gao, Chen Fu, and Hongwei Yang. "Finite Element Method of BBM-Burgers Equation with Dissipative Term Based on Adaptive Moving Mesh." Discrete Dynamics in Nature and Society 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/3427376.
Повний текст джерелаАнотація:
A finite element model is proposed for the Benjamin-Bona-Mahony-Burgers (BBM-Burgers) equation with a high-order dissipative term; the scheme is based on adaptive moving meshes. The model can be applied to the equations with spatial-time mixed derivatives and high-order derivative terms. In this scheme, new variables are needed to make the equation become a coupled system, and then the linear finite element method is used to discretize the spatial derivative and the fifth-order Radau IIA method is used to discretize the time derivative. The simulations of 1D and 2D BBM-Burgers equations with high-order dissipative terms are presented in numerical examples. The numerical results show that the method keeps a second-order convergence in space and provides a smaller error than that based on the fixed mesh, which demonstrates the effectiveness and feasibility of the finite element method based on the moving mesh. We also study the effect of the dissipative terms with different coefficients in the equation; by numerical simulations, we find that the dissipative termuxxplays a more important role thanuxxxxin dissipation.
14
Li, Ruo, and Wei Zhong. "Improvement of the WENO-NIP Scheme for Hyperbolic Conservation Laws." Axioms 11, no. 5 (April 20, 2022): 190. http://dx.doi.org/10.3390/axioms11050190.
Повний текст джерелаАнотація:
The WENO-NIP scheme was obtained by developing a class of L1-norm smoothness indicators based on Newton interpolation polynomial. It recovers the optimal convergence order in smooth regions regardless of critical points and achieves better resolution than the classical WENO-JS scheme. However, the WENO-NIP scheme produces severe spurious oscillations when solving 1D linear advection problems with discontinuities at long output times, and it is also very oscillatory near discontinuities for 1D Riemann problems. In this paper, we find that the spectral property of WENO-NIP exhibits the negative dissipation characteristic, and this is the reason why WENO-NIP is unstable near discontinuities. Using this knowledge, we develop a way of improving the WENO-NIP scheme by introducing an additional term to eliminate the negative dissipation interval. The proposed scheme, denoted as WENO-NIP+, maintains the same convergence property, as well as the same low-dissipation property, as the corresponding WENO-NIP scheme. Numerical examples confirm that the proposed scheme is much more stable near discontinuities for 1D linear advection problems with large output times and 1D Riemann problems than the WENO-NIP scheme. Furthermore, the new scheme is far less dissipative in the region with high-frequency waves. In addition, the improved WENO-NIP+ scheme can remove or at least greatly decrease the post-shock oscillations that are commonly produced by the WENO-NIP scheme when simulating 2D Euler equations with strong shocks.
15
Yang, Youfa, Feihu Li, and Feiyu Wang. "Analysis of the Seismic Performance of a Masonry Structure with an RC Frame on the First Story with a Concrete-Filled Steel Tubular Damper." Applied Sciences 13, no. 4 (February 13, 2023): 2408. http://dx.doi.org/10.3390/app13042408.
Повний текст джерелаАнотація:
The concrete shear walls of masonry structures with an RC frame on the first story are low-rise shear walls with a height–width ratio of less than 1. The strength, stiffness, and ductility of these low-rise shear walls are not matched, resulting in poor seismic performance. Based on the idea of the passive control theory and multi-seismic defensive lines, the scheme of a masonry structure with an RC frame on the first story with a concrete-filled steel tubular (CFST) damper is proposed in this paper. To explore the seismic mitigation effect of a CFST damper applied to a masonry structure with an RC frame on the first story, the seismic performance under low-reversed cyclic loading of the frame with the CFST damper is first compared with that of the energy-dissipated low-rise concrete shear wall proposed by previous researchers and the ordinary low-rise concrete shear wall. Furthermore, the response of the masonry structure model with an RC frame on the first story with a CFST damper and two other comparative structural models under earthquake action are discussed. The results show that a masonry structure with an RC frame on the first story with a CFST damper has a fuller hysteretic loop, lighter pinching, better energy dissipation ability, and better seismic performance. Compared with the other two structures, the energy dissipation capacity of the masonry structure with an RC frame on the first story with a CFST damper is significantly improved, by 1.25~1.5 times. The amplification effect of the deformation angle allows the CFST damper to play a significant role in energy dissipation, whereas the main structure still undergoes a small deformation. The CFST damper can dissipate more seismic energy to protect the main structure from damage and improve the seismic performance of masonry structures with an RC frame on the first story.
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Appadu, A. R., and A. A. I. Peer. "Optimized Weighted Essentially Nonoscillatory Third-Order Schemes for Hyperbolic Conservation Laws." Journal of Applied Mathematics 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/428681.
Повний текст джерелаАнотація:
We describe briefly how a third-order Weighted Essentially Nonoscillatory (WENO) scheme is derived by coupling a WENO spatial discretization scheme with a temporal integration scheme. The scheme is termed WENO3. We perform a spectral analysis of its dispersive and dissipative properties when used to approximate the 1D linear advection equation and use a technique of optimisation to find the optimal cfl number of the scheme. We carry out some numerical experiments dealing with wave propagation based on the 1D linear advection and 1D Burger’s equation at some different cfl numbers and show that the optimal cfl does indeed cause less dispersion, less dissipation, and lowerL1errors. Lastly, we test numerically the order of convergence of the WENO3 scheme.
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Bašták Ďurán, Ivan, and Pascal Marquet. "Les travaux sur la turbulence : les origines, Toucans, Cost-ES0905 et influence de l'entropie." La Météorologie, no. 112 (2021): 079. http://dx.doi.org/10.37053/lameteorologie-2021-0023.
