There has been a recent resurgence of interest in the structure of the gravitational field at null infinity, sparked by new results on soft charges and infrared issues related to the S matrix theory ...in perturbative quantum gravity. We summarize these developments and put them in the broader context of research in the relativity community that dates back to several decades. In keeping with intent of this series, this overview is addressed to gravitational scientists who are not experts in this specific area.
Full text
Available for:
EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
In this article, we study the problem of identification for the 1-D Burgers equation. This problem consists in identifying the set of initial data evolving to a given target at a final time. Due to ...the property of nonbackward uniqueness of the Burgers equation, there may exist multiple initial data leading to the same given target. In articles "Initial data identification in conservation laws and Hamilton-Jacobi equations" ( arXiv:1903.06448 , 2019) and "The inverse problem for Hamilton-Jacobi equations and semiconcave envelopes" ( SIAM Journal on Mathematical Analysis , vol. 52, the authors fully characterize the set of initial data leading to a given target using the classical Lax-Hopf formula. In this article, an alternative proof based only on generalized backward characteristics is given. This leads to the hope of investigating systems of conservation laws in 1-D, where the classical Lax-Hopf formula no more holds. Moreover, numerical illustrations are presented using as a target, a function optimized for minimum pressure rise in the context of sonic-boom minimization problems. All of initial data leading to this given target are constructed using a wavefront tracking algorithm.
Numerical schemes provably preserving the positivity of density and pressure are highly desirable for ideal magnetohydrodynamics (MHD), but the rigorous positivity-preserving (PP) analysis remains ...challenging. The difficulties mainly arise from the intrinsic complexity of the MHD equations as well as the indeterminate relation between the PP property and the divergence-free condition on the magnetic field. This paper presents the first rigorous PP analysis of conservative schemes with the Lax-Priedrichs (LF) flux for ID and multidimensional ideal MHD. The significant innovation is the discovery of the theoretical connection between the PP property and a discrete divergence-free (DDF) condition. This connection is established through the generalized LF splitting properties, which are alternatives to the usually expected LF splitting property that does not hold for ideal MHD. The generalized LF splitting properties involve a number of admissible states strongly coupled by the DDF condition, making their derivation very difficult. We derive these properties via a novel equivalent form of the admissible state set and an important inequality, which is skillfully constructed by technical estimates. Rigorous analysis is then presented for finite volume and discontinuous Galerkin schemes with the LF flux on uniform Cartesian meshes. In the 1D case, the PP property is proved for the first-order scheme with proper numerical viscosity, and also for arbitrarily high-order schemes under conditions accessible by a PP limiter. In the 2D case, we show that the DDF condition is necessary and crucial for achieving the PP property. It is observed that even slightly violating the proposed DDF condition may cause failure to preserve the positivity of pressure. We prove that the 2D LF type scheme with proper numerical viscosity preserves both the positivity and the DDF condition. Sufficient conditions are derived for 2D PP high-order schemes, and extension to 3D is discussed. Numerical examples provided in the supplementary material further confirm the theoretical findings.
Full text
Available for:
BFBNIB, INZLJ, NMLJ, NUK, PNG, SAZU, UL, UM, UPUK, ZRSKP
It is known that Flux Corrected Transport algorithms can produce entropy-violating solutions of hyperbolic conservation laws. Our purpose is to design flux correction with
maximal
antidiffusive ...fluxes to obtain entropy solutions of scalar hyperbolic conservation laws. To do this we consider a hybrid difference scheme that is a linear combination of a monotone scheme and a scheme of high-order accuracy. The flux limiters for the hybrid scheme are calculated from a corresponding optimization problem. Constraints for the optimization problem consist of inequalities that are valid for the monotone scheme and applied to the hybrid scheme. We apply the discrete cell entropy inequality with the proper numerical entropy flux to single out a physically relevant solution of scalar hyperbolic conservation laws. A nontrivial approximate solution of the optimization problem yields expressions to compute the required flux limiters. We present examples that show that not all numerical entropy fluxes guarantee to single out a physically correct solution of scalar hyperbolic conservation laws.
