Relaxation Procedure Research Articles

The number of steps and the final configuration of relaxation procedures on graphs

This paper considers the relaxation procedure on a graph G with V(G)={v1,v2,…,vn}. Initially, a configuration X=(x1,x2,…,xn) which is an n-tuple of real numbers having a positive sum is given. If there is a negative label xi, then the player can transform X into X′=(x1′,x2′,…,xn′), where xi′=−xi, xj′=xj+2dixi for each vj adjacent to vi where vi has exactly di neighbors, and xk′=xk for all other k. Wegert and Reiher (Wegert and Reiher (2009)) proved the finiteness of the procedure and proposed the problem of determining graphs for which the final configurations and/or the numbers of steps are unique. In this paper, we give a complete solution to the problem.

Parallelizing the Kolmogorov-Fokker-Planck equation

We design two parallel schemes, based on Schwarz Waveform Relaxation (SWR) procedures, for the numerical solution of the Kolmogorov equation. The latter is a simplified version of the Fokker–Planck equation describing the time evolution of the probability density of the velocity of a particle. SWR procedures decompose the spatio-temporal computational domain into subdomains and solve (in parallel) subproblems, that are coupled through suitable conditions at the interfaces to recover the solution of the global problem. We consider coupling conditions of both Dirichlet (Classical SWR) and Robin (Optimized SWR) types. We prove well-posedeness of the schemes subproblems and convergence for the proposed algorithms. We corroborate our findings with some numerical tests.

Solving difficult mixed integer and disjunctive non-linear problems on single and parallel processors

Difficult non-linear, mixed integer non-linear and general disjunctive programming (NLP/MINLP/GDP) problems are considered in the present study. We show using random relaxation procedures that sampling over a subset of the integer variables and parallel processing have potential to simplify large scale MINLP/GDP problems and hence to solve them faster and more reliably than conventional approaches on single processors. Gray coding can be utilized to assign problems to the local processors. Some efficient non-linear solvers have been connected to the Genetic Hybrid Algorithm (GHA) through a switch board minlp_machine(), monitoring a vector of caller functions. The switch board is tested on single processor computers and massively parallel supercomputers in a sample of optimization problems. A new line search algorithm based on multi-sectioning, i.e. repeated bi-sectioning of parallel threads is applied to a set of irregular NLP-problems. Simulations indicate that step search based on multi-sectioning and re-centering is robust. Time recording indicates that the step search procedure is fast also in large optimization problems. Parallel processing with Gray coding and random sampling over a subset of the integer variables improves the performance of the sequential quadratic programming algorithm with multi-sectioning in large-scale problems. An early mesh interrupt guarantees load balancing in regular problems. General disjunctive programming (GDP) problems can be simplified through parallel processing. Certain problems are solved in larger scale than reported previously. Function pointer logic and intelligent switching procedures provide a fruitful basis for solving high-order GDP problems, where the computational challenge in direct MINLP-formulations would be insurmountable.

Successful Practice of Electroacupuncture Analgesia in Equine Surgery

Electroacupuncture analgesia was used for surgery in horses and donkeys. A KWD-808 electrical stimulator was used to incrementally induce a dense, dispersed wave output at frequencies from 20 to 55 Hz, which was maintained at a frequency of 55 Hz, and to change the amplitude of the wave to the best grading number for the suggested operation in each animal. Induction of analgesia lasted for 20–30 minutes, and the effect of analgesia was maintained for 20–45 minutes depending on the type of surgery performed. The exhibited clinical signs, physical examination data, and the responses of all animals were used for evaluating the periods of analgesia. Although the majority of the cases (95%) had no response to strong surgical pain, they experienced significant increases in heart rates and respiratory rates during induction. The lack of pain, relaxed surgical procedures, reduced intraoperative bleeding, and improved healing without complications were all definite benefits of using electroacupuncture analgesia in surgery. Thus, this study has provided surgical evidence supporting the effectiveness of electroacupuncture analgesia, as well as confirming its reliability, in the field of equine anesthesia and surgery.

Analytical modeling of residual stress and the induced deflection of a milled thin plate

Predictions of residual stress-induced deformations on thin aerospace parts are still among the most challenging and relevant problems in engineering applications. In this paper, a new methodology based on analytical modeling of machining mechanics is introduced in order to predict thin plate deflection induced by residual stresses given material attributes, process configurations, and parameters. The model uses an elasto-plastic constitutive behavior algorithm to predict the plastic stress, strain, and thus residual stresses. A relaxation procedure is applied upon residual stresses in order to quantify the elastic deflection when the plate is unloaded from cutting forces. Experimental validations are presented on multi-pass milling of aerospace grade aluminum alloy Al7050-T7451. The newly developed analytical model shows promise to predict the residual stresses and the thin plate deflection profile under various cutting conditions.

