Shift of percolation thresholds for epidemic spread between static and dynamic small-world networks

The study compares the epidemic spread on static and dynamic small-world networks. They are constructed as a 2-dimensional Newman and Watts model (500 × 500 square lattice with additional shortcuts), where the dynamics involves rewiring shortcuts in every time step of the epidemic spread. We assume susceptible-infectious-removed (SIR) model of the disease. We study the behaviour of the epidemic over the range of shortcut probability per underlying bond ϕ = 0–0.5. We calculate percolation thresholds for the epidemic outbreak, for which numerical results are checked against an approximate analytical model. We find a significant lowering of percolation thresholds on the dynamic network in the parameter range given. The result shows the behaviour of the epidemic on dynamic network is that of a static small world with the number of shortcuts increased by 20.7±1.4 %, while the overall qualitative behaviour stays the same. We derive corrections to the analytical model which account for the effect. For both dynamic and static small worlds we observe suppression of the average epidemic size dependence on network size in comparison with the finite-size scaling known for regular lattice. We also study the effect of dynamics for several rewiring rates relative to infectious period of the disease.     

On the structural properties of small-world networks with range-limited shortcut links

We explore a new variant of Small-World Networks (SWNs), in which an additional parameter (r$r$) sets the length scale over which shortcuts are uniformly distributed. When r=0$r=0$ we have an ordered network, whereas r=1$r=1$ corresponds to the original Watts–Strogatz SWN model. These limited range SWNs have a similar degree distribution and scaling properties as the original SWN model. We observe the small-world phenomenon for r?1$r?1$, indicating that global shortcuts are not necessary for the small-world effect. For limited range SWNs, the average path length changes nonmonotonically with system size, whereas for the original SWN model it increases monotonically. We propose an expression for the average path length for limited range SWNs based on numerical simulations and analytical approximations.     

Two-Point Resistance on the Centered-Triangular Lattice

The resistance between any two lattice points in an infinite,centered-triangular lattice of equal resistors is determined using the lattice Green function method.It is shown that the two-point resistance on the centeredtriangular lattice is expressed in terms of the resistance of a triangular lattice.Some exact values for the resistance near the origin of the lattice are presented.For large separation between lattice points the asymptotic forms of the resistance are calculated.     

Lamellar pattern formation in small-world media

Numerical and analytical techniques are used to investigate the effects of quenched disorder of small-world networks on the phase ordering dynamics of lamellar patterns as modeled by the Swift-Hohenberg equation. Morphologies for small and large values of the network randomness are quite different. It is found that addition of shortcuts to an underlying regular lattice makes the growth of domains evolving from random initial conditions much slower at late times. As the randomness increases, the evolution is eventually frozen.     

金属纳米颗粒的热导率

本文使用统计模拟方法对金属纳米颗粒的电子平均自由程进行了计算,并考察了纳米颗粒的晶格比热和声子平均群速度,最后应用动力学理论对纳米颗粒的电子热导率和声子热导率分别进行了求解.研究结果表明:具有相同特征尺寸的方形、球形纳米颗粒的无量纲电子(或声子)平均自由程比较接近.金属纳米颗粒的电子热导率远大于声子热导率;电子、声子热导率随着直径减小呈现降低趋势,而电子热导率的颗粒尺度依赖性比声子热导率更为明显;随着颗粒直径进一步减小,声子热导率与电子热导率趋于同一数量级.当纳米颗粒特征尺寸大于4倍块材电子(或声子)平均自由程,其电子(或声子)热导率的颗粒尺度依赖性将减弱.     

Synchronization of Coupled Oscillators on Newman-Watts Small-World Networks

We investigate the collection behaviour of coupled phase oscillators on Newman-Watts small-world networks in one and two dimensions. Each component of the network is assumed as an oscillator and each interacts with the others following the Kuramoto model We then study the onset of global synchronization of phases and frequencies based on dynamic simulations and finite-size scaling. Both the phase and frequency synchronization are observed to emerge in the presence of a tiny fraction of shortcuts and enhanced with the increases of nearest neighbours and lattice dimensions.     

Renormalization group improved lattice action and Monte Carlo calculations for the non-linear O(3) sigma model

Monte Carlo calculations for the two-dimensional O(3) nonlinear sigma model are performed with a renormalization group improved lattice action proposed previously. The relation between the correlation function on the renormalized trajectory and that on a canonical curve is discussed from the viewpoint of the renormalization group and is investigated numerically. The scaling behavior of the correlation length and the magnetic susceptibility is also examined. A comment on a large discrepancy between the Symanzik one-loop improved model and other models is given.     

