The correction procedure via reconstruction (CPR, formerly known as flux reconstruction) is a framework of high order methods for conservation laws, unifying some discontinuous Galerkin, spectral ...difference and spectral volume methods. Linearly stable schemes were presented by Vincent et al. (2011, 2015), but proofs of non-linear (entropy) stability in this framework have not been published yet (to the knowledge of the authors). We reformulate CPR methods using summation-by-parts (SBP) operators with simultaneous approximation terms (SATs), a framework popular for finite difference methods, extending the results obtained by Gassner (2013) for a special discontinuous Galerkin spectral element method. This reformulation leads to proofs of conservation and stability in discrete norms associated with the method, recovering the linearly stable CPR schemes of Vincent et al. (2011, 2015). Additionally, extending the skew-symmetric formulation of conservation laws by additional correction terms, entropy stability for Burgers' equation is proved for general SBP CPR methods not including boundary nodes.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
Equilibrium spatiotemporal correlation functions are central to understanding weak nonequilibrium physics. In certain local one-dimensional classical systems with three conservation laws they show ...universal features. Namely, fluctuations around ballistically propagating sound modes can be described by the celebrated Kardar-Parisi-Zhang (KPZ) universality class. Can such a universality class be found also in quantum systems? By unambiguously demonstrating that the KPZ scaling function describes magnetization dynamics in the SU(2) symmetric Heisenberg spin chain we show, for the first time, that this is so. We achieve that by introducing new theoretical and numerical tools, and make a puzzling observation that the conservation of energy does not seem to matter for the KPZ physics.
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CMK, CTK, FMFMET, IJS, NUK, PNG, UL, UM
We develop methods to deal with non-dynamical contributions to event-by-event fluctuation measurements of net-particle numbers in relativistic nuclear collisions. These contributions arise from ...impact parameter fluctuations and from the requirement of overall net-baryon number or net-charge conservation and may mask the dynamical fluctuations of interest, such as those due to critical endpoints in the QCD phase diagram. Within a model of independent particle sources we derive formulae for net-particle fluctuations and develop a rigorous approach to take into account contributions from participant fluctuations in realistic experimental environments and at any cumulant order. Interestingly, contributions from participant fluctuations to the second and third cumulants of net-baryon distributions are found to vanish at mid-rapidity for LHC energies while higher cumulants of even order are non-zero even when the net-baryon number at mid-rapidity is zero. At lower beam energies the effect of participant fluctuations increases and induces spurious higher moments. The necessary corrections become large and need to be carefully taken into account before comparison to theory. We also provide a procedure for selecting the optimal phase–space coverage of particles for fluctuation analyses and discuss quantitatively the necessary correction due to global charge conservation.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
This paper develops a new fifth order accurate Hermite WENO (HWENO) reconstruction method for hyperbolic conservation schemes in the framework of the two-stage fourth order accurate temporal ...discretization in Li and Du (2016) 13. Instead of computing the first moment of the solution additionally in the conventional HWENO or DG approach, we can directly take the interface values, which are already available in the numerical flux construction using the generalized Riemann problem (GRP) solver, to approximate the first moment. The resulting scheme is fourth order temporal accurate by only invoking the HWENO reconstruction twice so that it becomes more compact. Numerical experiments show that such compactness makes significant impact on the resolution of nonlinear waves.
