An Efficient Modified "Walk On Spheres" Algorithm for the Linearized Poisson-Boltzmann Equation

A discrete random walk method on grids was proposed and used to solve the linearized Poisson-Boltzmann equation (LPBE) \cite{Rammile}. Here, we present a new and efficient grid-free random walk method. Based on a modified `` Walk On Spheres" (WOS) algorithm \cite{Elepov-Mihailov1973} for the LPBE, this Monte Carlo algorithm uses a survival probability distribution function for the random walker in a continuous and free diffusion region. The new simulation method is illustrated by computing four analytically solvable problems. In all cases, excellent agreement is observed.Comment: 12 pages, 5 figure

On the Rapid Estimation of Permeability for Porous Media Using Brownian Motion Paths

We describe two efficient methods of estimating the fluid permeability of standard models of porous media by using the statistics of continuous Brownian motion paths that initiate outside a sample and terminate on contacting the porous sample. The first method associates the "penetration depth" with a specific property of the Brownian paths, then uses the standard relation between penetration depth and permeability to calculate the latter. The second method uses Brownian paths to calculate an effective capacitance for the sample, then relates the capacitance, via angle-averaging theorems to the translational hydrodynamic friction of the sample. Finally, a result of Felderhof is used to relate the latter quantity to the permeability of the sample. We find that the penetration depth method is highly accurate in predicting permeability of porous material

Algebraic Properties of Riemannian Manifolds

Algebraic properties are explored for the curvature tensors of Riemannian manifolds, using the irreducible decomposition of curvature tensors. Our method provides a powerful tool to analyze the irreducible basis as well as an algorithm to determine the linear dependence of arbitrary Riemann polynomials. We completely specify 13 independent basis elements for the quartic scalars and explicitly find 13 linear relations among 26 scalar invariants. Our method provides several completely new results, including some clues to identify 23 independent basis elements from 90 quintic scalars, that are difficult to find otherwise.Comment: A few typos corrected; 40 pages (4 appendices: 16 pages). To appear in General Relativity and Gravitatio

Yang-Lee Zeros of the Triangular Ising Antiferromagnets

Using both the exact enumeration method (microcanonical transfer matrix) for a small system (L = 9) and the Wang-Landau Monte Carlo algorithm for large systems to L = 30, we obtain the exact and approximate densities of states g(M,E), as a function of magnetization M and exchange energy E, for the triangular-lattice Ising model. Based on the density of states g(M,E), we investigate the phase transition properties of Yang-Lee zeros for the triangular Ising antiferromagnets and obtain the magnetic exponents at various temperatures

Clinical Role of Interstitial Pneumonia in Patients with Scrub Typhus: A Possible Marker of Disease Severity

Interstitial pneumonia (IP) frequently occurs in patients with scrub typhus, but its clinical significance is not well known. This study was designed to evaluate interstitial pneumonia as a marker of severity of the disease for patients with scrub typhus. We investigated clinical parameters representing the severity of the disease, and the chest radiographic findings for 101 patients with scrub typhus. We then compared these clinical factors between patients with and without IP. We also studied the relationship between IP and other chest radiographic findings. The chest radiography showed IP (51.4%), pleural effusion (42.6%), cardiomegaly (14.9%), pulmonary alveolar edema (20.8%), hilar lymphadenopathy (13.8%) and focal atelectasis (11.8%), respectively. The patients with IP (n=52) had higher incidences in episode of hypoxia (p=0.030), hypotension (p=0.024), severe thrombocytopenia (p=0.036) and hypoalbuminemia (p=0.013) than the patients without IP (n=49). The patients with IP also had higher incidences of pleural effusion (p<0.001), focal atelectasis (p=0.019), cardiomegaly (p<0.001), pulmonary alveolar edema (p=0.011) and hilar lymphadenopathy (p<0.001) than the patients without IP. Our data suggest that IP frequently occurs for patients with scrub typhus and its presence is closely associated with the disease severity of scrub typhus

Walk-on-Hemispheres first-passage algorithm

Abstract Due to the isomorphism between an electrostatic problem and the corresponding Brownian diffusion one, the induced charge density on a conducting surface by a charge is isomorphic to the first-passage probability of the diffusion initiated at the location of the charge. Based on the isomorphism, many diffusion algorithms such as “Walk-on-Spheres” (WOS), “Walk-on-Planes” and so on have been developed. Among them, for fast diffusion simulations WOS algorithm is generally applied with an $$\varepsilon$$ ε -layer, which is used for diffusion convergence on the boundary but induces another error from the $$\varepsilon$$ ε -layer in addition to the intrinsic Monte Carlo error. However, for a finite flat boundary it is possible to terminate a diffusion process via “Walk-on-Hemispheres” (WOH) algorithm without the $$\varepsilon$$ ε -layer. In this paper, we implement and demonstrate this algorithm for the induced charge density distribution on parallel infinite planes when a unit charge is between the plates. In addition, we apply it to the mutual capacitance of two circular parallel plates. In both simulations, WOH algorithm shows much better performance than the previous WOS algorithm

Dual Geometry of Entanglement Entropy via Deep Learning

For a given entanglement entropy of QFT, we investigate how to reconstruct its dual geometry by applying the Ryu-Takayanagi formula and the deep learning method. In the holographic setup, the radial direction of the dual geometry is identified with the energy scale of the dual QFT. Therefore, the holographic dual geometry can describe how the QFT changes along the RG flow. Intriguingly, we show that the reconstructed geometry only from the entanglement entropy data can give us more information about other physical properties like thermodynamic quantities in the IR region.Comment: 17 pages, 9 figure