A Numerical Lagrangian Approach for Analysis of Contact Viscoelastic Problems

The objective of this paper is to develop a finite-element formulation associated with an incremental adaptive procedure established for analysis of frictional contact problems in viscoelastic solids. A generalized Maxwell model has been used to model the viscoelastic constitutive equations in which bulk and shear relaxation functions are represented by the sum of a series of decaying exponential functions of time. A generalized finite-element approach, based on the principle of virtual work, has been developed using an incremental relaxation procedure. The application of the finite element method to contact viscoelastic problems is investigated. The contact treatment between bodies has been studied through an augmented Lagrangian approach. Finally, an example is presented to evaluate the computational solution procedure presented.

GNCCP-Graduated NonConvexityand Concavity Procedure.

In this paper we propose the graduated nonconvexity and concavity procedure (GNCCP) as a general optimization framework to approximately solve the combinatorial optimization problems defined on the set of partial permutation matrices. GNCCP comprises two sub-procedures, graduated nonconvexity which realizes a convex relaxation and graduated concavity which realizes a concave relaxation. It is proved that GNCCP realizes exactly a type of convex-concave relaxation procedure (CCRP), but with a much simpler formulation without needing convex or concave relaxation in an explicit way. Actually, GNCCP involves only the gradient of the objective function and is therefore very easy to use in practical applications. Two typical related NP-hard problems, partial graph matching and quadratic assignment problem (QAP), are employed to demonstrate its simplicity and state-of-the-art performance.

On mathematical modeling of fluid–structure interactions with nonlinear effects: Finite element approximations of gust response

In this paper the numerical simulation of aeroelastic interactions of flexibly supported two-degrees of freedom (2-DOF) airfoil in two-dimensional (2D) incompressible viscous turbulent flow subjected to a gust (sudden change of flow conditions) is considered. The flow is modeled by Reynolds averaged Navier–Stokes equations (RANS), and by k−ω turbulence model. The considered flow problem is discretized in space using the fully stabilized finite element (FE) method implemented in the developed in-house program, which allows to solve interaction problems. In order to treat the time dependent inlet boundary condition the standard stabilization procedure was modified. Further, the under relaxation procedure was introduced in order to overcome the artificial instability of the coupling algorithm. The aeroelastic response to a sudden gust is numerically analyzed with the aid of the developed FE code.

Relax and refill: xylem rehydration prior to hydraulic measurements favours embolism repair in stems and generates artificially low PLC values

Diurnal changes in percentage loss of hydraulic conductivity (PLC), with recorded values being higher at midday than on the following morning, have been interpreted as evidence for the occurrence of cycles of xylem conduits' embolism and repair. Recent reports have suggested that diurnal PLC changes might arise as a consequence of an experimental artefact, that is, air entry into xylem conduits upon cutting stems, even if under water, while under substantial tension generated by transpiration. Rehydration procedures prior to hydraulic measurements have been recommended to avoid this artefact. In the present study, we show that xylem rehydration prior to hydraulic measurements might favour xylem refilling and embolism repair, thus leading to PLC values erroneously lower than those actually experienced by transpiring plants. When xylem tension relaxation procedures were performed on stems where refilling mechanisms had been previously inhibited by mechanical (girdling) or chemical (orthovanadate) treatment, PLC values measured in stems cut under native tension were the same as those measured after sample rehydration/relaxation. Our data call for renewed attention to the procedures of sample collection in the field and transport to the laboratory, and suggest that girdling might be a recommendable treatment prior to sample collection for PLC measurements.

Relaxation of atomic orbitals in a plane-wave basis

We present a first-principles calculation scheme for crystals that diagonalizes an effective Hamiltonian in a small atomic orbital basis set which is expanded in plane waves, yielding initial trial wave functions. A simple relaxation procedure applied to the trial wave functions expanded in a plane-wave basis can be used to generate a set of correction wave functions. We show that a subsequent diagonalization of the effective Hamiltonian in the subspace of the trial and correction wave functions is sufficient to obtain results quite close from a full converged calculation on the plane-wave basis set used for the projection. The proposed method should be simple to implement in other plane-wave computer programs and leads to substantial gains in computation speed while maintaining reasonable accuracy.