•This scheme is very compact because only two reconstruction steps are taken for fourth order temporal accurate method.•Interface values are adopted in HWENO so that no extra effort needs making for the construction of moments and the resulting scheme is more compact.•The interface values are already available in the computation of numerical fluxes, and no extra effort is made.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
Using the theoretical framework of algebraic flux correction and invariant domain preserving schemes, we introduce a monolithic approach to convex limiting in continuous finite element schemes for ...linear advection equations, nonlinear scalar conservation laws, and hyperbolic systems. In contrast to flux-corrected transport (FCT) algorithms that apply limited antidiffusive corrections to bound-preserving low-order solutions, our new limiting strategy exploits the fact that these solutions can be expressed as convex combinations of bar states belonging to a convex invariant set of physically admissible solutions. Each antidiffusive flux is limited in a way which guarantees that the associated bar state remains in the invariant set and preserves appropriate local bounds. There is no free parameter and no need for limit fluxes associated with the consistent mass matrix of time derivative term separately. Moreover, the steady-state limit of the nonlinear discrete problem is well defined and independent of the pseudo-time step. In the case study for the Euler equations, the components of the bar states are constrained sequentially to satisfy local maximum principles for the density, velocity, and specific total energy in addition to positivity preservation for the density and pressure. The results of numerical experiments for standard test problems illustrate the ability of built-in convex limiters to resolve steep fronts in a sharp and nonoscillatory manner.
•A new approach to algebraic flux correction for hyperbolic problems.•Parameter-free limiting of fluxes that produce bound-violating states.•Continuous dependence on the data, well-defined steady-state limit.•Convexity-based proofs of invariant domain preservation properties.•A tailor-made positivity-preserving limiter for the Euler equations.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Recently a WENO scheme, with smoothness indicators constructed based on L1 measure is introduced by Ha et al. (2013) and the improved version of this scheme is presented by Kim et al. (2016), ...referred to as WENO-NS and WENO-P schemes respectively. These schemes perform better than the existing many fifth-order WENO schemes for the problems which contain discontinuities and attain fifth-order accuracy at the critical points where the first derivative vanishes but not at the points where the second derivatives are zero. This paper deals with modification of the above said methods to obtain a new fifth-order weighted essentially non-oscillatory (WENO) scheme. A new global-smoothness indicator is proposed which shows an improved behavior over the solutions of WENO-NS and WENO-P schemes and the proposed scheme attains an optimal order of approximation, even at the critical points where the first and second derivatives vanish but not the third derivative. Examples are taken in the numeric section to check the robustness and accuracy of the proposed scheme for one and two-dimensional system of Euler equations.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Abstract
There are analyzed two physically reasonable generalizations of the Kardar-Parisi-Zhang equation describing the spin glasses growth models and possessing important from physical point of ...view properties. The first one proved to be a completely integrable Hamiltonian dynamical system with an infinite hierarchy of commuting to each other conservation laws, and the second one proved to be linearized modulo some nonlinear constraints, imposed on its solutions.
In embryonic development or tumor evolution, cells often migrate collectively within confining tracks defined by their microenvironment 1,2. In some of these situations, the displacements within a ...cell strand are antiparallel 3, giving rise to shear flows. However, the mechanisms underlying these spontaneous flows remain poorly understood. Here, we show that an ensemble of spindle-shaped cells plated in a well-defined stripe spontaneously develop a shear flow whose characteristics depend on the width of the stripe. On wide stripes, the cells self-organize in a nematic phase with a director at a well-defined angle with the stripe's direction, and develop a shear flow close to the stripe's edges. However, on stripes narrower than a critical width, the cells perfectly align with the stripe's direction and the net flow vanishes. A hydrodynamic active gel theory provides an understanding of these observations and identifies the transition between the non-flowing phase oriented along the stripe and the tilted phase exhibiting shear flow as a Fréedericksz transition driven by the activity of the cells. This physical theory is grounded in the active nature of the cells and based on symmetries and conservation laws, providing a generic mechanism to interpret in vivo antiparallel cell displacements.
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IJS, NUK, SBMB, UL, UM, UPUK
A fourth-order nonlinear generalized Boussinesq water wave equation is studied in this work, which describes the propagation of long waves in shallow water. We employ Lie symmetry method to study its ...vector fields and optimal systems. Moreover, we derive its symmetry reductions and twelve families of soliton wave solutions by using the optimal systems, including hyperbolic-type, trigonometric-type, rational-type, Jacobi elliptic-type and Weierstrass elliptic-type solutions. Two of reduced equations are Painlevé-like equations. Finally, the complete set of local conservation laws is presented with a detailed derivation by using the conservation law multiplier.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
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