Mobility Matrices Research Articles

Diffusion-driven microstructure evolution in OpenCalphad

The diffusion process in multicomponent alloys has a significant influence on the evolution of the microstructure. The Calphad approach is a powerful method for describing the equilibrium state as well as the kinetics of non-equilibrium systems via the Gibbs energy. In this work, the principles of multicomponent diffusion theory are considered intensively, and an equation for the fluxes in the case of substitutional-interstitial diffusion is given for implementation. Additionally, the calculation of mobility matrices and thermodynamic factors is addressed. As an application case, substitutional diffusion is implemented in OpenCalphad and is used for calculating the growth rate for spherical precipitates from a supersaturated aluminum matrix. The growth rate has been integrated into the Kampmann–Wagner numerical model, which describes nucleation, growth, and coarsening for spherical precipitates. A AlMgZnCu alloy is considered, which has great significance in the field of materials processing.

A general perturbative approach for bead-based microswimmers reveals rich self-propulsion phenomena

Studies of model microswimmers have significantly contributed to the understanding of the principles of self-propulsion we have today. However, only a small number of microswimmer types have been amenable to analytic modeling, and further development of such approaches is necessary to identify the key features of these active systems. Here we present a general perturbative calculation scheme for swimmers composed of beads interacting by harmonic potentials and via hydrodynamics, driven by an arbitrary force protocol. The approach can be used with mobility matrices of arbitrary accuracy, and we illustrate it with the Oseen and Rotne–Prager approximations. We validate our approach by using 3 bead assemblies and comparing the results with the numerically obtained full-solutions of the governing equations of motion, as well as with existing analytic models for the linear and the triangular swimmer geometry. While recovering the relation between the force and swimming velocity, our detailed analysis and the controlled level of approximation allow us to find qualitative differences already in the far field flow of the devices. Consequently, we are able to identify a behavior of the swimmer that is richer than predicted in previous models. Given its generality, the framework can be applied to any swimmer geometry, driving protocol and bead interactions, as well as in problems involving many swimmers.

Coupled dynamics of a viscoelastically supported infinite string and a number of discrete mechanical systems moving with uniform speed

The mutual interaction between a number of multi degrees of freedom mechanical systems moving with uniform speed along an infinite taut string supported by a viscoelastic layer has been studied using the substructure synthesis method when base excitations of a common frequency are given to the mechanical systems. The mobility or impedance matrices of the string have been calculated analytically by Fourier transform method as well as wave propagation technique. The above matrices are used to calculate the response of the discrete mechanical systems. Special attention is paid to the contact forces between the discrete and the continuous systems which are estimated by numerical simulation. The effects of phase difference, the distance between the systems and different base excitation amplitudes on the collective behaviour of the mechanical systems are also studied. The present study has relevance to the coupled dynamic problem of more than one railway pantographs and an overhead catenary system where the pantographs are modelled as discrete systems and the catenary is modelled as a taut string supported by continuous viscoelastic layer.

Multi-patch and multi-group epidemic models: a new framework.

We develop a multi-patch and multi-group model that captures the dynamics of an infectious disease when the host is structured into an arbitrary number of groups and interacts into an arbitrary number of patches where the infection takes place. In this framework, we model host mobility that depends on its epidemiological status, by a Lagrangian approach. This framework is applied to a general SEIRS model and the basic reproduction number [Formula: see text] is derived. The effects of heterogeneity in groups, patches and mobility patterns on [Formula: see text] and disease prevalence are explored. Our results show that for a fixed number of groups, the basic reproduction number increases with respect to the number of patches and the host mobility patterns. Moreover, when the mobility matrix of susceptible individuals is of rank one, the basic reproduction number is explicitly determined and was found to be independent of the latter if the matrix is also stochastic. The cases where mobility matrices are of rank one capture important modeling scenarios. Additionally, we study the global analysis of equilibria for some special cases. Numerical simulations are carried out to showcase the ramifications of mobility pattern matrices on disease prevalence and basic reproduction number.

