Systems Of Laws Research Articles

The influence of parasitic modes on stable lattice Boltzmann schemes and weakly unstable multi-step Finite Difference schemes

Numerical analysis for linear constant-coefficient multi-step Finite Difference schemes is a longstanding topic, developed approximately fifty years ago. It relies on the stability of the scheme, and thus—within the L2 setting—on the absence of multiple roots of the amplification polynomial on the unit circle. This allows for the decoupling, while discussing the convergence of the method, of the study of the consistency of the scheme from the precise knowledge of its parasitic/spurious modes, so that the methods can be essentially studied as if they had only one step. Furthermore, stability alleviates the need to delve into the complexities of floating-point arithmetic on computers, which can be challenging topics to address. In this paper, we demonstrate that in the case of “weakly” unstable Finite Difference schemes with multiple roots on the unit circle, although the schemes may remain stable, considering parasitic modes is essential in studying their consistency and, consequently, their convergence. This research was prompted by unexpected numerical results on stable lattice Boltzmann schemes, which can be rewritten in terms of multi-step Finite Difference schemes. Unlike Finite Difference schemes, rigorous numerical analysis for lattice Boltzmann schemes is a contemporary topic with much left for future discoveries. Initial expectations suggested that third-order initialization schemes would suffice to maintain the accuracy of fourth-order schemes. However, this assumption proved incorrect for weakly unstable Finite Difference schemes and for stable lattice Boltzmann methods. This borderline scenario underscores that particular care must be adopted for lattice Boltzmann schemes, and the significance of genuine stability in facilitating the construction of Lax-Richtmyer-like theorems and in mastering the impact of round-off errors concerning Finite Difference schemes. Despite the simplicity and apparent lack of practical usage of the linear transport equation at constant velocity considered throughout the paper, we demonstrate that high-order lattice Boltzmann schemes for this equation can be used to tackle nonlinear systems of conservation laws relying on a Jin-Xin approximation and high-order splitting formulæ.

Miscegenation and militarization: undoing racial colonial citizenship for the next century

ABSTRACT This essay considers the Immigration Act of 1924, otherwise known as the Johnson-Reed Act (JRA), within historical and contemporary contexts of anti-miscegenation and Indigenous erasure that are undercurrents of citizenship and immigration processes. By using a framework of settler colonialism carried out by the U.S. nation-state, we explore connections among racialized peoples in U.S. American empire and the push for racial purity through systems of blood quantum and anti-miscegenation laws. With attention to how colonialism from the continental USA flows to locales such as Guåhan/Guam, a place enacting sovereignty despite occupation and colonial possession, we consider how immigration and citizenship are wielded as tools of U.S. American militarization. Ultimately, we argue that critiquing miscegenation and militarism is necessary to overcome racial and colonial violences of empire.

Efficient spectral element method for the Euler equations on unbounded domains

Mitigating the impact of waves leaving a numerical domain has been a persistent challenge in numerical modeling. Reducing wave reflection at the domain boundary is crucial for accurate simulations. Absorbing layers, while common, often incur significant computational costs. This paper introduces an efficient application of a Legendre-Laguerre basis for absorbing layers for two-dimensional non-linear compressible Euler equations. The method couples a spectral-element bounded domain with a semi-infinite region, employing a tensor product of Lagrange and scaled Laguerre basis functions. Semi-infinite elements are used in the absorbing layer with Rayleigh damping. In comparison to existing methods with similar absorbing layer extensions, this approach, a pioneering application to the Euler equations of compressible and stratified flows, demonstrates substantial computational savings. The study marks the first application of semi-infinite elements to mitigate wave reflection in the solution of the Euler equations, particularly in nonhydrostatic atmospheric modeling. A comprehensive set of tests demonstrates the method's versatility for general systems of conservation laws, with a focus on its effectiveness in damping vertically propagating mountain gravity waves, a benchmark for atmospheric models. Across all tests, the model presented in this paper consistently exhibits notable performance improvements compared to a traditional Rayleigh damping approach.

