Third order nonoscillatory central scheme for hyperbolic conservation laws

Summary. A third-order accurate Godunov-type scheme for the approximate solution of hyperbolic systems of conservation laws is presented. Its two main ingredients include: 1. A non-oscillatory piecewise-quadratic reconstruction of pointvalues from their given cell averages; and 2. A central differencing based on staggered evolution of the reconstructed cell averages. This results in a third-order central scheme, an extension along the lines of the second-order central scheme of Nessyahu and Tadmor \cite{NT}. The scalar scheme is non-oscillatory (and hence – convergent), in the sense that it does not increase the number of initial extrema (– as does the exact entropy solution operator). Extension to systems is carried out by componentwise application of the scalar framework. In particular, we have the advantage that, unlike upwind schemes, no (approximate) Riemann solvers, field-by-field characteristic decompositions, etc., are required. Numerical experiments confirm the high-resolution content of the proposed scheme. Thus, a considerable amount of simplicity and robustness is gained while retaining the expected third-order resolution. Received April 10, 1996 / Revised version received January 20, 1997     

$$(O( V \oplus F), O( V))$$ is a Gelfand pair for any quadratic space V over a local field F

Let V be a quadratic space with a form q over an arbitrary local field F of characteristic different from 2. Let with the form Q extending q with Q(e) = 1. Consider the standard embedding and the two-sided action of on . In this note we show that any -invariant distribution on is invariant with respect to transposition. This result was earlier proven in a bit different form in van Dijk (Math Z 193:581–593, 1986) for , in Aparicio and van Dijk (Complex generalized Gelfand pairs. Tambov University, 2006) for and in Bosman and van Dijk (Geometriae Dedicata 50:261–282, 1994) for p-adic fields. Here we give a different proof. Using results from Aizenbud et al. (arXiv:0709.1273 (math.RT), submitted), we show that this result on invariant distributions implies that the pair (O(V), O(W)) is a Gelfand pair. In the archimedean setting this means that for any irreducible admissible smooth Fréchet representation (π, E) of we have A stronger result for p-adic fields is obtained in Aizenbud et al. (arXiv:0709.4215 (math.RT), submitted).     

Analysis of Alternating-Priority Queueing Models with (Cross) Correlated Switchover Times

This paper analyzes a single server queueing system in which service is alternated between two queues and the server requires a (finite) switchover time to switch from one queue to the other. The distinction from classical results is that the sequence of switchover times from each of the queues need not be i.i.d. nor independent from each other; each sequence is merely required to form a stationary ergodic sequence. With the help of stochastic recursive equations explicit expressions are derived for a number of performance measures, most notably for the average delay of a customer and the average queue lengths under different service disciplines. With these expressions a comparison is made between the service disciplines and the influence of correlation is studied. Finally, through a number of examples it is shown that the correlation can significantly increase the mean delay and the average queue lengths indicating that the correlation between switchover times should not be ignored. This has important implications for communication systems in which a common communication channel is shared amongst various users and where the time between consecutive data transfers is correlated (for example in ad-hoc networks). In addition to this a number of notational mistakes in well-known existing literature are pointed out. AMS subject classification: 68M20, 60J85 A shorter version of this work has been published in the proceedings of IEEE Infocom 2005. This work was partly sponsored by the EURONGI network of excellence.     

Zero-sum constrained stochastic games with independent state processes

We consider a zero-sum stochastic game with side constraints for both players with a special structure. There are two independent controlled Markov chains, one for each player. The transition probabilities of the chain associated with a player as well as the related side constraints depend only on the actions of the corresponding player; the side constraints also depend on the player’s controlled chain. The global cost that player 1 wishes to minimize and that player 2 wishes to maximize, depend however on the actions and Markov chains of both players. We obtain a linear programming formulations that allows to compute the value and saddle point policies for this problem. We illustrate the theoretical results through a zero-sum stochastic game in wireless networks in which each player has power constraints     

On the stability of retrial queues

We consider the following Type of problems. Calls arrive at a queue of capacity K (which is called the primary queue), and attempt to get served by a single server. If upon arrival, the queue is full and the server is busy, the new arriving call moves into an infinite capacity orbit, from which it makes new attempts to reach the primary queue, until it finds it non-full (or it finds the server idle). If the queue is not full upon arrival, then the call (customer) waits in line, and will be served according to the FIFO order. If λ is the arrival rate (average number per time unit) of calls and μ is one over the expected service time in the facility, it is well known that μ > λ is not always sufficient for stability. The aim of this paper is to provide general conditions under which it is a sufficient condition. In particular, (i) we derive conditions for Harris ergodicity and obtain bounds for the rate of convergence to the steady state and large deviations results, in the case that the inter-arrival times, retrial times and service times are independent i.i.d. sequences and the retrial times are exponentially distributed; (ii) we establish conditions for strong coupling convergence to a stationary regime when either service times are general stationary ergodic (no independence assumption), and inter-arrival and retrial times are i.i.d. exponentially distributed; or when inter-arrival times are general stationary ergodic, and service and retrial times are i.i.d. exponentially distributed; (iii) we obtain conditions for the existence of uniform exponential bounds of the queue length process under some rather broad conditions on the retrial process. We finally present conditions for boundedness in distribution for the case of nonpatient (or non persistent) customers. This revised version was published online in June 2006 with corrections to the Cover Date.     

