微观数据和宏观汇总数据在统计分析上的差异——以C-D生产函数为例

基于2008年经济普查的数据,从描述统计分析和回归分析两方面分别对微观数据和宏观汇总数据在统计分析上的差异进行了实证分析.在描述统计分析中发现,宏观汇总数据比微观数据更接近正态分布,但对数化处理后的数据并非如此;在回归分析中发现,基于微观数据和宏观汇总数据估计的生产函数,在消除异方差和多重共线性之前,无论是在生产函数的规模效应、生产要素的贡献率以及生产要素对产出的解释力度上均存在着差异,但是在消除异方差和多重共线性之后,在要素对产出的解释力度上仍存在很大差异.     

Multiscale method based on discontinuous Galerkin methods for homogenization problems

We propose a multiscale method for elliptic problems with highly oscillating coefficients based on a coupling of macro and micro methods in the framework of the heterogeneous multiscale method. The macro method, defined on a macroscopic triangulation, aims at recovering the effective (homogenized) solution of an unknown macro model. The unspecified data of this model are computed by micro methods on sampling domains during the macro assembly process. In this Note, we show how to construct such a coupling with a discontinuous macro finite element space. We show that the flux information needed in this formulation in order to impose weak interelement continuity can be recovered from the known micro calculations on the sampling domains. A fully discrete analysis is presented. To cite this article: A. Abdulle, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Exploitation of Configurational Forces in Extended Nonlocal Continua with Microstructure

We investigate aspects of the application of configurational forces in extended nonlocal continua with microstructure. Focussing on multifield approaches to gradient–type inelastic solids, the coupled problem is governed by the macroscopic deformation field, while nonlocal inelastic effects on the microstructure are described by a family of order parameter fields. The dual macro– and micro–field equations are derived within an incremental variational framework. Using an incremental principle, due to the variation with respect to the material position, an additional balance in the material space appears with the dual macro–micro–balances in the physical space. In view of the numerical implementation of this coupled problem by a finite element method, the incremental variational framework is recast into a discrete format in terms of discrete macro– and micro–physical nodal forces and configurational nodal forces. Applying a staggered solution scheme, the configurational branch is used as a postprocessing procedure with all the ingredients known from the solution of the coupled macro–micro–problem. The procedure is implemented for a nonlocal, viscous damage model. The consequences with regard to the configurational nodal forces are assessed by means of a numerical example. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Well-posedness and inverse Robin estimate for a multiscale elliptic/parabolic system

Abstract

We establish the well-posedness of a coupled micro–macro parabolic–elliptic system modeling the interplay between two pressures in a gas–liquid mixture close to equilibrium that is filling a porous media with distributed microstructures. Additionally, we prove a local stability estimate for the inverse micro–macro Robin problem, potentially useful in identifying quantitatively a micro–macro interfacial Robin transfer coefficient given microscopic measurements on accessible fixed interfaces. To tackle the solvability issue we use two-scale energy estimates and two-scale regularity/compactness arguments cast in the Schauder’s fixed point theorem. A number of auxiliary problems, regularity, and scaling arguments are used in ensuring the suitable Fréchet differentiability of the solution and the structure of the inverse stability estimate.     

Influence of Multiple Micro Cracks on the Damage Behavior of a Macro-Crack Tip北大核心CSCD

The solution of an infinite plane containing a macro crack and a cluster of micro cracks under uniaxial tensile load was presented based on Muskhelishvili’s complex function method and the stepwise recursive method. The stress field and stress intensity factor K were obtained. Combined with the damage mechanics, damage parameter D of the macro-crack tip and the micro-crack tip under uniaxial tension was redefined, and the influence of different damage zone forms on the damage of the crack tip was analyzed. The results show that, both the chain-distribution and the reverse-chain-distribution micro cracks have an amplifying effect on the macro crack growth, and the damage parameter increases with the decrease of the inclination angle of the micro crack and the reduction of the distance between the macro crack and the micro cracks. For a relatively small inclination angle of the micro crack, the damage parameters of the macro crack and the micro crack heightens, and the damage parameter of the macro crack increases with the micro-crack length. For evenly distributed micro cracks in the continuous damage zone, the micro cracks have an amplifying effect on the macro-crack growth, and the damage parameter of the macro crack increases with the micro-crack number. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Macroscopic finite element analyses of discretematerials based on directly evaluated micro‐macro transitions