Повний текст джерелаАнотація:
Le schéma de turbulence Toucans est utilisé dans la configuration opérationnelle Alaro du modèle Aladin depuis début 2015. Son développement a été initié, guidé et en grande partie conçu par Jean-François Geleyn. Ce développement a commencé avec le prédécesseur du schéma Toucans, le schéma « pseudo-pronostique » en énergie cinétique turbulente, lui-même basé sur l'ancien schéma de turbulence de Louis, mais étendu dans Toucans à un schéma pronostique. Le schéma Toucans a pour objectif de traiter de manière cohérente les fonctions qui dépendent de la stabilité verticale de l'atmosphère, de l'influence de l'humidité et des échelles de longueur de la turbulence (de mélange et de dissipation). De plus, de nouvelles caractéristiques ont été ajoutées : une représentation améliorée pour les stratifications très stables (absence de nombre de Richardson critique), une meilleure représentation de l'anisotropie, un paramétrage unifié de la turbulence et des nuages par l'ajout d'une deuxième énergie turbulente pronostique et la paramétrisation des moments du troisième ordre. The Toucans turbulence scheme is a turbulence scheme that is used in the operational Alaro configuration of the Aladin model since early 2015. Its development was initiated, guided and to a large extend authored by Jean-François Geleyn. The development started with the predecessor of the Toucans scheme, the "pseudo-prognostic" turbulent kinetic energy scheme which itself was built on the "Louis" turbulence scheme, but extended to a prognostic scheme. The Toucans scheme aims for a consistent treatment of stability dependency functions, influence of moisture, and turbulence length scales. Additionally, new features were added to the turbulence scheme: improved representation of turbulence in very stable stratification (absence of critical gradient Richardson number), better representation of anisotropy, unified parameterization of turbulence and clouds via addition of second prognostic turbulence energy, and parameterization of third order moments.
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Mamaev, M., L. C. G. Govia, and A. A. Clerk. "Dissipative stabilization of entangled cat states using a driven Bose-Hubbard dimer." Quantum 2 (March 27, 2018): 58. http://dx.doi.org/10.22331/q-2018-03-27-58.
Повний текст джерелаАнотація:
We analyze a modified Bose-Hubbard model, where two cavities having on-site Kerr interactions are subject to two-photon driving and correlated dissipation. We derive an exact solution for the steady state of this interacting driven-dissipative system, and use it show that the system permits the preparation and stabilization of pure entangled non-Gaussian states, so-called entangled cat states. Unlike previous proposals for dissipative stabilization of such states, our approach requires only a linear coupling to a single engineered reservoir (as opposed to nonlinear couplings to two or more reservoirs). Our scheme is within the reach of state-of-the-art experiments in circuit QED.
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Wang, Jingqun, Jing Li, and Lixin Tian. "Global well-posedness for the two-component Camassa–Holm equation with fractional dissipation." Asian-European Journal of Mathematics 12, no. 04 (July 2, 2019): 1950051. http://dx.doi.org/10.1142/s1793557119500517.
Повний текст джерелаАнотація:
In this paper, we investigate the two-component Camassa–Holm equation with fractional dissipation [Formula: see text] where [Formula: see text] denotes the fractional dissipative operator which is defined by the Fourier transform [Formula: see text]. We prove the local-posedness of this equation via the Littlewood–Paley theory and the suitable iterative scheme. Furthermore, under appropriate discussions, we give the global well-posedness of the above equation.
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Najafiyazdi, Mostafa, Luc Mongeau, and Siva Nadarajah. "Low-dissipation low-dispersion explicit Taylor-Galerkin schemes from the Runge-Kutta kernels." International Journal of Aeroacoustics 17, no. 1-2 (February 24, 2018): 88–113. http://dx.doi.org/10.1177/1475472x17743657.
Повний текст джерелаАнотація:
A multi-stage approach was adopted to investigate similarities and differences between the explicit Taylor-Galerkin and the explicit Runge-Kutta time integration schemes. It was found that the substitution of some, but not all, of second-order temporal derivatives in a Taylor-Galerkin scheme by additional stages makes it analogous to a Runge-Kutta scheme while preserving its original dissipative property for node-to-node oscillations. The substitution of all second-order temporal derivatives transforms Taylor-Galerkin schemes into Runge-Kutta schemes with zero attenuation at the grid cut-off. The application of this approach to an existing two-stage Taylor-Galerkin scheme yields a low-dissipation low-dispersion Taylor-Galerkin formulation. Two one-dimensional benchmarks were simulated to study the performance of this new scheme. The reverse process yields a general approach for transforming m-stage Runge-Kutta schemes into ( m−1)-stage Taylor-Galerkin schemes while preserving the same order of accuracy. The dissipation and dispersion properties for several new Taylor-Galerkin schemes were compared to those of their corresponding Runge-Kutta form.
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CHRISTOV, C. I. "DISSIPATIVE QUASI-PARTICLES: THE GENERALIZED WAVE EQUATION APPROACH." International Journal of Bifurcation and Chaos 12, no. 11 (November 2002): 2435–44. http://dx.doi.org/10.1142/s0218127402005959.
Повний текст джерелаАнотація:
Generalized Wave Equations containing dispersion, dissipation and energy-production (GDWE) are considered in lieu of dissipative NEE as more suitable models for two-way interaction of localized waves. The quasi-particle behavior and the long-time evolution of localized solutions upon take-over and head-on collisions are investigated numerically by means of an adequate difference scheme which represents faithfully the balance/conservation laws. It is shown that in most cases the balance between energy production/dissipation and nonlinearity plays a similar role to the classical Boussinesq balance between dispersion and nonlinearity, namely it can create and support localized solutions which behave as quasi-particles upon collisions and for a reasonably long time after that.