Mobility power flows of thin circular plate carrying concentrated masses based on structural circumferential periodicity

A new method was presented by utilizing the structural circumferential periodicity of the inertia excitation due to the concentrated masses to compute the transverse vibration for thin circular plate carrying concentrated masses. Comparison between the calculated fundamental frequency coefficients and those from other approaches validates the method. And then, the point mobility matrices and the power flows were solved on the basis of modal function solutions and the analytical results of simply supported case were presented. Finally, the parametric effect of the single concentrate mass on the power flows was investigated.

Long-Run Earnings Mobility among Low-Income Individuals

<p><em>We construct earnings mobility matrices for low-income individuals over 6-year and 13-year periods. Our sample of low-income individuals is drawn from the population of SNAP recipients in Georgia. Using Georgia administrative records, we identify SNAP participants in 2000 and their earnings for each year through 2013 using matched employment security records. We find that a substantial percentage of these individuals have zero earnings in both the initial and ending years. We find that there is a heavier concentration of males, whites, and disabled individuals with zero earnings in the initial and ending years than in the overall SNAP sample. This contradicts some of the characterizations of SNAP recipients in the popular press which often characterizes those stuck in poverty as single black mothers. In fact, the disabled represent the vast majority of those stuck in the no earnings category. Another interesting finding is that single mothers with zero earnings in 2000 have a greater probability, in some cases a much greater probability, of escaping the zero earnings category than the general population of SNAP recipients. We also find that individuals with positive earnings in the initial year experience substantial earnings mobility. </em></p>

Lattice Boltzmann Stokesian dynamics.

Lattice Boltzmann Stokesian dynamics (LBSD) is presented for simulation of particle suspension in Stokes flows. This method is developed from Stokesian dynamics (SD) with resistance and mobility matrices calculated using the time-independent lattice Boltzmann algorithm (TILBA). TILBA is distinguished from the traditional lattice Boltzmann method (LBM) in that a background matrix is generated prior to the calculation. The background matrix, once generated, can be reused for calculations for different scenarios, thus the computational cost for each such subsequent calculation is significantly reduced. The LBSD inherits the merits of the SD where both near- and far-field interactions are considered. It also inherits the merits of the LBM that the computational cost is almost independent of the particle shape.

Many-body microhydrodynamics of colloidal particles with active boundary layers

Colloidal particles with active boundary layers—regions surrounding the particles where non-equilibrium processes produce large velocity gradients—are common in many physical, chemical and biological contexts. The velocity or stress at the edge of the boundary layer determines the exterior fluid flow and, hence, the many-body interparticle hydrodynamic interaction. Here, we present a method to compute the many-body hydrodynamic interaction between N spherical active particles induced by their exterior microhydrodynamic flow. First, we use a boundary integral representation of the Stokes equation to eliminate bulk fluid degrees of freedom. Then, we expand the boundary velocities and tractions of the integral representation in an infinite-dimensional basis of tensorial spherical harmonics and, on enforcing boundary conditions in a weak sense on the surface of each particle, obtain a system of linear algebraic equations for the unknown expansion coefficients. The truncation of the infinite series, fixed by the degree of accuracy required, yields a finite linear system that can be solved accurately and efficiently by iterative methods. The solution linearly relates the unknown rigid body motion to the known values of the expansion coefficients, motivating the introduction of propulsion matrices. These matrices completely characterize hydrodynamic interactions in active suspensions just as mobility matrices completely characterize hydrodynamic interactions in passive suspensions. The reduction in the dimensionality of the problem, from a three-dimensional partial differential equation to a two-dimensional integral equation, allows for dynamic simulations of hundreds of thousands of active particles on multi-core computational architectures. In our simulation of 104 active colloidal particle in a harmonic trap, we find that the necessary and sufficient ingredients to obtain steady-state convective currents, the so-called ‘self-assembled pump’, are (a) one-body self-propulsion and (b) two-body rotation from the vorticity of the Stokeslet induced in the trap.

