This paper develops deterministic upper and lower bounds on the influence measure in a network, more precisely, the expected number of nodes that a seed set can influence in the independent cascade model. In particula...
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This paper develops deterministic upper and lower bounds on the influence measure in a network, more precisely, the expected number of nodes that a seed set can influence in the independent cascade model. In particular, our bounds exploit r-nonbacktracking walks and Fortuin--Kasteleyn--Ginibre (FKG) type inequalities, and are computed by message passing algorithms. Further, we provide parameterized versions of the bounds that control the trade-off between efficiency and accuracy. Finally, the tightness of the bounds is illustrated on various network models.
Stealthy interactions are an emerging class of nontrivial, bounded long-ranged oscillatory pair potentials with classical ground states that can be disordered, hyperuniform, and infinitely degenerate. Their hybrid cry...
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A Stieltjes integral representation for the effective diffusivity in turbulent transport is developed. This formula is valid for all Peclet numbers and yields a rigorous resummation of the divergent perturbation serie...
A Stieltjes integral representation for the effective diffusivity in turbulent transport is developed. This formula is valid for all Peclet numbers and yields a rigorous resummation of the divergent perturbation series in Peclet number provided that all diagrams are computed exactly. Another consequence of the integral representation is convergent upper and lower bounds on effective diffusivity for all Peclet numbers utilizing a prescribed finite number of terms in their perturbation series.
Following the ideas of operator product expansion, the velocity v, kinetic energy K=1/2v2, and dissipation rate ε=ν0(∂vi/∂xj)2 are treated as independent dynamical variables, each obeying its own equation of motion....
Following the ideas of operator product expansion, the velocity v, kinetic energy K=1/2v2, and dissipation rate ε=ν0(∂vi/∂xj)2 are treated as independent dynamical variables, each obeying its own equation of motion. The relations Δu(ΔK)2 ∝ r, Δu(Δε)2 ∝ r0, and (Δu)5≊rΔεΔK are derived. If velocity scales as (Δv)rms∝ r(γ/3)−1, then simple power counting gives (ΔK)rms ∝ r1−(γ/6) and (Δε)rms ∝ 1/√(Δv)rms ∝ r(1/2)−(γ/6). In the Kolmogorov turbulence (γ=4) the intermittency exponent μ=(γ/3)-1=1/3 and (Δε)2=O(Re1/4). The scaling relation for the ε fluctuations is a consequence of cancellation of ultraviolet divergences in the equation of motion for the dissipation rate.
Statistical properties of solutions of the random-force–driven Burgers equation are investigated by use of the dynamic renormalization group and direct numerical simulations. The agreement between computed and analyt...
Statistical properties of solutions of the random-force–driven Burgers equation are investigated by use of the dynamic renormalization group and direct numerical simulations. The agreement between computed and analytical results on both exponents and amplitudes of the correlation functions is good. It is shown that a small-scale noise dominates large-scale, long-time (k→0,ω→0) behavior of the system and, as a consequence, no microscopic system of interacting particles described by Burgers equation in the hydrodynamic limit (k→0,ω→0) exists.
The dynamics of velocity fluctuations, governed by the one-dimensional Burgers equation, driven by a white-in-time random force f with the spatial spectrum ‖f(k)‖2∝k−1, is considered. High-resolution numerical expe...
The dynamics of velocity fluctuations, governed by the one-dimensional Burgers equation, driven by a white-in-time random force f with the spatial spectrum ‖f(k)‖2∝k−1, is considered. High-resolution numerical experiments conducted in this work give the energy spectrum E(k)∝k−β with β=5/3±0.02. The observed two-point correlation function C(k,ω) reveals ω∝kz with the ‘‘dynamic exponent’’ z≊2/3. High-order moments of velocity differences show strong intermittency and are dominated by powerful large-scale shocks. The results are compared with predictions of the one-loop renormalized perturbation expansion.
We introduce a lattice Boltzmann model for simulating immiscible binary fluids in two dimensions. The model, based on the Boltzmann equation of lattice-gas hydrodynamics, incorporates features of a previously introduc...
We introduce a lattice Boltzmann model for simulating immiscible binary fluids in two dimensions. The model, based on the Boltzmann equation of lattice-gas hydrodynamics, incorporates features of a previously introduced discrete immiscible lattice-gas model. A theoretical value of the surface-tension coefficient is derived and found to be in excellent agreement with values obtained from simulations. The model serves as a numerical method for the simulation of immiscible two-phase flow; a preliminary application illustrates a simulation of flow in a two-dimensional microscopic model of a porous medium. Extension of the model to three dimensions appears straightforward.
The quantitative interpretation of the recent experiments on turbulent diffusivity in high‐Reynolds‐number Couette–Taylor flow by Tam and Swinney [Phys. Rev. A 36, 1374 (1987)], is presented.
The quantitative interpretation of the recent experiments on turbulent diffusivity in high‐Reynolds‐number Couette–Taylor flow by Tam and Swinney [Phys. Rev. A 36, 1374 (1987)], is presented.
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