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Bailo, Rafael, José A. Carrillo, Hideki Murakawa, and Markus Schmidtchen. "Convergence of a fully discrete and energy-dissipating finite-volume scheme for aggregation-diffusion equations." Mathematical Models and Methods in Applied Sciences 30, no. 13 (November 12, 2020): 2487–522. http://dx.doi.org/10.1142/s0218202520500487.
Повний текст джерелаАнотація:
We study an implicit finite-volume scheme for nonlinear, non-local aggregation-diffusion equations which exhibit a gradient-flow structure, recently introduced in [R. Bailo, J. A. Carrillo and J. Hu, Fully discrete positivity-preserving and energy-dissipating schemes for aggregation-diffusion equations with a gradient flow structure, arXiv:1811.11502 ]. Crucially, this scheme keeps the dissipation property of an associated fully discrete energy, and does so unconditionally with respect to the time step. Our main contribution in this work is to show the convergence of the method under suitable assumptions on the diffusion functions and potentials involved.
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Li, Yan, Xingli Li, and Jiasen Jin. "Dissipation-Induced Information Scrambling in a Collision Model." Entropy 24, no. 3 (February 27, 2022): 345. http://dx.doi.org/10.3390/e24030345.
Повний текст джерелаАнотація:
In this paper, we present a collision model to stroboscopically simulate the dynamics of information in dissipative systems. In particular, an all-optical scheme is proposed to investigate the information scrambling of bosonic systems with Gaussian environmental states. Varying the states of environments, in the presence of dissipation, transient tripartite mutual information of system modes may show negative value, signaling the appearance of information scrambling. We also find that dynamical indivisibility based non-Markovianity plays dual roles in affecting the dynamics of information.
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Materassi, Massimo, and Emanuele Tassi. "Algebrizing friction: a brief look at the Metriplectic Formalism." Intellectual Archive 1, no. 3 (July 28, 2012): 45–52. http://dx.doi.org/10.32370/ia_2012_07_3.
Повний текст джерелаАнотація:
The formulation of Action Principles in Physics, and the introduction of the Hamiltonian framework, reduced dynamics to bracket algebra of observables. Such a framework has great potentialities, to understand the role of symmetries, or to give rise to the quantization rule of modern microscopic Physics. Conservative systems are easily algebrized via the Hamiltonian dynamics: a conserved observable H generates the variation of any quantity f via the Poisson bracket {f,H}. Recently, dissipative dynamical systems have been algebrized in the scheme presented here, referred to as metriplectic framework: the dynamics of an isolated system with dissipation is regarded as the sum of a Hamiltonian component, generated by H via a Poisson bracket algebra; plus dissipation terms, produced by a certain quantity S via a new symmetric bracket. This S is in involution with any other observable and is interpreted as the entropy of those degrees of freedom statistically encoded in friction. In the present paper, the metriplectic framework is shown for two original “textbook” examples. Then, dissipative Magneto-Hydrodynamics (MHD), a theory of major use in many space physics and nuclear fusion applications, is reformulated in metriplectic terms.
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Chandramouli, Sathyanarayanan, Aseel Farhat, and Ziad H Musslimani. "Time-dependent Duhamel renormalization method with multiple conservation and dissipation laws." Nonlinearity 35, no. 3 (February 1, 2022): 1286–310. http://dx.doi.org/10.1088/1361-6544/ac4815.
Повний текст джерелаАнотація:
Abstract The time dependent spectral renormalization (TDSR) method was introduced by Cole and Musslimani as a novel way to numerically solve initial boundary value problems. An important and novel aspect of the TDSR scheme is its ability to incorporate physics in the form of conservation laws or dissipation rate equations. However, the method was limited to include a single conserved or dissipative quantity. The present work significantly extends the computational features of the method with the (i) incorporation of multiple conservation laws and/or dissipation rate equations, (ii) ability to enforce versatile boundary conditions, and (iii) higher order time integration strategy. The TDSR method is applied on several prototypical evolution equations of physical significance. Examples include the Korteweg–de Vries, multi-dimensional nonlinear Schrödinger and the Allen–Cahn equations.
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Appadu, A. R. "Numerical Solution of the 1D Advection-Diffusion Equation Using Standard and Nonstandard Finite Difference Schemes." Journal of Applied Mathematics 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/734374.
Повний текст джерелаАнотація:
Three numerical methods have been used to solve the one-dimensional advection-diffusion equation with constant coefficients. This partial differential equation is dissipative but not dispersive. We consider the Lax-Wendroff scheme which is explicit, the Crank-Nicolson scheme which is implicit, and a nonstandard finite difference scheme (Mickens 1991). We solve a 1D numerical experiment with specified initial and boundary conditions, for which the exact solution is known using all these three schemes using some different values for the space and time step sizes denoted byhandk, respectively, for which the Reynolds number is 2 or 4. Some errors are computed, namely, the error rate with respect to theL1norm, dispersion, and dissipation errors. We have both dissipative and dispersive errors, and this indicates that the methods generate artificial dispersion, though the partial differential considered is not dispersive. It is seen that the Lax-Wendroff and NSFD are quite good methods to approximate the 1D advection-diffusion equation at some values ofkandh. Two optimisation techniques are then implemented to find the optimal values ofkwhenh=0.02for the Lax-Wendroff and NSFD schemes, and this is validated by numerical experiments.