Novel spectral methods for shock capturing and the removal of tygers in computational fluid dynamics

Spectral methods yield numerical solutions of the Galerkin-truncated versions of nonlinear partial differential equations (PDEs) involved especially in fluid dynamics. In the presence of discontinuities, such as shocks, spectral approximations develop Gibbs oscillations near the discontinuity. This causes the numerical solution to deviate quickly from the true solution. For spectral approximations of the inviscid Burgers equation in one-dimension (1D), nonlinear wave resonances lead to the formation of localised oscillatory structures called tygers in well-resolved areas of the flow, far from the shock. Recently, the author of [1] has proposed novel spectral relaxation (SR) and spectral purging (SP) schemes for the removal of tygers and Gibbs oscillations in spectral approximations of nonlinear conservation laws. For the 1D inviscid Burgers equation, it is shown in [1] that the novel SR and SP approximations of the solution converge strongly in L2 norm to the entropic weak solution, under an appropriate choice of kernels and related parameters. In this work, we carry out a detailed numerical investigation of SR and SP schemes when applied to the 1D inviscid Burgers equation and report the efficiency of shock capture and the removal of tygers. We then extend our study to systems of nonlinear hyperbolic conservation laws, such as the 2×2 system of the shallow water equations and the standard 3×3 system of 1D compressible Euler equations. For the latter, we generalise the implementation of SR methods to non-periodic problems using Chebyshev polynomials. We then turn to singular flow in the 1D wall approximation of the 3D-axisymmetric wall-bounded incompressible Euler equation [2]. Here, in order to determine the blowup time of the solution, we compare the decay of the width of the analyticity strip, obtained from the pure pseudospectral method (PPS), with the improved estimate obtained using the novel spectral relaxation scheme.

Современная банковская система Китайской Народной Республики

Cooperation with banks of the People’s Republic of China (hereinafter referred to as China, the PRC) becomes a crucial component for successful development of large and small business in Russia. The Chinese banking system has proven its efficiency as an important development institution of one of the world’s leading powers. This experience may be in great demand in the Russian reality. Besides, the situation in the Russian-Chinese financial and banking logistics proves relevance of using experience of the PRC in the development of the national banking system. The authors emphasize special aspects of the banking system of the PRC that characterize its levels, the system of laws that govern banking activities and the current status taking into account the development of banking relations between Russia and China against the background of escalation of Chinese-American relations, U.S. sanctions.

$$\delta '''$$-shock wave solution to a nonstrictly hyperbolic system of conservation laws using weak asymptotic method

$$\delta '''$$-shock wave solution to a nonstrictly hyperbolic system of conservation laws using weak asymptotic method

General boundary conditions for a Boussinesq model with varying bathymetry

AbstractThis paper is devoted to the theoretical and numerical investigation of the initial boundary value problem for a system of equations used for the description of waves in coastal areas, namely, the Boussinesq–Abbott system in the presence of topography. We propose a procedure that allows one to handle very general linear or nonlinear boundary conditions. It consists in reducing the problem to a system of conservation laws with nonlocal fluxes and coupled to an ordinary differential equation. This reformulation is used to propose two hybrid finite volumes/finite differences schemes of first and second order, respectively. The possibility to use many kinds of boundary conditions is used to investigate numerically the asymptotic stability of the boundary conditions, which is an issue of practical relevance in coastal oceanography since asymptotically stable boundary conditions would allow one to reconstruct a wave field from the knowledge of the boundary data only, even if the initial data are not known.

Semi-implicit-Type Order-Adaptive CAT2 Schemes for Systems of Balance Laws with Relaxed Source Term

AbstractIn this paper, we present two semi-implicit-type second-order compact approximate Taylor (CAT2) numerical schemes and blend them with a local a posteriori multi-dimensional optimal order detection (MOOD) paradigm to solve hyperbolic systems of balance laws with relaxed source terms. The resulting scheme presents the high accuracy when applied to smooth solutions, essentially non-oscillatory behavior for irregular ones, and offers a nearly fail-safe property in terms of ensuring the positivity. The numerical results obtained from a variety of test cases, including smooth and non-smooth well-prepared and unprepared initial conditions, assessing the appropriate behavior of the semi-implicit-type second order CATMOOD schemes. These results have been compared in the accuracy and the efficiency with a second-order semi-implicit Runge-Kutta (RK) method.

