1,318 research outputs found
Discretization of the velocity space in solution of the Boltzmann equation
We point out an equivalence between the discrete velocity method of solving
the Boltzmann equation, of which the lattice Boltzmann equation method is a
special example, and the approximations to the Boltzmann equation by a Hermite
polynomial expansion. Discretizing the Boltzmann equation with a BGK collision
term at the velocities that correspond to the nodes of a Hermite quadrature is
shown to be equivalent to truncating the Hermite expansion of the distribution
function to the corresponding order. The truncated part of the distribution has
no contribution to the moments of low orders and is negligible at small Mach
numbers. Higher order approximations to the Boltzmann equation can be achieved
by using more velocities in the quadrature
Efficient kinetic method for fluid simulation beyond the Navier-Stokes equation
We present a further theoretical extension to the kinetic theory based
formulation of the lattice Boltzmann method of Shan et al (2006). In addition
to the higher order projection of the equilibrium distribution function and a
sufficiently accurate Gauss-Hermite quadrature in the original formulation, a
new regularization procedure is introduced in this paper. This procedure
ensures a consistent order of accuracy control over the non-equilibrium
contributions in the Galerkin sense. Using this formulation, we construct a
specific lattice Boltzmann model that accurately incorporates up to the third
order hydrodynamic moments. Numerical evidences demonstrate that the extended
model overcomes some major defects existed in the conventionally known lattice
Boltzmann models, so that fluid flows at finite Knudsen number (Kn) can be more
quantitatively simulated. Results from force-driven Poiseuille flow simulations
predict the Knudsen's minimum and the asymptotic behavior of flow flux at large
Kn
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Epidemiologic data and pathogen genome sequences: a powerful synergy for public health
Epidemiologists aim to inform the design of public health interventions with evidence on the evolution, emergence and spread of infectious diseases. Sequencing of pathogen genomes, together with date, location, clinical manifestation and other relevant data about sample origins, can contribute to describing nearly every aspect of transmission dynamics, including local transmission and global spread. The analyses of these data have implications for all levels of clinical and public health practice, from institutional infection control to policies for surveillance, prevention and treatment. This review highlights the range of epidemiological questions that can be addressed from the combination of genome sequence and traditional ‘line lists’ (tables of epidemiological data where each line includes demographic and clinical features of infected individuals). We identify opportunities for these data to inform interventions that reduce disease incidence and prevalence. By considering current limitations of, and challenges to, interpreting these data, we aim to outline a research agenda to accelerate the genomics-driven transformation in public health microbiology
Developing the Business Process Management Performance of an Information System Using the Delphi Study Technique
Information systems are used to manage an organisation’s business process management (BPM), its operations and performance. Thus, organisations will benefit from systematic processes for evaluating their business information systems with the aim of developing BPM and business information systems performance. The Delphi Study Technique (DST) is a structured business study technique that can be used as a systematic and interactive assessment process based on controlled feedback from business experts, professionals, or others with relevant experience. The Delphi study technique (also known as the Delphi method) has produced significant achievements in evaluating and improving BPM through identifying BPM values to be used as key indicators. This paper describes the essential stages for measuring the performance of an information system by combining the Delphi method and BPM values to improve an organisation’s business performance. The paper provides examples of the use of DST and discusses empirical results from the published literature
Microscopic Derivation of Causal Diffusion Equation using Projection Operator Method
We derive a coarse-grained equation of motion of a number density by applying
the projection operator method to a non-relativistic model. The derived
equation is an integrodifferential equation and contains the memory effect. The
equation is consistent with causality and the sum rule associated with the
number conservation in the low momentum limit, in contrast to usual acausal
diffusion equations given by using the Fick's law. After employing the Markov
approximation, we find that the equation has the similar form to the causal
diffusion equation. Our result suggests that current-current correlations are
not necessarily adequate as the definition of diffusion constants.Comment: 10 pages, 1 figure, Final version published in Phys. Rev.
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Reconnection of magnetic lines in an ideal fluid
The rate of reconnection of magnetic lines at an X-point, also growth of a ''tearing'' configuration have always been related to the presence of resistivity or other dissipative mechanisms. These phenomena, exhibiting nonconservation of magnetic line topology, are shown to occur in an ideal, nondissipative fluid, thereby violating beliefs, theorems, and calculations of over a century (including the mathematically equivalent questions involving vortex lines in an ideal fluid)
Incorporating Forcing Terms in Cascaded Lattice-Boltzmann Approach by Method of Central Moments
Cascaded lattice-Boltzmann method (Cascaded-LBM) employs a new class of
collision operators aiming to improve numerical stability. It achieves this and
distinguishes from other collision operators, such as in the standard single or
multiple relaxation time approaches, by performing relaxation process due to
collisions in terms of moments shifted by the local hydrodynamic fluid
velocity, i.e. central moments, in an ascending order-by-order at different
relaxation rates. In this paper, we propose and derive source terms in the
Cascaded-LBM to represent the effect of external or internal forces on the
dynamics of fluid motion. This is essentially achieved by matching the
continuous form of the central moments of the source or forcing terms with its
discrete version. Different forms of continuous central moments of sources,
including one that is obtained from a local Maxwellian, are considered in this
regard. As a result, the forcing terms obtained in this new formulation are
Galilean invariant by construction. The method of central moments along with
the associated orthogonal properties of the moment basis completely determines
the expressions for the source terms as a function of the force and macroscopic
velocity fields. In contrast to the existing forcing schemes, it is found that
they involve higher order terms in velocity space. It is shown that the
proposed approach implies "generalization" of both local equilibrium and source
terms in the usual lattice frame of reference, which depend on the ratio of the
relaxation times of moments of different orders. An analysis by means of the
Chapman-Enskog multiscale expansion shows that the Cascaded-LBM with forcing
terms is consistent with the Navier-Stokes equations. Computational experiments
with canonical problems involving different types of forces demonstrate its
accuracy.Comment: 55 pages, 4 figure
Explicit coercivity estimates for the linearized Boltzmann and Landau operators
We prove explicit coercivity estimates for the linearized Boltzmann and
Landau operators, for a general class of interactions including any
inverse-power law interactions, and hard spheres. The functional spaces of
these coercivity estimates depend on the collision kernel of these operators.
They cover the spectral gap estimates for the linearized Boltzmann operator
with Maxwell molecules, improve these estimates for hard potentials, and are
the first explicit coercivity estimates for soft potentials (including in
particular the case of Coulombian interactions). We also prove a regularity
property for the linearized Boltzmann operator with non locally integrable
collision kernels, and we deduce from it a new proof of the compactness of its
resolvent for hard potentials without angular cutoff.Comment: 32 page
Blow-up of the hyperbolic Burgers equation
The memory effects on microscopic kinetic systems have been sometimes
modelled by means of the introduction of second order time derivatives in the
macroscopic hydrodynamic equations. One prototypical example is the hyperbolic
modification of the Burgers equation, that has been introduced to clarify the
interplay of hyperbolicity and nonlinear hydrodynamic evolution. Previous
studies suggested the finite time blow-up of this equation, and here we present
a rigorous proof of this fact
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