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Cai, Wenjun, Huai Zhang, and Yushun Wang. "Modelling damped acoustic waves by a dissipation-preserving conformal symplectic method." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2199 (March 2017): 20160798. http://dx.doi.org/10.1098/rspa.2016.0798.
Повний текст джерелаАнотація:
We propose a novel stable and efficient dissipation-preserving method for acoustic wave propagations in attenuating media with both correct phase and amplitude. Through introducing the conformal multi-symplectic structure, the intrinsic dissipation law and the conformal symplectic conservation law are revealed for the damped acoustic wave equation. The proposed algorithm is exactly designed to preserve a discrete version of the conformal symplectic conservation law. More specifically, two subsystems in conjunction with the original damped wave equation are derived. One is actually the conservative Hamiltonian wave equation and the other is a dissipative linear ordinary differential equation (ODE) system. Standard symplectic method is devoted to the conservative system, whereas the analytical solution is obtained for the ODE system. An explicit conformal symplectic scheme is constructed by concatenating these two parts of solutions by the Strang splitting technique. Stability analysis and convergence tests are given thereafter. A benchmark model in homogeneous media is presented to demonstrate the effectiveness and advantage of our method in suppressing numerical dispersion and preserving the energy dissipation. Further numerical tests show that our proposed method can efficiently capture the dissipation in heterogeneous media.
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Gawade, Rohit D., and S. L. Nalbalwar. "A Centralized Energy Efficient Distance Based Routing Protocol for Wireless Sensor Networks." Journal of Sensors 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/8313986.
Повний текст джерелаАнотація:
Wireless sensor network (WSN) typically consists of a large number of low cost wireless sensor nodes which collect and send various messages to a base station (BS). WSN nodes are small battery powered devices having limited energy resources. Replacement of such energy resources is not easy for thousands of nodes as they are inaccessible to users after their deployment. This generates a requirement of energy efficient routing protocol for increasing network lifetime while minimizing energy consumption. Low Energy Adaptive Clustering Hierarchy (LEACH) is a widely used classic clustering algorithm in WSNs. In this paper, we propose a Centralized Energy Efficient Distance (CEED) based routing protocol to evenly distribute energy dissipation among all sensor nodes. We calculate optimum number of cluster heads based on LEACH’s energy dissipation model. We propose a distributed cluster head selection algorithm based on dissipated energy of a node and its distance to BS. Moreover, we extend our protocol by multihop routing scheme to reduce energy dissipated by nodes located far away from base station. The performance of CEED is compared with other protocols such as LEACH and LEACH with Distance Based Thresholds (LEACH-DT). Simulation results show that CEED is more energy efficient as compared to other protocols. Also it improves the network lifetime and stability period over the other protocols.
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Fülöp, Tamás, Róbert Kovács, Mátyás Szücs, and Mohammad Fawaier. "Thermodynamical Extension of a Symplectic Numerical Scheme with Half Space and Time Shifts Demonstrated on Rheological Waves in Solids." Entropy 22, no. 2 (January 28, 2020): 155. http://dx.doi.org/10.3390/e22020155.
Повний текст джерелаАнотація:
On the example of the Poynting–Thomson–Zener rheological model for solids, which exhibits both dissipation and wave propagation, with nonlinear dispersion relation, we introduce and investigate a finite difference numerical scheme. Our goal is to demonstrate its properties and to ease the computations in later applications for continuum thermodynamical problems. The key element is the positioning of the discretized quantities with shifts by half space and time steps with respect to each other. The arrangement is chosen according to the spacetime properties of the quantities and of the equations governing them. Numerical stability, dissipative error, and dispersive error are analyzed in detail. With the best settings found, the scheme is capable of making precise and fast predictions. Finally, the proposed scheme is compared to a commercial finite element software, COMSOL, which demonstrates essential differences even on the simplest—elastic—level of modeling.
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Ji, Yi, and Yufeng Xing. "A Two-Sub-Step Generalized Central Difference Method for General Dynamics." International Journal of Structural Stability and Dynamics 20, no. 07 (June 23, 2020): 2050071. http://dx.doi.org/10.1142/s0219455420500716.
Повний текст джерелаАнотація:
This paper proposes an implicit and unconditionally stable two-sub-step composite time integration method with controllable numerical dissipation for general dynamics called the two-sub-step generalized central difference (TGCD) method. The proposed method is established by performing the generalized central difference scheme in two sub-steps as the nondissipative and dissipative parts to ensure amplitude accuracy and controllable damping, respectively. It is accurate to the second order, with the amount of numerical dissipation controlled exactly by the spectral radius [Formula: see text]. In addition, the related parameters of the proposed method are determined by optimizing the amplitude and phase accuracy of the free vibration of a single degree-of-freedom system. Several representative linear and nonlinear numerical examples are analyzed to demonstrate the advantages of the proposed method in terms of accuracy, stability and efficiency, especially its stability in solving nonlinear problems.
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Tallent, James R., Takao Yamashita, and Yoshito Tsuchiya. "FIELD CALCULATIONS OF WAVE ENERGY DISSIPATION AND RELATED BEACH PROFILE." Coastal Engineering Proceedings 1, no. 21 (January 29, 1988): 135. http://dx.doi.org/10.9753/icce.v21.135.