GRP – A direct Godunov extension

The classical paper [40] by S. K. Godunov had a revolutionary effect on the field of numerical simulations of compressible fluid flows. Yet, for some twenty years after its publication, it was mostly used by the mathematical community in the Soviet Union. The seminal paper of van Leer [85] has inaugurated the period of universal interest in high-resolution extensions of Godunov's scheme. The first step to take was to modify the (locally) self-similar solution to the Riemann Problem (at discontinuities) by allowing piecewise-polynomial (rather than piecewise-constant) initial data. The GRP (Generalized Riemann Problem) analysis [6] provided analytical solutions (for piecewise-linear data) that could be readily implemented in a high-resolution robust code. This review paper focuses on the evolution of some mathematical aspects of this method. It addresses the three concepts of consistency, stability and convergence in the context of compact finite difference (or finite volume) schemes for systems of nonlinear hyperbolic conservation laws. The treatment utilizes the framework of “balance laws”, a common viewpoint in relevant physical conservation laws. The first significant observation is that under very mild conditions a weak solution is indeed a solution to the balance law (obtained by a formal application of the Gauss-Green formula). Since high-resolution schemes require the computation of several quantities per mesh cell (e.g., slopes), the notion of “consistency” must be extended to this framework. A combination of consistency hypothesis with stability of the scheme leads to a suitable convergence theorem, generalizing the classical convergence theorem of Lax and Wendroff [52]. Finally, the limit functions are shown to be entropy solutions by using a notion of “Godunov compatibility”, which serves as a substitute to the entropy condition.

Prandtl-Meyer Reflection Configurations, Transonic Shocks, and Free Boundary Problems

We are concerned with the Prandtl-Meyer reflection configurations of unsteady global solutions for supersonic flow impinging upon a symmetric solid wedge. Prandtl (1936) first employed the shock polar analysis to show that there are two possible steady configurations: the steady weak shock solution and the steady strong shock solution, when a steady supersonic flow impinges upon the solid wedge – the half-angle of which is less than a critical angle (i.e., the detachment angle), and then conjectured that the steady weak shock solution is physically admissible since it is the one observed experimentally. The fundamental issue of whether one or both of the steady weak and strong shocks are physically admissible has been vigorously debated over the past eight decades and has not yet been settled in a definitive manner. On the other hand, the Prandtl-Meyer reflection configurations are core configurations in the structure of global entropy solutions of the two-dimensional Riemann problem, while the Riemann solutions themselves are local building blocks and determine local structures, global attractors, and large-time asymptotic states of general entropy solutions of multidimensional hyperbolic systems of conservation laws. In this sense, we have to understand the reflection configurations in order to understand fully the global entropy solutions of two-dimensional hyperbolic systems of conservation laws, including the admissibility issue for the entropy solutions. In this monograph, we address this longstanding open issue and present our analysis to establish the stability theorem for the steady weak shock solutions as the long-time asymptotics of the Prandtl-Meyer reflection configurations for unsteady potential flow for all the physical parameters up to the detachment angle. To achieve these, we first reformulate the problem as a free boundary problem involving transonic shocks and then obtain appropriate monotonicity properties and uniform a priori estimates for admissible solutions, which allow us to employ the Leray-Schauder degree argument to complete the theory for all the physical parameters up to the detachment angle.

‘LIKE SHEEP TO THE SLAUGHTER’: ANIMAL AGENCY AND ECHOES OF THE HOLOCAUST IN WOLFDIETRICH SCHNURRE'S WRITING

ABSTRACTThis article examines the writings of Wolfdietrich Schnurre (1920–89) through a combined lens of zoocriticism and Holocaust studies. Drawing on Anna Barcz's concept of ‘vulnerable realism’, it posits an analogy between Jews targeted by the Nazis’ exterminatory programme, who struggled to articulate their suffering in the language of empirical historiography, and animals who, excluded from the human system of moral rights and laws, have no means of voicing the oppression they endure. The article argues, however, that, rather than portraying animals as mute and helpless victims, Schnurre's short stories – ‘Die Tat’, ‘Der Verrat’ and ‘Das Manöver’ (1958) – endow their nonhuman protagonists with moral agency and with an ensuing capacity to resist their tormentors. Read in dialogue with Schnurre's Holocaust novel, Ein Unglücksfall (1981), and in the light of the human–animal entanglement advocated by his writings, these stories can be interpreted as a subtle contestation of the idea of Jewish passivity during the Nazi era.