Euclidean quantum gravity on a lattice

We construct a number of related euclidean lattice formulations of quantum gravity. The first version incorporates a path integral over discrete manifolds built out of four-cubes embedded in a higher dimensional flat hypercubic lattice. We show this expression is equal to a corresponding path integral in a local lattice field theory. The field theoretic path integral diverges and lacks a satisfactory vacuum state. This divergence can be interpreted as a consequence of a divergent phase space available for topological fluctuations in the four-manifolds of the original path integral. A modified version of the path integral over manifolds converges. We construct a Schrödinger equation and hamiltonian for the modified theory. The hamiltonian is self-adjoint, but as a result of the large phase space available for topological fluctuations, the hamiltonian's spectrum is probably not bounded from below. We show briefly how the flat enveloping space—time can be removed from most of the theories we present and how matter fields can be included.     

Critical temperature of interacting Bose gases in two and three dimensions

We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=10;{5} particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3 < or approximately 10(-4). This value is different from the estimate na3 < or approximately 10(-6) for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |psi|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.     

Estimation of partial optical path length in the brain in subject-specific head models for near-infrared spectroscopy

Three-dimensional head models with the structures constructed from the MR head images of 40 volunteers were constructed to analyze light propagation in the subject-specific head models. The mean optical path length in the head and the partial optical path length in the brain at 13 fiducial points for each volunteer were estimated to evaluate the intersubject and spatial variability in the optical path lengths. Although the intersubject variability in the optical path lengths is very high, the spatial variability in the average of the mean optical path length and partial optical path length is similar to the previously reported data. The mean optical path length in the head increases, whereas the partial optical path length in the brain decreases with an increase in the depth of the brain surface. The partial optical path length is highly correlated with the depth of the brain surface in comparison to the mean optical path length in the head.     

Gauge theory on a random lattice

A general formulation of gauge theory on a random lattice is developed and the strong coupling limit of the Wilson string tension worked out. The confining force found in this strong coupling limit is identical to that predicted by the relativistic string model. In particular, the force between two color-triplet charges is a constant for large separation and the tube of electric flux joining the charges fluctuates, giving it a net thickness proportional to the logarithm of its length.     

Longest path in percolating hierarchical lattice

We determine numerically the probability distribution for the longest self-avoiding path lengths connecting two distant points on a diluted hierarchical lattice at the percolation threshold. The evolution of this distribution with the system size is studied and the distribution is observed to approach a universal scale-invariant form under proper rescaling of its argument. The longest path length scales as |p ^max| and our estimate for _max=1.816±0.013 is clearly different from the previously estimated _min=1.531+0.002 for the shortest path lengths on the same hierarchical lattice. This gives support to the multifractal behavior of SAWs on percolating clusters.     

Free Path Lengths in Quasicrystals

Previous studies of kinetic transport in the Lorentz gas have been limited to cases where the scatterers are distributed at random (e.g., at the points of a spatial Poisson process) or at the vertices of a Euclidean lattice. In the present paper we investigate quasicrystalline scatterer configurations, which are non-periodic, yet strongly correlated. A famous example is the vertex set of a Penrose tiling. Our main result proves the existence of a limit distribution for the free path length, which answers a question of Wennberg. The limit distribution is characterised by a certain random variable on the space of higher dimensional lattices, and is distinctly different from the exponential distribution observed for random scatterer configurations. The key ingredients in the proofs are equidistribution theorems on homogeneous spaces, which follow from Ratner’s measure classification.     

Errors in two-point sound reproduction

This paper deals with the problem of reproducing two signals at two points in space by using two acoustic sources. While much is now known about the techniques available for the design of matrices of inverse filters that enable this objective to be achieved in practice, it is still the basic physics of the sound field produced that controls the effectiveness of such systems and which ultimately dictates their design. The basic physical processes involved in producing the cross-talk cancellation that enables the reproduction of the desired signals is revisited here by using a simple two source/two field point free field model. The singular value decomposition is used to identify those frequencies where the inversion problem becomes ill-conditioned and to explain physically the origin of the ill-conditioning. As observed previously, it is found that cross-talk cancellation becomes problematic when the path length difference between the two sources and one of the field points becomes equal to one half the acoustic wavelength. The ill-conditioned frequencies are also found to be associated with a limited spatial region of cross-talk cancellation and with large source outputs manifested in the time domain by responses of long duration.     