Повний текст джерелаАнотація:
The process by which wave energy dissipates across the surf zone and its affect on the bed profile is, of course, a topic of immediate concern and debate. Various concepts of the wave energy dissipation process have been modeled, however, additional research is needed before confidence can be placed in a particular calculation scheme. In addition to the problems associated with proper model derivation a method of application and result interpretation of actual surf zone field data must be devised and understood. This is, of course, prerequisite to any realistic use of a wave energy dissipation model in an engineering project. The following study was therefore conducted in order to examine the applicability of surf zone field data to wave energy dissipation models and to investigate the bed profile relationship. Two wave energy dissipation models were selected for comparison in this study, the 'Undertow Model'(UM) which is based on the conservation of wave energy flux across the surf zone (3), and the 'Turbulent Bore Model'(TBM) which is based on hydraulic jump theory (2). Individual waves were identified in the wave record by employing the zero up-crossing method, and wave energy calculations were based on small amplitude wave theory, Svendsen's nonlinearity parameter Bo (4), and the 1/3 Significant Wave classification.
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Liu, Xu, Keyong Zhu, Yijie Wei, Ziwei Chen, Mingming Ge, and Yong Huang. "Experimental Investigation into the Effect of Fin Shapes on Heat Dissipation Performance of Phase Change Heat Sink." Aerospace 9, no. 11 (October 28, 2022): 664. http://dx.doi.org/10.3390/aerospace9110664.
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In this paper, the thermal management of missile-borne components in a flight state is studied. Avoiding excessive component temperatures under the high-temperature circumstances brought by aerodynamic heat is a requirement to guarantee the equipment’s safe and reliable operation. In this work, we designed four finned shell constructions for a phase change module using the phase change temperature control method and then studied their effects on the module’s ability to dissipate heat using an experimental approach. Three sizes of 30 mm, 40 mm, and 50 mm heating pads were used to replicate heat sources with various heat flux densities and heat dissipation regions, with reference to the heating characteristics of various chips. The results demonstrated that the square-shaped fin had the best heat dissipation effect after operating for 10 min under the power of 10 W and 20 W, while the strip-shaped fins exhibited the highest performance under the power of 30 W. The square-shaped fins had the best heat dissipation effect when reducing working time to 5 min. This paper proposes the optimal fin scheme under different power densities, as well as an enhanced heat dissipation idea for the melting process of the phase change materials based on the test results.
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Cho, Hyunjin, Dongsu Ryu, and Heysung Kang. "Effects of Forcing on Shocks and Energy Dissipation in Interstellar and Intracluster Turbulences." Astrophysical Journal 926, no. 2 (February 1, 2022): 183. http://dx.doi.org/10.3847/1538-4357/ac41cc.
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Abstract Observations indicate that turbulence in the interstellar medium (ISM) is supersonic (M turb ≫ 1) and strongly magnetized (β ∼ 0.01–1), while in the intracluster medium (ICM) it is subsonic (M turb ≲ 1) and weakly magnetized (β ∼ 100). Here, M turb is the turbulent Mach number and β is the plasma beta. We study the properties of shocks induced in these disparate environments, including the distribution of the shock Mach number, M s , and the dissipation of the turbulent energy at shocks, through numerical simulations using a high-order, accurate code based on the weighted essentially nonoscillatory scheme. In particular, we investigate the effects of different modes of the forcing that drives turbulence: solenoidal, compressive, and a mixture of the two. In ISM turbulence, while the density distribution looks different with different forcings, the velocity power spectrum, P v , on small scales exhibits only weak dependence. Hence, the statistics of shocks depend weakly on forcing either. In the ISM models with M turb ≈ 10 and β ∼ 0.1, the fraction of the turbulent energy dissipated at shocks is estimated to be ∼15%, not sensitive to the forcing mode. In contrast, in ICM turbulence, P v as well as the density distribution show strong dependence on forcing. The frequency and average Mach number of shocks are greater for compressive forcing than for solenoidal forcing; so is the energy dissipation. The fraction of the ensuing shock dissipation is in the range of ∼10%–35% in the ICM models with M turb ≈ 0.5 and β ∼ 106. The rest of the turbulent energy should be dissipated through turbulent cascade.
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Yilmaz, Cagri, and Eyup Sabri Topal. "Virial and Energy Dissipation in Measurement of Dynamic Acoustic Forces Using Bimodal-frequency Excitation of Micro-cantilever Array." Academic Perspective Procedia 4, no. 1 (October 16, 2021): 332–40. http://dx.doi.org/10.33793/acperpro.04.01.50.
Повний текст джерелаАнотація:
Virial and energy dissipation, related to oscillation observable responses, possess complementary information regarding acoustic force measurements. In this paper, we introduce a mathematical framework describing the analytic relationship between oscillation observables and energy quantities at the second eigenmode in the measurement of dynamic acoustic forces. We utilize a bimodal-frequency excitation scheme for actuation of the micro-cantilever array to obtain high-sensitivity frequency bands. Herein, we analyze the virials of acoustic force interaction and the energy dissipation levels on the domain of acoustic force frequency. For our case, we obtain the high-frequency bands of around 200-270 kHz and 440-570 kHz for the force strengths in the range of 4.0-36.0 pN. In addition, results of virials and dissipated power with respect to acoustic force strengths are introduced for low- and high-sensitivity frequency regions. Therefore, the energy quantities can be robustly utilized to determine high-sensitivity frequency windows in the measurement of dynamic acoustic forces.
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Frost, Miroslav, and Jan Valdman. "Vectorized MATLAB Implementation of the Incremental Minimization Principle for Rate-Independent Dissipative Solids Using FEM: A Constitutive Model of Shape Memory Alloys." Mathematics 10, no. 23 (November 23, 2022): 4412. http://dx.doi.org/10.3390/math10234412.