Construction of Approximate Entropy Measure-Valued Solutions for Hyperbolic Systems of Conservation Laws

Entropy solutions have been widely accepted as the suitable solution framework for systems of conservation laws in several space dimensions. However, recent results in De Lellis and Székelyhidi Jr (Ann Math 170(3):1417–1436, 2009) and Chiodaroli et al. (2013) have demonstrated that entropy solutions may not be unique. In this paper, we present numerical evidence that state-of-the-art numerical schemes need not converge to an entropy solution of systems of conservation laws as the mesh is refined. Combining these two facts, we argue that entropy solutions may not be suitable as a solution framework for systems of conservation laws, particularly in several space dimensions. We advocate entropy measure-valued solutions, first proposed by DiPerna, as the appropriate solution paradigm for systems of conservation laws. To this end, we present a detailed numerical procedure which constructs stable approximations to entropy measure-valued solutions, and provide sufficient conditions that guarantee that these approximations converge to an entropy measure-valued solution as the mesh is refined, thus providing a viable numerical framework for systems of conservation laws in several space dimensions. A large number of numerical experiments that illustrate the proposed paradigm are presented and are utilized to examine several interesting properties of the computed entropy measure-valued solutions.     

Urchin-like α-MnO<Subscript>2</Subscript> formed by nanoneedles for high-performance lithium batteries

MnO₂ nanoneedles (NNs) were synthesized by sol-gel assisted by a redox reaction between ascorbic acid and KMnO₄. X-ray powder diffraction (XRD), thermogravimetric analysis (TGA), Raman, far-infrared spectroscopy, and magnetic measurements confirm the tunnel structure of the tetragonal α-MnO₂ phase. The MnO₂ NNs prepared by sol-gel at moderate temperature (T ≈ 350 °C) aggregate with an urchin-like morphology observed by scanning electron (SEM) and high-resolution transmission electron (TEM) microscopy. Electrochemical investigations show an outstanding initial specific capacity ca. 230 mAh g^?1 and 45 % capacity retention at 100th cycle was obtained for these MnO₂ nanoneedles.     

Synchronized cluster formation in coupled laser networks

We experimentally investigate the phase dynamics of laser networks with homogenous time-delayed mutual coupling and establish the fundamental rules that govern their state of synchronization. We identified a specific substructure that imposes its synchronization state on the entire network and show that for any coupling configuration the network forms at most two synchronized clusters. Our results indicate that the synchronization state of the network is a nonlocal phenomenon and cannot be deduced by decomposing the network into smaller substructures, each with its individual synchronization state.     

Improved dynamic programming algorithms for bandwidth minimization and the MinCut Linear Arrangement problem

The dynamic programming algorithm of [12.] for the bandwidth minimization problem is improved. It is shown that, for all k > 1, BANDWIDTH(k) can be solved in O(n^k) steps and simultaneous O(n^k) space, where n is the number of vertices in the graph, and that each such problem is in NSPACE(log n). The same improved dynamic programming algorithm approach works to show that the MINCUT LINEAR ARRANGEMENT problem restricted to the fixed value k, denoted by MINCUT(k), is solvable in O(n^k) steps and simultaneous O(n^k) space and is in the class NSPACE(log n).     

Local coordination of Fe3+ in Li[Co(0.98)Fe(0.02)]O2 as cathode material for lithium ion batteries-multi-frequency EPR and Monte-Carlo Newman-superposition model analysis

The local coordination of the Fe(3+)-centers in Li[Co(0.98)Fe(0.02)]O(2) cathode materials for lithium-ion batteries has been investigated by means of XRD and multi-frequency EPR spectroscopy. EPR clearly showed the Fe(3+) being in a high-spin state with S = 5/2. The set of spin-Hamiltonian parameters obtained from multi-frequency EPR experiments with Larmor frequencies ranging between 9.8 and 406 GHz was transformed into structural information by means of an expansion to standard Newton-superposition modeling, termed as Monte-Carlo Newman superposition modeling. Based on this analysis, an isovalent incorporation of the Fe(3+)-ions on the Co(3+)-sites, i.e. Fe(x)(Co), has been shown. With that respect, the positive sign of the axial second-order fine-structure interaction parameter B(0)(2) is indicative of an elongated oxygen octahedron, whereas B(0)(2) < 0 points to a compressed octahedron coordinated about the Fe(3+)-center. Furthermore, the results obtained here suggest that the oxygen octahedron about the Fe(3+)-ion is slightly distorted as compared to the CoO(6) octahedron, which in turn may impose mechanical strain to the cathode material.