Efficient entropy-stable discontinuous spectral-element methods using tensor-product summation-by-parts operators on triangles and tetrahedra

We present a new class of efficient and robust discontinuous spectral-element methods of arbitrary order for nonlinear hyperbolic systems of conservation laws on curved triangular and tetrahedral unstructured grids. Such discretizations employ a recently introduced family of sparse tensor-product summation-by-parts (SBP) operators in collapsed coordinates within an entropy-conservative modal formulation, which is rendered entropy stable when a dissipative numerical flux is used at element interfaces. The proposed algorithms exploit the structure of such SBP operators alongside that of the Proriol–Koornwinder–Dubiner polynomial basis used to represent the numerical solution on the reference triangle or tetrahedron, and a weight-adjusted approximation is employed in order to efficiently invert the local mass matrix for curvilinear elements. Using such techniques, we obtain an improvement in time complexity from O(p2d) to O(pd+1) relative to existing entropy-stable formulations using multidimensional SBP operators not possessing such a tensor-product structure, where p is the polynomial degree of the approximation and d is the number of spatial dimensions. The number of required entropy-conservative two-point flux evaluations between pairs of quadrature nodes is accordingly reduced by a factor ranging from 1.56 at p=2 to 4.57 at p=10 for triangles, and from 1.88 at p=2 to 10.99 at p=10 for tetrahedra. Through numerical experiments involving smooth solutions to the compressible Euler equations on isoparametric triangular and tetrahedral grids, the proposed methods using tensor-product SBP operators are shown to exhibit similar levels of accuracy for a given mesh and polynomial degree to those using multidimensional operators based on symmetric quadrature rules, with both approaches achieving order p+1 convergence with respect to the element size in the presence of interface dissipation as well as exponential convergence with respect to the polynomial degree. Furthermore, both operator families are shown to give rise to entropy-stable schemes which exhibit excellent robustness for test problems characteristic of under-resolved turbulence simulations. Such results suggest that the algorithmic advantages resulting from the use of tensor-product operators are obtained without compromising accuracy or robustness, enabling the efficient extension of the benefits of entropy stability to higher polynomial degrees than previously considered for triangular and tetrahedral elements.

The Influence of Theorie Von Stufenbau Der Rechtsordnung in the Indonesian Legal System

The aim of this research is to analyze the influence of Hans Kelsen's Theorie Von Stufenufbau Der Rechtsordnung on the Indonesian legal system. The research method employed is legal research with a statutory and conceptual approach. Primary and secondary legal materials are analyzed using normative analysis. The findings reveal that Theorie Von Stufenufbau Der Rechtsordnung significantly impacts the Indonesian legal system. There are at least two main influences identified. First, the system of laws and regulations in Indonesia has been structured hierarchically since the enactment of the Temporary People's Consultative Assembly Decree No. XX/1966 up to the present day. However, this hierarchy is not absolute, especially concerning the positions of Perppu and People's Consultative Assembly Decrees. Second, there is a recognized mechanism for reviewing legal norms to ensure their validity, whether through judicial review, political review, or executive review. The hierarchical structure of Indonesia's legal system reflects Kelsen's theory, which posits that law consists of interrelated levels of norms. Each level derives its authority from the norm above it, with the basic norm at the apex, serving as the source of legitimacy for the entire legal system. In the Indonesian context, this basic norm can be identified as the UUD NRI 1945, which underpins all subordinate legislation. The review mechanism for legal norms also illustrates the influence of Kelsen's theory. Judicial review, conducted by the Constitutional Court, assesses whether a law aligns with the Constitution. Political review is undertaken by legislative bodies such as the DPR, which can evaluate and amend legislation. Executive review is carried out by executive bodies, such as the President or ministers, who have the authority to adjust or repeal regulations deemed inappropriate.