Повний текст джерелаАнотація:
The incremental energy minimization principle provides a compact variational formulation for evolutionary boundary problems based on constitutive models of rate-independent dissipative solids. In this work, we develop and implement a versatile computational tool for the resolution of these problems via the finite element method (FEM). The implementation is coded in the MATLAB programming language and benefits from vector operations, allowing all local energy contributions to be evaluated over all degrees of freedom at once. The monolithic solution scheme combined with gradient-based optimization methods is applied to the inherently nonlinear, non-smooth convex minimization problem. An advanced constitutive model for shape memory alloys, which features a strongly coupled rate-independent dissipation function and several constraints on internal variables, is implemented as a benchmark example. Numerical simulations demonstrate the capabilities of the computational tool, which is suited for the rapid development and testing of advanced constitutive laws of rate-independent dissipative solids.
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Fernández-Fidalgo, Javier, Luis Ramírez, Panagiotis Tsoutsanis, Ignasi Colominas, and Xesús Nogueira. "A reduced-dissipation WENO scheme with automatic dissipation adjustment." Journal of Computational Physics 425 (January 2021): 109749. http://dx.doi.org/10.1016/j.jcp.2020.109749.
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Jiang, Yi, Meiliang Mao, Xiaogang Deng, and Huayong Liu. "Extending Seventh-Order Dissipative Compact Scheme Satisfying Geometric Conservation Law to Large Eddy Simulation on Curvilinear Grids." Advances in Applied Mathematics and Mechanics 7, no. 4 (May 29, 2015): 407–29. http://dx.doi.org/10.4208/aamm.2013.m404.
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AbstractSeventh-order hybrid cell-edge and cell-node dissipative compact scheme (HDCS-E8T7) is extended to a new implicit large eddy simulation named HILES on stretched and curvilinear meshes. Although the conception of HILES is similar to that of monotone integrated LES (MILES), i.e., truncation error of the discretization scheme itself is employed to model the effects of unresolved scales, HDCS-E8T7 is a new high-order finite difference scheme, which can eliminate the surface conservation law (SCL) errors and has inherent dissipation. The capability of HILES is tested by solving several benchmark cases. In the case of flow past a circular cylinder, the solutions of HILES fulfilling the SCL have good agreement with the corresponding experiment data, however, the flowfield is gradually contaminated when the SCL error is enlarged. With the help of fulling the SCL, ability of HILES for handling complex geometry has been enhanced. The numerical solutions of flow over delta wing demonstrate the potential of HILES in simulating turbulent flow on complex configuration.
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Mentaschi, Lorenzo, Michalis Vousdoukas, Tomas Fernandez Montblanc, Georgia Kakoulaki, Evangelos Voukouvalas, Giovanni Besio, and Peter Salamon. "Assessment of global wave models on regular and unstructured grids using the Unresolved Obstacles Source Term." Ocean Dynamics 70, no. 11 (September 24, 2020): 1475–83. http://dx.doi.org/10.1007/s10236-020-01410-3.
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Abstract The Unresolved Obstacles Source Term (UOST) is a general methodology for parameterizing the dissipative effects of subscale islands, cliffs, and other unresolved features in ocean wave models. Since it separates the dissipation from the energy advection scheme, it can be applied to any numerical scheme or any type of mesh. UOST is now part of the official release of WAVEWATCH III, and the freely available package alphaBetaLab automates the estimation of the parameters needed for the obstructed cells. In this contribution, an assessment of global regular and unstructured (triangular) wave models employing UOST is presented. The results in regular meshes show an improvement in model skill, both in terms of spectrum and of integrated parameters, thanks to the UOST modulation of the dissipation with wave direction, and to considering the cell geometry. The improvement is clear in wide areas characterized by the presence of islands, like the whole central-western Pacific Basin. In unstructured meshes, the use of UOST removes the need of high resolution in proximity of all small features, leading to (a) a simplification in the development process of large scale and global meshes, and (b) a significant decrease of the computational demand of accurate large-scale models.
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Corr, Lawrence R., and William W. Clark. "A Novel Semi-Active Multi-Modal Vibration Control Law for a Piezoceramic Actuator." Journal of Vibration and Acoustics 125, no. 2 (April 1, 2003): 214–22. http://dx.doi.org/10.1115/1.1547682.
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In this paper, a novel semi-active energy rate multi-modal vibration control technique is developed for a piezoceramic actuator coupled to a switching resistor/inductor shunt. The technique works by briefly connecting a resistor/inductor shunt to a piezoceramic actuator in order to apply the necessary signed charge to allow energy dissipation. The switch timing is determined by a control scheme that observes the rate of energy change in controlled modes. The control scheme is developed in the paper, and is simplified to enable practical implementation. This new multi-modal control law is applied to both a simple numerical and an experimental test structure. The results from the numerical and experimental tests show that the energy rate multi-mode control law is able to dissipate energy from one, two and three modes of the flexible structures using a single actuator.
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Hammerton, P. W., and D. G. Crighton. "Overturning of nonlinear acoustic waves. Part 1 A general method." Journal of Fluid Mechanics 252 (July 1993): 585–99. http://dx.doi.org/10.1017/s0022112093003891.
