Complete entrainment of Kuramoto oscillators with inertia on networks via gradient-like flow

We study the asymptotic complete entrainment of Kuramoto oscillators with inertia on symmetric and connected network. We provide several sufficient conditions for the asymptotic complete entrainment in terms of initial phase-frequency configurations, strengths of inertia and coupling, and natural frequency distributions. For this purpose, we reinterpret the Kuramoto oscillators with inertia as a second-order gradient-like flow, and adopt analytical methods based on several Lyapunov functions to apply the convergence estimate studied by Haraux and Jendoubi [21]. Our approach does not require any spectral information of the graph associated with the given network structure.     

多维Kramers公式的研究

本文研究了鞍点附近多维的位能曲面及鞍点所在位置;并用Werner Wheeler及无旋液体等两种方法计算了多维的质量系数与粘滞系数,然后用多维Kramers公式计算了裂变速率.发现裂变速率随着维数的增加而适当增大.不同的形变参量以及不同的计算质量和粘滞系数方法对计算核裂变速率影响不大.从结果看,采用三维计算裂变几率已足够准确.     

Numerical calculation of equivalent moment of inertia for a fluid in a cylindrical container with partitions

A 3-D numerical code was developed to solve the irrotational flow of an ideal fluid inside a moving cylindrical container with partitions. The problem is formulated in terms of two Poisson equations, the velocity equation and the pressure equation. These are expressed in terms of finite differences and solved by a procedure of line over relaxation. From the fluid pressure we computed the resultant moment on the container which was then expressed in terms of the equivalent moment of inertia. The code was checked against analytical results of Moiseyev and we found an agreement of 2–5 per cent even for a sparse mesh. We then demonstrated the capability of the code by computing the equivalent moment of inertia for various configurations with full and partial partitions.     

On the Reality of Minkowski Space

Should physicists deal with the question of the reality of Minkowski space (or any relativistic spacetime)? It is argued that they should since this is a question about the dimensionality of the world at the macroscopic level and it is physics that should answer it.     

Material aspects of dynamic neck retardation

Neck retardation in stretching of ductile materials is promoted by strain hardening, strain-rate hardening and inertia. Retardation is usually beneficial because necking is often the precursor to ductile failure. The interaction of material behavior and inertia in necking retardation is complicated, in part, because necking is highly nonlinear but also because the mathematical character of the response changes in a fundamental way from rate-independent necking to rate-dependent necking, whether due to material constitutive behavior or to inertia. For rate-dependent behavior, neck development requires the introduction of an imperfection, and the rate of neck growth in the early stages is closely tied to the imperfection amplitude. When inertia is important, multiple necks form. In contrast, for rate-independent materials deformed quasi-statically, single necks are preferred and they can emerge in an imperfection-free specimen as a bifurcation at a critical strain. In this paper, the interaction of material properties and inertia in determining neck retardation is unraveled using a variety of analysis methods for thin sheets and plates undergoing plane strain extension. Dimensionless parameters are identified, as are the regimes in which they play an important role.     

微机在用刚体转动仪测刚体转动惯量实验中的应用

用刚体转动仪测量刚体转动惯量实验所要测量的主要物理量是时间,所测量的实验数据繁多,且要求准确,而后续的实验数据处理计算复杂。本介绍了一种测量时间、计算转动惯量数值两项工作全部由PC机来完成的新方法。     

Error Analysis in Trifilar Inertia Measurements

Accurate calculation of the moment of inertia of an irregular body is made difficult by the large number of quantities which must be measured. A popular method is to use a trifilar suspension system to measure the period of oscillation of the body in the horizontal plane. In this paper, some sources of error are discussed with particular attention given to the alignment of the test object’s center of mass on the trifilar platform. The procedure is described, the necessary calculations are derived and the relative importance of accuracy in different measurements is assesed. It is determined that the accurate alignment of the centre of mass of the body being tested with the centre of the trifilar plate is insignificant compared to the accuracy of the other measurements required in the calculations.     

Towards the generalized purely wild inertia conjecture for product of alternating and symmetric groups

We obtain new evidence for the Purely Wild Inertia Conjecture posed by Abhyankar and for its generalization. We show that this generalized conjecture is true for any product of simple Alternating groups in odd characteristics, and for any product of certain Symmetric or Alternating groups in characteristic two. We also obtain important results towards the realization of the inertia groups which can be applied to more general set up. We further show that the Purely Wild Inertia Conjecture is true for any product of perfect quasi p-groups (groups generated by their Sylow p-subgroups) if the conjecture is established for individual groups.     

Inertia groups and abelian surfaces

This paper classifies the finite groups that occur as inertia groups associated to abelian surfaces. These groups can be viewed as Galois groups for the smallest totally ramified extension over which an abelian surface over a local field acquires semistable reduction. The results extend earlier elliptic curves results of Serre and Kraus.