Dynamic characteristics of a periodic rib-skin structure

Periodic rib-skin structure is composed of an array of identical elements connected in parallel and each element is a stiffened structure consisting of skins and ribs which are modeled as elastic beams and rigid bodies respectively. The periodic structure is designed to gain excellent longitudinal and flexural vibration band gaps in which corresponding waves cannot propagate in the structure freely. Firstly, longitudinal and flexural vibration mobility matrices of the skins and ribs are derived to obtain mobility equations of single-floor and multi-floor periodic elements. Then, propagation constants of the infinite rib-skin structure are calculated and an in-depth numerical study is performed to examine the relationships between the wave propagation constants and dynamic response of semi-infinite and finite periodic structures. Furthermore, flexural vibration reduction performances of the periodic rib-skin structure below 3000 Hz are discussed in detail. Finally, an experimental setup for measuring the acceleration frequency response of a two-floor periodic rib-skin structure is carried out to verify the numerical solution. Both predicted and measured results have demonstrated that longitudinal and flexural band gaps exist in the periodic rib-skin structure. The flexural vibration transmitted through the structure is substantially suppressed in a wide frequency range below 3000 Hz.

Rotne–Prager–Yamakawa approximation for different-sized particles in application to macromolecular bead models

AbstractThe Rotne–Prager–Yamakawa (RPY) approximation is a commonly used approach to model the hydrodynamic interactions between small spherical particles suspended in a viscous fluid at a low Reynolds number. However, when the particles overlap, the RPY tensors lose their positive definiteness, which leads to numerical problems in the Brownian dynamics simulations as well as errors in calculations of the hydrodynamic properties of rigid macromolecules using bead modelling. These problems can be avoided by using regularizing corrections to the RPY tensors; so far, however, these corrections have only been derived for equal-sized particles. Here we show how to generalize the RPY approach to the case of overlapping spherical particles of different radii and present the complete set of mobility matrices for such a system. In contrast to previous ad hoc approaches, our method relies on the direct integration of force densities over the sphere surfaces and thus automatically provides the correct limiting behaviour of the mobilities for the touching spheres and for a complete overlap, with one sphere immersed in the other one. This approach can then be used to calculate hydrodynamic properties of complex macromolecules using bead models with overlapping, different-sized beads, which we illustrate with an example.

Interface mobilities for characterization of structure-borne sound sources resiliently mounted via multiple contact points

This paper introduces an expansion of the interface mobility method for structure-borne sound sources that are resiliently mounted to a receiving structure at multiple discrete contact points. Subsystems of source, receiver and isolators are represented by Fourier transforms of their mobility matrices. Along with the source activity, a formulation for the transmitted power fed into the receiver is obtained. Furthermore, the source descriptor and a coupling function for resiliently mounted multi-point sources are obtained which both form recognized concepts for structure-borne sound source characterization. The method is based on a neglection of cross-order terms which describe a coupling between Fourier coefficients of different order. With regard to a subsystem of discretely placed isolators, cross-order terms were found to account for variations of isolator parameters along the contact points. In a set of numerical studies it was shown that errors introduced by neglecting cross-order terms are most pronounced in the higher frequency region where isolators show resonant behavior due to internal wave effects. A subsystem of identical isolators is completely described by equal-order terms, therefore no error is introduced considering such cases. Moreover, errors inherent in the rigidly mounted case due to cross-order source or receiver mobilities are reduced significantly when isolator mobilities are large compared to those from source and receiver. Findings from theoretical studies were validated in practical settings considering structure-borne sound transmission from a ship diesel engine and a magnetic resonance imaging (MRI) device.