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We consider model nonlinear wave equations of the form ut + uux = [Hscr ](x,t;u, ux,…) arising in gasdynamics and other fields, [Hscr ] incorporating various linear mechanisms of dissipation and dispersion. If [Hscr ] includes a thermoviscous dissipation term ∈uxx, then it is generally believed that u(x,t) will remain single-valued for all t > 0 and all single-valued u(x, 0), for any ∈ > 0. The question addressed here is whether, if thermoviscous dissipation is excluded from [Hscr ], u(x, t) remains single-valued for all t > 0, or whether certain dissipative-dispersive mechanisms (such as relaxation processes) are in themselves insufficient to prevent wave overturning. To answer this we propose a numerical scheme based on the use of intrinsic coordinates ψ = ψ(s, t) to describe the waveform at each time. In this paper, the method is described and validated by comparisons with the exact solutions for certain [Hscr ] ([Hscr ] = 0, [Hscr ] = -αu, [Hscr ] = ∈uxx). These comparisons show that the scheme is free of numerical viscosity effects which preclude the solution of the problem by finite-difference or spectral methods applied to the signal u(x, t), that it can reliably distinguish between finite-time overturning and merely the formation of steep gradients, and that it can accurately predict the time of overturning when it does occur. Having established the validity of the method, attention can then be turned to those cases where criteria for overturning have not as yet been determined by conventional methods. In Part 2, harmonic wave propagation through a relaxing gas is investigated.
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Mu, Wei-Lin, Xiao-Xuan Li, and Xiao-Qiang Shao. "Cooling neutral atoms into maximal entanglement in the Rydberg blockade regime." Optics Letters 47, no. 17 (August 26, 2022): 4491. http://dx.doi.org/10.1364/ol.471591.
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We propose a cooling scheme to prepare stationary entanglement of neutral atoms in the Rydberg blockade regime by the combination of periodically collective laser pumping and dissipation. In each cycle, the controlled unitary dynamics process can selectively pump atoms away from the nontarget state while keeping the target state unchanged. The subsequent dissipative process redistributes the populations of ground states through the engineered spontaneous emission. After a number of cycles, the system will eventually be stabilized into the desired steady state, independent of the initial state. This protocol does not rely on coherent addressing of individual neutral atoms or fine control of Rydberg interaction intensity, which can, in principle, greatly improve the feasibility of experiments in related fields.
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Aregba–Driollet, D., J. Breil, S. Brull, B. Dubroca, and E. Estibals. "Modelling and numerical approximation for the nonconservative bitemperature Euler model." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 4 (July 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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Nochnichenko, Ihor, Oleg Yakhno, Dmytro Kostiuk, and Vladyslav Kryvosheiev. "THE TRANSFER PHENOMENON OF ENERGY IN MECHANICAL SYSTEMS OF VIBRATION DAMPING." Journal of the Technical University of Gabrovo 67 (November 20, 2023): 21–24. http://dx.doi.org/10.62853/eoqv4312.
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The article is devoted to the analysis of transfer processes from the point of view of the energy balance in the damping system. It is shown that damping systems are based on the physical process of converting mechanical energy into thermal energy, with subsequent dissipation into the environment. The full distribution of energy in damping problems takes the following form: the mechanical energy of movement is absorbed due to the hydraulic resistance of the fluid and is transformed into a dissipative component, which can reach up to 80% of the total energy in the system. The dependence of the total power loss of the shock absorber in variable operating conditions and the scheme of physical processes and energy transformations in damping problems, which are in dissipative processes, are given. The article provides principles that can be used to design devices and modules of a wide class of damper systems with the possibility of energy recovery and storage due to the introduction of a damper system, for example, a motor-generator, an induction coil, and other energy storage systems.
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Chen, Wei, and Song Ping Wu. "Perfectly Matched Layer as an Absorbing Boundary Condition for Computational Aero-Acoustic." Advanced Materials Research 726-731 (August 2013): 3153–58. http://dx.doi.org/10.4028/www.scientific.net/amr.726-731.3153.
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Advances in Computational Aeroacoustics (CAA) depend critically on the availability of accurate, nondispersive, least dissipative computation algorithm as well as high quality numerical boundary treatments. This paper focuses on the Perfectly Matched Layer (PML) for external boundaries in CAA. To achieve low dissipation and dispersion errors, Dispersion-Relation-Preserving (DRP) Schemes are used for spatial discretization of the acoustic equations. The classical fourth-order Runge-Kutta time scheme is applied to the acoustic equations for time discretization. Four cases are given to illustrate the 2D PML equations for the linearized/nonlinear Euler equations in Cartesian coordinates and Cylindrical coordinates. The results show that the PML is effective as absorbing boundary condition. Those are basis for PML in actual computations of acoustic problems.
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O’Reilly, Ossian, and Jan Nordström. "Provably non-stiff implementation of weak coupling conditions for hyperbolic problems." Numerische Mathematik 150, no. 2 (January 5, 2022): 551–89. http://dx.doi.org/10.1007/s00211-021-01263-y.
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AbstractIn the context of coupling hyperbolic problems, the maximum stable time step of an explicit numerical scheme may depend on the design of the coupling procedure. If this is the case, the coupling procedure is sensitive to changes in model parameters independent of the Courant–Friedrichs–Levy condition. This sensitivity can cause artificial stiffness that degrades the performance of a numerical scheme. To overcome this problem, we present a systematic and general procedure for weakly imposing coupling conditions via penalty terms in a provably non-stiff manner. The procedure can be used to construct both energy conservative and dissipative couplings, and the user is given control over the amount of dissipation desired. The resulting formulation is simple to implement and dual consistent. The penalty coefficients take the form of projection matrices based on the coupling conditions. Numerical experiments demonstrate that this procedure results in both optimal spectral radii and superconvergent linear functionals.
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Zhu, CY, YH Zhao, and L. Sun. "Seismic performance of FRP-reinforced concrete-filled thin-walled steel tube considering local buckling." Journal of Reinforced Plastics and Composites 37, no. 9 (February 10, 2018): 592–608. http://dx.doi.org/10.1177/0731684418756514.