We consider a homogenized macro‐continuum with locally attached microstructure of granules and derive specific micromacro transitions by a consistent transfer of discrete micro‐variables to field variables on a continuous macrostructure. Displacements and rotational constraints are imposed on the granules on the defined boundary frame of the microstructure. The constraints for linear displacements and uniform tractions on the surface yield upper and lower bound characteristics for periodic boundary conditions with regard to the aggregate stiffness. Secondly, we perform two‐scale analyses where we link simulations on the macro‐ and the microscales. Therein, coupled boundary‐value problems are solved on both scales. The macroscopic homogeneous problem is solved by a finite element method where the material model is implemented using the directly evaluated micro‐macro transitions on the basis of the discrete microstructures. Finally, a model problem is investigated to clarify the proposed method. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Discontinuous Galerkin finite element heterogeneous multiscale method for advection–diffusion problems with multiple scales

A discontinuous Galerkin finite element heterogeneous multiscale method is proposed for advection–diffusion problems with highly oscillatory coefficients. The method is based on a coupling of a discontinuous Galerkin discretization for an effective advection–diffusion problem on a macroscopic mesh, whose a priori unknown data are recovered from micro finite element calculations on sampling domains within each macro element. The computational work involved is independent of the high oscillations in the problem at the smallest scale. The stability of our method (depending on both macro and micro mesh sizes) is established for both diffusion dominated and advection dominated regimes without any assumptions about the type of heterogeneities in the data. Fully discrete a priori error bounds are derived for locally periodic data. Numerical experiments confirm the theoretical error estimates.     

Inferring social structure from continuous‐time interaction data

Relational event data, which consist of events involving pairs of actors over time, are now commonly available at the finest of temporal resolutions. Existing continuous‐time methods for modeling such data are based on point processes and directly model interaction “contagion,” whereby one interaction increases the propensity of future interactions among actors, often as dictated by some latent variable structure. In this article, we present an alternative approach to using temporal‐relational point process models for continuous‐time event data. We characterize interactions between a pair of actors as either spurious or as resulting from an underlying, persistent connection in a latent social network. We argue that consistent deviations from expected behavior, rather than solely high frequency counts, are crucial for identifying well‐established underlying social relationships. This study aims to explore these latent network structures in two contexts: one comprising of college students and another involving barn swallows.     

Note on “Obtaining the Maximum Likelihood Estimates in Incomplete R × C Contingency Tables Using a Poisson Generalized Linear Model”

Abstract

This note extends the construction of the design matrix used for estimating cell probabilities with ignorable missing data described by Lipsitz, Parzen, and Molenberghs. A reformulation for the general case of an n-way table is described and implemented in a SAS macro program. The macro constructs this design matrix and offset variable, estimates the cell probabilities, and returns a table with the estimates, their standard errors, and fitted cell frequencies.     

On a micro‐macro model for polymeric fluids near equilibrium

In this paper, we study a micro‐macro model for polymeric fluid. The system involves coupling between the macroscopic momentum equation and a microscopic evolution equation describing the combined effects of the microscopic potential and thermofluctuation. We employ an energetic variation procedure to explore the relation between the macroscopic transport of the particles and the induced elastic stress due to the microscopic structure. For the initial data not far from the equilibrium, we prove the global existence and uniqueness of classical solutions to the system. © 2006 Wiley Periodicals, Inc.     

Cumulative curves for exploration of demographic data: a case study of Northwest England

Summary  The paper introduces the idea of generalising a cumulative frequency curve to show arbitrary cumulative counts. For example, in demographic studies generalised cumulative curves can represent the distribution of population or area. Generalised cumulative curves can be a valuable instrument for exploratory data analysis. The use of cumulative curves in an investigation of population statistics in Northwest England allowed us to discover interesting facts about relationships between the distribution of national minorities and the degree of deprivation. We detected that, while high concentration of national minorities occurs, in general, in underprivileged districts, there are some differences related to the origin of the minorities. The paper sets the applicability conditions for generalised cumulative curves and compares them with other graphical tools for exploratory data analysis.     

Ellipsoidal BGK model for polyatomic molecules near Maxwellians: A dichotomy in the dissipation estimate

We consider the global existence and asymptotic behavior of classical solutions to the ellipsoidal BGK model for polyatomic molecules when the initial data starts sufficiently close to a global polyatomic Maxwellian. We observe that the linearized relaxation operator is decomposed into a truly polyatomic part and an essentially monatomic part, leading to a dichotomy in the dissipative property in the sense that the degeneracy of the dissipation shows an abrupt jump as the relaxation parameter θ reaches zero. Accordingly, we employ two different sets of micro–macro system to derive the full coercivity and close the energy estimate.     