Gradient-Based Monte Carlo Methods for Relaxation Approximations of Hyperbolic Conservation Laws

Particle methods based on evolving the spatial derivatives of the solution were originally introduced to simulate reaction-diffusion processes, inspired by vortex methods for the Navier–Stokes equations. Such methods, referred to as gradient random walk methods, were extensively studied in the ’90s and have several interesting features, such as being grid-free, automatically adapting to the solution by concentrating elements where the gradient is large, and significantly reducing the variance of the standard random walk approach. In this work, we revive these ideas by showing how to generalize the approach to a larger class of partial differential equations, including hyperbolic systems of conservation laws. To achieve this goal, we first extend the classical Monte Carlo method to relaxation approximation of systems of conservation laws, and subsequently consider a novel particle dynamics based on the spatial derivatives of the solution. The methodology, combined with asymptotic-preserving splitting discretization, yields a way to construct a new class of gradient-based Monte Carlo methods for hyperbolic systems of conservation laws. Several results in one spatial dimension for scalar equations and systems of conservation laws show that the new methods are very promising and yield remarkable improvements compared to standard Monte Carlo approaches, either in terms of variance reduction as well as in describing the shock structure.

Illocutionary logic as a tool for reconstructing Kant’s derivation of the formula of the categorical imperative from its mere concept

This paper aims to reconstruct Kant’s derivation of the formula of the categorical imperative from its mere concept with the help of the resources of Searle’s and Vanderveken’s illocutionary logic. The main exegetical hypothesis is that the derivation envisaged by Kant consists in deriving the formula from the success conditions of categorical imperatives. These conditions, which are analogous to the success conditions of ordinary orders, contain restrictions for the successful construction of a system of moral laws that determine what the content of the categorical imperative must be.

Coordination and Development of Public Interest Protection and Administrative Legal Construction

The purpose of this study is to deeply explore the internal relationship between the protection of public interests and the construction of administrative rule of law, and put forward some strategic suggestions to promote their coordinated development. By analyzing the relationship between public interest guarantee and administrative rule of law construction, this study reveals the mutual promotion relationship between them: public interest guarantee is an important goal of administrative rule of law construction, and administrative rule of law construction is an effective means to realize public interest guarantee. On this basis, this study puts forward a series of strategic suggestions, including improving the system of administrative laws and regulations to provide solid legal protection, strengthening administrative supervision to prevent power abuse and corruption, and promoting openness of government affairs, enhancing transparency and public participation in government decision-making, so as to promote democratic and scientific decision-making. These strategies are aimed at ensuring the maximum protection of public interests and promoting the continuous improvement and development of administrative rule of law. This study is of great theoretical and practical significance for deepening the understanding of the relationship between the protection of public interests and the construction of administrative rule of law, and guiding the policy formulation and implementation in practice.

Islam: The Complete, Functional and Practical Guide to Life

People say developed countries became developed by following secularism while Muslim countries became backward by following Islam. This is false perception. In fact developed countries are following Islamic principles unknowingly in all the areas of development; Islamic principles of rule of law, justice, honesty, integrity, research and knowledge learning, development and application. Developed countries and corruption ridden Muslim countries are self harming in all those areas where they are not following Islamic principles; resource intensive hedonism, predatory economic and financial policies, corruption, fraud, injustice, prejudice and selective exploitation of people. Latest development in many developed countries is adoption of prohibition of smoking in public places and this is also based on Islamic principle of avoiding greater harm. So Islam is an essential aspect of humanity’s existence. It teaches us how to conduct ourselves in all aspects of life in a morally and legally upright manner. Islam created a well-defined system of laws governing moral behavior, civil and political rights, social issues and rights, marriage and divorce laws, inheritance rights, and all other matters we deal with daily. It serves as a guide to life in all its facets and is not just for the mosque. Since Islam is logical and rational, it keeps a Muslim free from confusion of any kind. These are some of the main points raised in the paper regarding how Islam is a comprehensive, functional, and practical code of life. Nine major relevant and significant fields have been discussed: the Islamic political system, law and legal system, Jihad, economic system, education system, marriage and family, Islamic society, the mindset, and the hijab. The discussion is analytical and comparative addressing secular ideologies based on Islamic texts and social sciences. The paper establishes that the Islamic system is the alternative system that can replace secular ideologies. This paper has been summarized from a broader and larger discussion of the same topic.