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The objective of this study is to investigate the seismic performance of fiber-reinforced polymer-reinforced concrete-filled thin-walled steel tube (CFTST). Twelve specimens with different fiber-reinforced polymer types (glass fiber-reinforced polymer and carbon fiber-reinforced polymer) and reinforcing modes were tested under constant axially compressive load and cyclic lateral load. The failure mode and lateral load versus displacement relationship for each specimen were recorded during testing. The strength, ductility, and energy dissipation capacity were analyzed accordingly. Further, a stress–strain relationship and a restoring force model of the fiber-reinforced polymer confining steel tube with local buckling were proposed. A hysteretic model for the fiber-reinforced polymer-reinforced CFTST was developed subsequently. The results indicate that the seismic performance of fiber-reinforced polymer-reinforced CFTST can be effectively improved by optimizing the fiber-reinforced polymer type and corresponding reinforcing scheme. Carbon fiber-reinforced polymer and glass fiber-reinforced polymer are suitable materials for the confinement and bending reinforcement of the column, respectively. The modeling results show the energy imported into the column is mainly dissipated by the thin-walled steel tube. The energy dissipation proportion of the steel tube, concrete core, and longitudinal fiber-reinforced polymer are >80%, 10%–20%, and <8%, respectively. The energy dissipation value of the steel tube can be improved more than 40% after effectively restraining the local buckling.
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Razali, Noorhelyna, Nisa Balqis Masnoor, Shahrum Abdullah, and Muhammad Faiz Hilmi Mohd Zainaphi. "Acoustic Analysis Using Symmetrised Implicit Midpoint Rule." Frattura ed Integrità Strutturale 16, no. 61 (June 19, 2022): 214–29. http://dx.doi.org/10.3221/igf-esis.61.14.
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In wave propagation phenomena, time-advancing numerical methods must accurately represent the amplitude and phase of the propagating waves. The acoustic waves are non-dispersive and non-dissipative. However, the standard schemes both retain dissipation and dispersion errors. Thus, this paper aims to analyse the dissipation, dispersion, accuracy, and stability of the Runge–Kutta method and derive a new scheme and algorithm that preserves the symmetry property. The symmetrised method is introduced in the time-of-finite-difference method for solving problems in aeroacoustics. More efficient programming for solving acoustic problems in time and space, i.e. the IMR method for solving acoustic problems, an advection equation, compares the square-wave and step-wave Lax methods with symmetrised IMR (one-and two-step active). The results of conventional methods are usually unstable for hyperbolic problems. The forward time central space square equation is an unstable method with minimal usefulness, which can only study waves for short fractions of one oscillation period. Therefore, nonlinear instability and shock formation are controlled by numerical viscosities such as those discussed with the Lax method equation. The one- and two-step active symmetrised IMR methods are more efficient than the wave method.
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Melet, Angelique, Robert Hallberg, Sonya Legg, and Kurt Polzin. "Sensitivity of the Ocean State to the Vertical Distribution of Internal-Tide-Driven Mixing." Journal of Physical Oceanography 43, no. 3 (March 1, 2013): 602–15. http://dx.doi.org/10.1175/jpo-d-12-055.1.
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Abstract The ocean interior stratification and meridional overturning circulation are largely sustained by diapycnal mixing. The breaking of internal tides is a major source of diapycnal mixing. Many recent climate models parameterize internal-tide breaking using the scheme of St. Laurent et al. While this parameterization dynamically accounts for internal-tide generation, the vertical distribution of the resultant mixing is ad hoc, prescribing energy dissipation to decay exponentially above the ocean bottom with a fixed-length scale. Recently, Polzin formulated a dynamically based parameterization, in which the vertical profile of dissipation decays algebraically with a varying decay scale, accounting for variable stratification using Wentzel–Kramers–Brillouin (WKB) stretching. This study compares two simulations using the St. Laurent and Polzin formulations in the Climate Model, version 2G (CM2G), ocean–ice–atmosphere coupled model, with the same formulation for internal-tide energy input. Focusing mainly on the Pacific Ocean, where the deep low-frequency variability is relatively small, the authors show that the ocean state shows modest but robust and significant sensitivity to the vertical profile of internal-tide-driven mixing. Therefore, not only the energy input to the internal tides matters, but also where in the vertical it is dissipated.
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Sambath, P., D. S. Sankar, and K. K. Viswanathan. "A Numerical Study of Dissipative Chemically Reactive Radiative MHD Flow Past a Vertical Cone with Nonuniform Mass Flux." International Journal of Applied Mechanics and Engineering 25, no. 1 (March 1, 2020): 159–76. http://dx.doi.org/10.2478/ijame-2020-0011.
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AbstractA computational model is presented to explore the properties of heat source, chemically reacting radiative, viscous dissipative MHD flow of an incompressible viscous fluid past an upright cone under inhomogeneous mass flux. A numerical study has been carried out to explore the mass flux features with the help of Crank-Nicolson finite difference scheme. This investigation reveals the influence of distinct significant parameters and the obtained outputs for the transient momentum, temperature and concentration distribution near the boundary layer is discussed and portrayed graphically for the active parameters such as the Schmidt number Sc, thermal radiation Rd, viscous dissipation parameter ɛ, chemical reaction parameter λ, MHD parameter M and heat generation parameter Δ. The significant effect of parameters on shear stress, heat and mass transfer rates are also illustrated.
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Mai-Duy, N., N. Phan-Thien, and T. Tran-Cong. "An improved dissipative particle dynamics scheme." Applied Mathematical Modelling 46 (June 2017): 602–17. http://dx.doi.org/10.1016/j.apm.2017.01.086.
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