A multiscale approach to thermoplastic deformation

The paper applies a multiscale formulation to thermoplasticity problems. The plasticity model is based on the variationally consistent formulation at the micro level. It is suitable for problems involving large strains. The temperature field is calculated at the macro level and is assumed to be homogeneous at the micro level. The proposed formulation is implemented in the Abaqus software by means of user subroutines. User subroutines are introduced both at the macro and at the micro level. The consistent tangent operator is calculated by the numerical differentiation procedure. Implementation details are briefly addressed. Finally, the methodology is verified on a representative example and relevant results are presented and discussed. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Time-adaptive multirate generalized-structure additively partitioned Runge-Kutta schemes for mechanical fluid-structure interaction

We extend the multirate GARK approach by Günther and Sandu [1, 2] to the case of non-constant micro steps per macro step to be able to cover time adaptivity, arriving at our so-called TAMGARK scheme and derive order conditions for arbitrary non-constant micro step sizes. The TAMGARK scheme is applied to the classical piston problem [3] to study the interaction between the piston and inviscid fluid flow in one spatial dimension. We demonstrate the functionality of the chosen time-adaptation strategy and the ability of the overall scheme to preserve the order of the basic schemes. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Shakhov model near a global Maxwellian

Shakhov model is a relaxation approximation of the Boltzmann equation proposed to overcome the deficiency of the original BGK model, namely, the incorrect production of the Prandtl number. In this paper, we address the existence and the asymptotic stability of the Shakhov model when the initial data is a small perturbation of global equilibrium. We derive a dichotomy in the coercive estimate of the linearized relaxation operator between zero and non-zero Prandtl number, and observe that the linearized relaxation operator is more degenerate in the former case. To remove such degeneracy and recover the full coercivity, we consider a micro–macro system that involves an additional non-conservative quantity related to the heat flux.     

Tools of the mind: Techniques and methods for intellectual work: V. STIBIC North-Holland,Amsterdam, 1982, xiii + 297 pages,Dfl.85.00

Many location problems may be separated into a series of interrelated macro, meso and micro decision-making states. The macro scale decision determines the type, capacity and number of facilities, the meso scale decision determines the location and allocation of facilities and the micro scale decision determines such considerations as routing and scheduling of service vehicles. This paper concerns the first two levels of decision-making.The present paper demonstrates the use of two models: (i) an analytical model that uses continuum approximations and methods of calculus to determine the number of facilities, the capacity and the approximate location of each that minimizes the sum of the transportation and facility costs for a slowly varying demand rate, and (ii) a traditional location-allocation model that determines more exactly the resulting locations and allocations. These two approaches have specific requirements in terms of data input, cost of data collection and cost of solution and, consequently, yield unique insights and benefits for practising planners. The strengths and weaknesses of the two models are complementary. This thesis is developed with an analysis of the Calgary, Alberta refuse collection and disposal system.     

Limitations of computing time savings in variational multirate integrations

For systems that contain slow and fast dynamics, variational multirate integration schemes are used. These schemes split the system into parts which are simulated using a time grid consisting of micro and macro nodes. This leads to computing time savings, however not unlimited, for a certain number of micro steps per macro step the computing time is minimal. To find a relation between this minimum computing time and the number of variables in the system, the computing time for the Fermi-Pasta-Ulam problem (FPU) is measured for different numbers of masses and different numbers of micro steps. In addition, the numerical convergence of the variational multirate integration is shown for the FPU. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of a micro–macro acceleration method with minimum relative entropy moment matching

We analyse convergence of a micro–macro acceleration method for the simulation of stochastic differential equations with time-scale separation. The method alternates short bursts of path simulations with the extrapolation of macroscopic state variables forward in time. After extrapolation, a new microscopic state is constructed, consistent with the extrapolated macroscopic state, that minimises the perturbation caused by the extrapolation in a relative entropy sense. We study local errors and numerical stability of the method to prove its convergence to the full microscopic dynamics when the extrapolation time step tends to zero and the number of macroscopic state variables tends to infinity.     

A posteriori error estimates in quantities of interest for the finite element heterogeneous multiscale method

We present an “a posteriori” error analysis in quantities of interest for elliptic homogenization problems discretized by the finite element heterogeneous multiscale method. The multiscale method is based on a macro‐to‐micro formulation, where the macroscopic physical problem is discretized in a macroscopic finite element space, and the missing macroscopic data are recovered on‐the‐fly using the solutions of corresponding microscopic problems. We propose a new framework that allows to follow the concept of the (single‐scale) dual‐weighted residual method at the macroscopic level in order to derive a posteriori error estimates in quantities of interests for multiscale problems. Local error indicators, derived in the macroscopic domain, can be used for adaptive goal‐oriented mesh refinement. These error indicators rely only on available macroscopic and microscopic solutions. We further provide a detailed analysis of the data approximation error, including the quadrature errors. Numerical experiments confirm the efficiency of the adaptive method and the effectivity of our error estimates in the quantities of interest. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013