Extensions and investigations of space‐time generalized Riemann problems numerical schemes for linear systems of conservation laws with source terms

AbstractThe space‐time generalized Riemann problems method allows to obtain numerical schemes of arbitrary high order that can be used with very large time steps for systems of linear hyperbolic conservation laws with source term. They have been introduced in Berthon et al. (J. Sci. Comput. 55 (2013), 268–308.) in 1D and on 2D unstructured meshes made of triangles. The objective of this article is to complement them in order to answer some important questions arising when they are involved. The formulation is described in detail on quadrangle meshes, the choice of approximation basis is discussed and Legendre polynomials are used in practical cases. The addition of a limiter to preserve certain properties without compromising accuracy is also considered. Finally, the asymptotic behavior of the scheme in the diffusion regime is studied.

Public Control as a Tool for Combating Crime

The article is devoted to the analysis of the place and role of the institution of public control in the system of tools to combat crime. This institution of civil society is analyzed as the most important legal guarantee for the implementation, protection and defense of the system of constitutional principles in Russia, as well as the system of human and civil rights and freedoms, the rights and legitimate interests of numerous public associations and other non-governmental non-profit organizations. The authors substantiate the importance of the institution of public control in the Russian Federation as a tool for the prevention and suppression of crimes. At the same time, the role of this institution of civil society is particularly highlighted as a tool in the fight against corruption and other crimes committed by officials of public authorities, state and municipal organizations, and other bodies and organizations that exercise certain public powers on the basis of federal laws. The article formalizes and explores the main problems that impede the use of the institution of public control in the fight against crime in the Russian Federation, in particular due to: the lack of mention of this institution of civil society in the Basic Law of Russia; imperfect legislation on public control; weak powers of its subjects; removing from the scope of the Federal Law of dated of 21.06.2014 № 212-FL “On the Fundamentals of Public Control in the Russian Federation” the activities, acts and decisions of the majority of Russian law enforcement agencies, as well as types of public relations where there is a high crime rate; weak funding from the budgets of all levels of activities of subjects of public control; weak use of positive foreign experience of civil society institutions in the fight against crime; insufficient use of modern information and communication technologies. The authors have developed and justified a system of measures to resolve these problems, including by: incorporating public control into the Constitution of Russia; developing a system of federal laws devoted to the organization and implementation of public control in relation to the activities, acts and decisions of the country's law enforcement agencies; expanding the powers of subjects of public control; active use of foreign positive experience of civil society participation in the fight against crime; development of a system of federal programs for organizational, legal, financial, technical support for the institution of public control in Russia.

A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate

Understanding the dynamics of phase boundaries in fluids requires quantitative knowledge about the microscale processes at the interface. We consider the sharp-interface motion of the compressible two-component flow and propose a heterogeneous multiscale method (HMM) to describe the flow fields accurately. The multiscale approach combines a hyperbolic system of balance laws on the continuum scale with molecular-dynamics (MD) simulations on the microscale level. Notably, the multiscale approach is necessary to compute the interface dynamics because there is—at present—no closed continuum-scale model. The basic HMM relies on a moving-mesh finite-volume method and has been introduced recently for the compressible one-component flow with phase transitions by Magiera and Rohde in (J Comput Phys 469: 111551, 2022). To overcome the numerical complexity of the MD microscale model, a deep neural network is employed as an efficient surrogate model. The entire approach is finally applied to simulate droplet dynamics for argon-methane mixtures in several space dimensions. To our knowledge, such compressible two-phase dynamics accounting for microscale phase-change transfer rates have not yet been computed.