Efficient Population Transfer in a Λ-Type Quantum System Coupled to a Gold Nanoparticle Using STIRAP Shortcuts

A theoretical investigation on the population transfer in a Λ-type quantum system near a spherical gold nanoparticle under application of two stimulated Raman adiabatic passage (STIRAP) shortcuts and efficiency comparison with conventional STIRAP. It combines the density matrix approach for system dynamics, with classical electromagnetic calculations used to obtain the modified electric field amplitudes of the applied pulses and the Purcell factor of the quantum system due to the presence of the nanoparticle. The efficiency of population transfer is investigated by varying the distance between the quantum system and the nanoparticle, the free-space decay rate of quantum states, the mutual polarization, and the Rabi frequencies of each STIRAP shortcut pulses. In all cases, at least one of the applied shortcuts is more efficient than conventional STIRAP, while in most cases both perform better. When the pump and Stokes fields of the shortcuts have radial and tangential polarizations with respect to the nanoparticle surface, respectively, high transfer efficiency is obtained for small distances of the quantum system to the nanoparticle, moderate free space decay rates and large Rabi frequencies of the fields, while when the pulse polarizations are interchanged, the transfer becomes highly efficient only at large distances.     

Scattering of waves by irregularities in periodic discrete lattice spaces. I. Reduction of problem to quadratures on a discrete model of the Schrödinger equation

The scattering of plane waves and of point source pulses by irregularities in a discrete lattice model of the Schrödinger equation is considered. Closed form expressions are derived for the scattered wave function in terms of lattice Green's functions in the case that a finite number of lattice points or “bonds” are defective. The scattered wave function appears in the form of the ratio of two determinants. While in continuum scattering theory the scatterer must have some symmetry, perhaps spherical, cylindrical or elliptical, in order to allow separation of variables in the basic scattering differential equation, such symmetries are not necessary for the construction of scattered wave functions on discrete lattices. When the number of irregularities becomes large, the determinants in the solution of the scattering problem become large.     

汇聚式反射抛物面的宏观聚光测试

 目前反射式抛物面的检测主要是利用光的干涉法测量抛物面的光程来实现,虽然精度比较高,但却只能检测抛物面的光滑程度,而对抛物面的聚光效果无能力。该文从基本原理出发,重申反射式抛物面的聚焦成像本质,进而指出确定其聚光精度的关键是反射面各点的面积元方向与入射光的夹角关系,而不是光程关系。同时给出了应用特大口径平行光源或特大口径平行光源组合直接对反射抛物面进行检测的方法,它可以定性地检测出抛物面宏观的聚光效果和成像质量。     

面向成本-收益好的无标度耦合网络构建方法

较大平均路径长度的网络会带来较大的网络延迟, 难以支持时间敏感业务与应用. 通过增加连接可以降低源和目的节点之间的跳数, 进而降低网络平均延迟, 使得更加快速地传播信息, 但是增加连接的同时也增加了网络构建成本. 分层网络是研究网络耦合的一个有效方法, 但目前网络构建过程中将每层网络分别处理并认为每层网络之间没有强相关性. 本文提出了一种面向成本-收益的无标度网络动态构建方法. 此方法将网络分为多层, 基于连续论在高层网络中添加连接, 使得网络演化为无标度网络. 此连续过程包括节点度增加过程和局部网络半径增长两个连续过程, 在增加连接的过程中引入表征网络构建成本和收益的成本-收益指标. 模拟结果表明引入成本-收益指标的无标度耦合网络构建方法能够在合理范围内有效降低网络平均路径长度, 提升网络性能, 并且本文给出了耦合网络的动态业务性能, 通过调整高层网络避免网络拥塞.     

Gluon radiation outside a finite cone

The medium-induced gluon radiation angular distributions of light quarks and heavy quarks outside a finite jet cone are studied. We find the effect of destructive interference between the vacuum and medium-induced radiation plays an important role in gluon radiation for very small value of path length L, which leads to the negative value of medium-induced energy loss. The medium-induced radiative energy loss outside an angle for heavy quarks is found to have a minimum and a maximum at small angle for small path length, which are caused by dead cone effect and Brownian k _⊥-broadening effect, respectively. However for large path length the minimum and maximum disappear.