1,639 research outputs found

    Cylindrical Static and Kinetic Binary Space Partitions

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    P. K. Agarwal, L. Guibas, T. M. Murali, and J. S. Vitter. “Cylindrical Static and Kinetic Binary Space Partitions,” Computational Geometry, 16(2), 2000, 103–127. An extended abstract appears in Proceedings of the 13th Annual ACM Symposium on Computational Geometry (SCG ’97), Nice, France, June 1997, 39–48

    Cylindrical Static and Kinetic Binary Space Partitions

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    P. K. Agarwal, L. Guibas, T. M. Murali, and J. S. Vitter. “Cylindrical Static and Kinetic Binary Space Partitions,” Computational Geometry, 16(2), 2000, 103–127. An extended abstract appears in Proceedings of the 13th Annual ACM Symposium on Computational Geometry (SCG ’97), Nice, France, June 1997, 39–48

    A two-stage approach to relaxation in billiard systems of locally confined hard spheres

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    We consider the three-dimensional dynamics of systems of many interacting hard spheres, each individually confined to a dispersive environment, and show that the macroscopic limit of such systems is characterized by a coefficient of heat conduction whose value reduces to a dimensional formula in the limit of vanishingly small rate of interaction. It is argued that this limit arises from an effective loss of memory. Similarities with the diffusion of a tagged particle in binary mixtures are emphasized.Comment: Submitted to Chaos, special issue "Statistical Mechanics and Billiard-Type Dynamical Systems

    Multi-Particle Collision Dynamics -- a Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids

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    In this review, we describe and analyze a mesoscale simulation method for fluid flow, which was introduced by Malevanets and Kapral in 1999, and is now called multi-particle collision dynamics (MPC) or stochastic rotation dynamics (SRD). The method consists of alternating streaming and collision steps in an ensemble of point particles. The multi-particle collisions are performed by grouping particles in collision cells, and mass, momentum, and energy are locally conserved. This simulation technique captures both full hydrodynamic interactions and thermal fluctuations. The first part of the review begins with a description of several widely used MPC algorithms and then discusses important features of the original SRD algorithm and frequently used variations. Two complementary approaches for deriving the hydrodynamic equations and evaluating the transport coefficients are reviewed. It is then shown how MPC algorithms can be generalized to model non-ideal fluids, and binary mixtures with a consolute point. The importance of angular-momentum conservation for systems like phase-separated liquids with different viscosities is discussed. The second part of the review describes a number of recent applications of MPC algorithms to study colloid and polymer dynamics, the behavior of vesicles and cells in hydrodynamic flows, and the dynamics of viscoelastic fluids

    Kinetic and dynamic data structures for convex hulls and upper envelopes

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    AbstractLet S be a set of n moving points in the plane. We present a kinetic and dynamic (randomized) data structure for maintaining the convex hull of S. The structure uses O(n) space, and processes an expected number of O(n2βs+2(n)logn) critical events, each in O(log2n) expected time, including O(n) insertions, deletions, and changes in the flight plans of the points. Here s is the maximum number of times where any specific triple of points can become collinear, βs(q)=λs(q)/q, and λs(q) is the maximum length of Davenport–Schinzel sequences of order s on n symbols. Compared with the previous solution of Basch, Guibas and Hershberger [J. Basch, L.J. Guibas, J. Hershberger, Data structures for mobile data, J. Algorithms 31 (1999) 1–28], our structure uses simpler certificates, uses roughly the same resources, and is also dynamic

    Maximum mass and universal relations of rotating relativistic hybrid hadron-quark stars

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    We construct equilibrium models of uniformly and differentially rotating hybrid hadron-quark stars using equations of state (EOSs) with a first-order phase transition that gives rise to a third family of compact objects. We find that the ratio of the maximum possible mass of uniformly rotating configurations - the supramassive limit - to the Tolman-Oppenheimer-Volkoff (TOV) limit mass is not EOS-independent, and is between 1.15 and 1.31,in contrast with the value of 1.20 previously found for hadronic EOSs. Therefore, some of the constraints placed on the EOS from the observation of the gravitational wave event GW170817 do not apply to hadron-quark EOSs. However, the supramassive limit mass for the family of EOSs we treat is consistent with limits set by GW170817, strengthening the possibility of interpreting GW170817 with a hybrid hadron-quark EOSs. We also find that along constant angular momentum sequences of uniformly rotating stars, the third family maximum and minimum mass models satisfy approximate EOS-independent relations, and the supramassive limit of the third family is approximately 16.5 % larger than the third family TOV limit. For differentially rotating spheroidal stars, we find that a lower-limit on the maximum supportable rest mass is 123 % more than the TOV limit rest mass. Finally, we verify that the recently discovered universal relations relating angular momentum, rest mass and gravitational mass for turning-point models hold for hybrid hadron-quark EOSs when uniform rotation is considered, but have a clear dependence on the degree of differential rotation.Comment: 19 pages, 14 figures, submitted to EPJA Topical Issue "First joint gravitational wave and electromagnetic observations: Implications for nuclear and particle physics

    Sudden collapse of a colloidal gel

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    Metastable gels formed by weakly attractive colloidal particles display a distinctive two-stage time-dependent settling behavior under their own weight. Initially a space-spanning network is formed that for a characteristic time, which we define as the lag time \taud, resists compaction. This solid-like behavior persists only for a limited time. Gels whose age \tw is greater than \taud yield and suddenly collapse. We use a combination of confocal microscopy, rheology and time-lapse video imaging to investigate both the process of sudden collapse and its microscopic origin in an refractive-index matched emulsion-polymer system. We show that the height hh of the gel in the early stages of collapse is well described by the surprisingly simple expression, h(\ts) = \h0 - A \ts^{3/2}, with \h0 the initial height and \ts = \tw-\taud the time counted from the instant where the gel first yields. We propose that this unexpected result arises because the colloidal network progressively builds up internal stress as a consequence of localized rearrangement events which leads ultimately to collapse as thermal equilibrium is re-established.Comment: 14 pages, 11 figures, final versio

    On the Use of Group Theoretical and Graphical Techniques toward the Solution of the General N-body Problem

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    Group theoretic and graphical techniques are used to derive the N-body wave function for a system of identical bosons with general interactions through first-order in a perturbation approach. This method is based on the maximal symmetry present at lowest order in a perturbation series in inverse spatial dimensions. The symmetric structure at lowest order has a point group isomorphic with the S_N group, the symmetric group of N particles, and the resulting perturbation expansion of the Hamiltonian is order-by-order invariant under the permutations of the S_N group. This invariance under S_N imposes severe symmetry requirements on the tensor blocks needed at each order in the perturbation series. We show here that these blocks can be decomposed into a basis of binary tensors invariant under S_N. This basis is small (25 terms at first order in the wave function), independent of N, and is derived using graphical techniques. This checks the N^6 scaling of these terms at first order by effectively separating the N scaling problem away from the rest of the physics. The transformation of each binary tensor to the final normal coordinate basis requires the derivation of Clebsch-Gordon coefficients of S_N for arbitrary N. This has been accomplished using the group theory of the symmetric group. This achievement results in an analytic solution for the wave function, exact through first order, that scales as N^0, effectively circumventing intensive numerical work. This solution can be systematically improved with further analytic work by going to yet higher orders in the perturbation series.Comment: This paper was submitted to the Journal of Mathematical physics, and is under revie

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