A New Design Approach for Rapid Evaluation of Structural Modifications Using Neural Networks

Design optimization of structural systems is often iterative, time consuming and is limited by the knowledge of the designer. For that reason, a rapid design optimization scheme is desirable to avoid such problems. This paper presents and integrates two design methodologies for efficient conceptual design of structural systems involving computationally intensive analysis. The first design methodology used in this paper is structural modification technique (SMT). The SMT utilizes the frequency response functions (FRFs) of the original model for the reanalysis of the structure that is subjected to structural modification. The receptances of the original structure are coupled with the dynamic stiffness of the components that are added to or removed from the original structure to perform the structural modification. Then, the coupled matrices are used to calculate the mobility matrices of the modified structure in an efficient way. The second design methodology used in this paper is neural networks (NN). Once sufficient input and output relationships are obtained through SMT, a NN model is constructed to predict the FRF curves of the system for further analysis of the system performance while experimenting different design parameters. The input–output sets used for training the network are increased by applying an interpolation scheme to improve the accuracy of the NN model. The performance of the proposed method integrated through SMT and NN technique is demonstrated on a rectangular plate to observe the effect of the location and thickness of stiffeners on the frequency response of the structure. It is observed that both methods combined with the proposed interpolation scheme work very efficiently to predict the dynamic response of the structure when modifications are required to improve the system performance.

Adjustment of Origin–Destination Matrices Based on Traffic Counts and Bootstrapping Confidence Intervals

Mobility studies require, as a preliminary step, that a survey of a sample of users of the transportation system be conducted. The statistical reliability of the data determines the goodness of the results and the conclusions that can be inferred from the analyses and models generated. Because of the high costs of collection, data are partially reused in either a disaggregated or an aggregated manner. In the first case, statistical reliability is not always guaranteed; this condition affects the results that will be derived from projections and estimates of future hypothetical scenarios. A methodology is presented: it is based on bootstrapping techniques and is used for robust statistical estimation of mobility matrices. Confidence intervals of travel between origin–destination pairs defined by each matrix cell derived from a survey are generated. The result is applicable to defining the dimensions of certainty for matrix cells and subsequent adjustment by techniques based on aggregate data (e.g., traffic counts, cordon line matrices, paths). A statistically reliable data mobility study conducted in Spain at a regional level is used. Results derived from disaggregating data at an interprovincial level are presented, along with an application to the posterior mobility matrix adjustment based on traffic count data. The study results demonstrate the potential of the methodology developed and the usefulness of the conclusions.

Evaluation of Direct and Derived Mobility Metrics of Mobility Models and Its Impact on Reactive Routing Protocols

Mobile Ad-Hoc Network (MANET) routing protocols performance is perceptive to mobility and scalability of network, therefore, the objectives of the paper is to describe mobility models based on mobility matrices class and impact of these metrics on routing performance metrics in MANET. An effort for analyzing and evaluating the derived mobility metrics with direct mobility metrics are considered across mobility models i. e. Random waypoint, Reference Point Group, Manhattan, Freeway have been carried out into two parts of article. This article focuses impact analysis of mobility models on two prominent reactive routing protocols – Ad-hoc on demand distance vector (AODV) and dynamic source routing (DSR) with fixed scalability of network size with varying node speed, identical traffic load as well as mobility pattern and also extends an intuitive study to analysis the interplay between mobility patterns and protocols building blocks.

Application of dynamic vibration absorbers in floating raft system

To improve the isolation performance of the traditional floating raft system, dynamic vibration absorber (DVA) is introduced into floating raft in this research. The mathematical models of floating raft system consisting of beams are implemented by assembling the mobility matrices of the subsystems. Then the power flow transmission characteristics of the coupled system with/without the DVAs are investigated to evaluate the vibration reduction performance of DVAs. Numerical simulations are performed to explore the influence of several parameters, such as the setting positions, damping and mass of the passive DVAs, on the vibration reduction effects of DVAs. Moreover the vibration reduction performance of the semi-active absorber adjusting its stiffness adaptively is analyzed for the case of time-varying frequency excitation. In addition, the vibration reduction effects of semi-active DVAs under multi-frequency excitation are investigated. The results show that DVAs can significantly improve the isolation performance of floating raft system.