Full text
Available for:
EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
In this paper, we introduce a new property of two‐dimensional integrable hydrodynamic chains—existence of infinitely many local three‐dimensional conservation laws for pairs of integrable ...two‐dimensional commuting flows. Infinitely many local three‐dimensional conservation laws for the Benney commuting hydrodynamic chains are constructed. As a by‐product, we established a new method for computation of local conservation laws for three‐dimensional integrable systems. The Mikhalëv equation and the dispersionless limit of the Kadomtsev‐Petviashvili equation are investigated. All known local and infinitely many new quasilocal three‐dimensional conservation laws are presented. Also four‐dimensional conservation laws are considered for couples of three‐dimensional integrable quasilinear systems and for triplets of corresponding hydrodynamic chains.
Full text
Available for:
DOBA, FZAB, GIS, IJS, IZUM, KILJ, NLZOH, NUK, ODKLJ, OILJ, PILJ, PNG, SAZU, SBCE, SBMB, UILJ, UKNU, UL, UM, UPUK
We study a quantum Szilard engine that is not powered by heat drawn from a thermal reservoir, but rather by projective measurements. The engine is constituted of a system , a weight , and a ...Maxwell demon , and extracts work via measurement-assisted feedback control. By imposing natural constraints on the measurement and feedback processes, such as energy conservation and leaving the memory of the demon intact, we show that while the engine can function without heat from a thermal reservoir, it must give up at least one of the following features that are satisfied by a standard Szilard engine: (i) repeatability of measurements; (ii) invariant weight entropy; or (iii) positive work extraction for all measurement outcomes. This result is shown to be a consequence of the Wigner-Araki-Yanase theorem, which imposes restrictions on the observables that can be measured under additive conservation laws. This observation is a first-step towards developing 'second-law-like' relations for measurement-assisted feedback control beyond thermality.
Abstract
In this work, the tanh method is employed to compute some traveling wave patterns of the nonlinear third-order (2+1) dimensional Chaffee-Infante (CI) equation. The tanh technique is ...successfully used to get the traveling wave solutions of a considered model in the form of some hyperbolic functions. The Lie symmetry technique is used to analyze the Chaffee-Infante (CI) equation and compute the Infinitesimal generators under the invariance criteria of Lie groups. Then we construct the commutator table, adjoint representation table, and we have represented symmetry groups for each Infinitesimal generator. The optimal system and similarity reduction method is used to obtain some analytical solutions of the considered model. With the help of the similarity reduction method, we have converted the nonlinear partial differential equation into nonlinear ordinary differential equations (ODEs). Moreover, we have shown graphically obtained wave solutions by using the different values of involving parameters. Conserved quantities of nonlinear CI equation are obtained by the multiplier approach.
Abstract
Results are presented for the conservation laws (CLs) of the optical Bloch equations (OBEs) for the 4-level tripod atomic scheme under the action of three laser fields. CLs are constructed ...for OBEs that include the spontaneous emission, collisional broadening and time of flight relaxation, and also without these effects, i.e. for the Liouville von Neumann equation (LNE). We used the direct method to construct CLs as the linear combinations of the density matrix elements and their products. These CLs were in turn used to obtain another set of CLs that explicitly depend on time and stand with relaxation due to the time of flight in OBEs. We also constructed CLs for OBEs representing special case of the tripod system that supports the coherent population trapping (CPT), the phenomenon characterized by the ‘dark-state’. Tripod scheme has two dark-states with the same Hamiltonian eigenvalue. As we explain, this peculiarity of tripod scheme contributes to additional CLs of both LNE and OBEs with all relaxation and decoherence effects included, when CPT is present.
A typical weighted compact nonlinear scheme (WCNS) uses a convex combination of several low-order polynomials approximated over selected candidate stencils of the same width, achieving ...non-oscillatory interpolation near discontinuities and high-order accuracy for smooth solutions. In this paper, we present a new multi-resolution fifth-order WCNS by making use of the information of polynomials on three nested central spatial sub-stencils having first-, third- and fifth-order accuracy, respectively. The new scheme is capable of obtaining high-order spatial interpolation in smooth regions, and it is characterised by the feature of gradually degrading from fifth-order down to first-order accuracy as large stencils deemed to be crossing strong discontinuities. The advantages of the present scheme include the superior resolution for high-wavenumber fluctuations and the flexibility of implementing different numerical flux functions.
Full text
Available for:
BFBNIB, GIS, IJS, KISLJ, NUK, PNG, UL, UM, UPUK
You have reached the maximum number of search results that are displayed.
For better performance, the search offers a maximum of 1,000 results per query (or 50 pages if the option 10/page is selected).
Consider using result filters or changing the sort order to explore your results further.
PDF