Partial Ordering of Unpredictable Mobility with Welfare Implications

We propose a partial ordering of ‘unpredictable mobility’ in the spirit of Blackwell's ordering of information structures. The proposed ordering ranks mobility matrices according to the degree to which elements in a given set are likely to move from one state to another, independently of their origin. Furthermore, for an important class of transition structures, our proposed ordering implies ordering, thus carrying significant welfare implications. Moreover, whenever it exists, our partial ordering functions as a sufficient condition for a class of renowned mobility measures and thereby generates, for a subset of transition matrices, unanimous ranking among mobility indices that are not generally consistent with one another.

Elaboration of a sacttering matrix measurement procedure using the p‐v probe

The scattering matrix which relates traveling waves amplitudes as state variables has been shown to be more attractive than transfer or mobility matrices since it reflects the fundamental duct nature: it gives a more complete description of the transmission, reflection, and conversion properties of the duct. In the University of Technology of Compiègne, an experimental procedure was developed to measure this matrix: a p‐p probe mounted on a setup designed during DUCAT project is used to measure pressures at two cross sections on the both side of the test lined duct, then by using a modal decomposition and separation techniques, the scattering matrix is deduced. In this paper, a method to measure the multimodal scattering matrix based on the use of a p‐v probe getting simultaneously the acoustic pressure and velocity at one section on the both side of the test duct is developed. A comparison of some acoustics values (scattering matrix coefficients, acoustic powersœ) of a hard wall duct straight duct obtained by each technique with the theory is presented to evaluate its advantages and limitations.

Variance in predicted structure borne sound power due to simplified characterisation of the source

Theoretically the structure borne sound power transmission from a vibration source to a receiving structure can be predicted using the mobility method. In order for all the power transmission mechanisms to be accounted for the source and receiver mobility matrices must contain the mobilities for all degrees of freedom (three translational and three rotational) for each contact point and the transfer mobilities between; each contact point, each degree of freedom and each degree of freedom at each contact point. In practice reliable measured data for some degrees of freedom is difficult to obtain, so simplified source characterisation methods are required, for example using only certain degrees of freedom. The novel contribution of this paper is to investigate the variance in the predicted structure borne sound power transmission calculated when some degrees of freedom are missing, and when the source is approximated as a single equivalent excitation. The investigation was carried out using numerical simulations of simplified source and receiver structures.

Optimal Flexibility for Conformational Transitions in Macromolecules

Conformational transitions in macromolecular complexes often involve the reorientation of leverlike structures. Using a simple theoretical model, we show that the rate of such transitions is drastically enhanced if the lever is bendable, e.g., at a localized hinge. Surprisingly, the transition is fastest with an intermediate flexibility of the hinge. In this intermediate regime, the transition rate is also least sensitive to the amount of "cargo" attached to the lever arm, which could be exploited by molecular motors. To explain this effect, we generalize the Kramers-Langer theory for multidimensional barrier crossing to configuration-dependent mobility matrices.

Simplified calculation of structure-borne sound from an active machine component on a supporting substructure

The background to the work is the increasing interest in virtual acoustic prototypes, and the need to predict sound pressure radiated from machines without having to assemble them physically. The focus of the paper is on structure-borne sound, and the objective is to investigate ways of simplifying the calculation of contact forces between a vibro-acoustically active component and its passive supporting structure. An analysis shows the importance of the singular values of the mobility matrices in determining the error due to simplifications. Errors are also analysed using Monte Carlo simulations for the case of an electric motor installed on a machine frame. The results show that at frequencies above the first anti-resonance, the off-diagonal elements of the source mobility matrix can be neglected. However, at lower frequencies no such simplification is possible. A hybrid mobility matrix is therefore proposed: at high frequencies it is diagonal, consisting of measured point mobilities, and at low frequencies the entire matrix is calculated using a simple rigid mass-stiffness model. Only point mobilities need to be measured rather than a full set of point and transfer mobilities, giving a significant reduction in measurement and data handling. Validation measurements show that the contact forces calculated using the hybrid matrix are, if anything, more accurate than those based on a purely measured matrix. It is argued that this is because the mass model is more robust than measured mobilities for this type of behaviour, being based on radii of inertia and mass only. It is noted that the conclusions are likely to apply to other structure-borne sound sources because of general similarities in low-frequency behaviour.