Graph Matching by Simplified Convex-Concave Relaxation Procedure

The convex and concave relaxation procedure (CCRP) was recently proposed and exhibited state-of-the-art performance on the graph matching problem. However, CCRP involves explicitly both convex and concave relaxations which typically are difficult to find, and thus greatly limit its practical applications. In this paper we propose a simplified CCRP scheme, which can be proved to realize exactly CCRP, but with a much simpler formulation without needing the concave relaxation in an explicit way, thus significantly simplifying the process of developing CCRP algorithms. The simplified CCRP can be generally applied to any optimizations over the partial permutation matrix, as long as the convex relaxation can be found. Based on two convex relaxations, we obtain two graph matching algorithms defined on adjacency matrix and affinity matrix, respectively. Extensive experimental results witness the simplicity as well as state-of-the-art performance of the two simplified CCRP graph matching algorithms.

A branch and bound method for the solution of multiparametric mixed integer linear programming problems

In this paper, we present a novel algorithm for the solution of multiparametric mixed integer linear programming (mp-MILP) problems that exhibit uncertain objective function coefficients and uncertain entries in the right-hand side constraint vector. The algorithmic procedure employs a branch and bound strategy that involves the solution of a multiparametric linear programming sub-problem at leaf nodes and appropriate comparison procedures to update the tree. McCormick relaxation procedures are employed to overcome the presence of bilinear terms in the model. The algorithm generates an envelope of parametric profiles, containing the optimal solution of the mp-MILP problem. The parameter space is partitioned into polyhedral convex critical regions. Two examples are presented to illustrate the steps of the proposed algorithm.

Prediction of Residual Stress Induced Distortions in Micro-Milling of Al7050 Thin Plate

In this paper, a new analytical model based on a mechanistic force prediction and elastoplastic relaxation procedure predicting the deflections induced by the residual stresses in a milled micro part is proposed. The force model defines the Hertzian type distribution applied by the tool on the part. The proposed deflection model is valid for thin rectangular parts typically produced only using a micro-milling process. The deflection and the force model were analytically developed and experimentally tested on thin Al 7050 micro plates. The force model was validated using micro dynamometer and the deflection profile was verified using the white light interferometer. The proposed model showed that it has a reasonable ability to predict the residual stress induced deflection in the context of stress gradient and intensity.

Assessment of Driver Stress from Physiological Signals collected under Real-Time Semi-Urban Driving Scenarios

AbstractDesigning a wearable driver assist system requires extraction of relevant features from physiological signals like galvanic skin response and photoplethysmogram collected from automotive drivers during real-time driving. In the discussed case, four stress-classes were identified using cascade forward neural network (CASFNN) which performed consistently with minimal intra- and inter-subject variability. Task-induced stress-trends were tracked using Triggs’ Tracking Variable-based regression model with CASFNN configuration. The proposed framework will enable proactive initiation of rescue and relaxation procedures during accidents and emergencies.

A Gas-Kinetic Scheme for Six-Equation Two-Phase Flow Model

A kinetic flux-vector splitting (KFVS) scheme is applied for solving a reduced six-equation two-phase flow model of Saurel et al. [1]. The model incorporates single velocity, two pressures and relaxation terms. An additional seventh equation, describing the total mixture energy, is added to the model to guarantee the correct treatment of shocks in the single phase limit. Some salient features of the model are that it is hyperbolic with only three wave propagation speeds and the volume fraction remains positive. The proposed numerical scheme is based on the direct splitting of macroscopic flux functions of the system of equations. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge-Kutta time stepping method. Moreover, a pressure relaxation procedure is used to fulfill the interface conditions. For validation, the results of suggested scheme are compared with those from the high resolution central upwind and HLLC schemes. The central upwind scheme is also applied for the first time to this model. The accuracy, efficiency and simplicity of the KFVS scheme demonstrate its potential for modeling two-phase flows.

A Greedy Multistage Convex Relaxation Algorithm Applied to Structured Group Sparse Reconstruction Problems Based on Iterative Support Detection

We propose a new effective algorithm for recovering a group sparse signal from very limited observations or measured data. As we know that a better reconstruction quality can be achieved when encoding more structural information besides sparsity, the commonly employedl2,1-regularization incorporating the prior grouping information has a better performance than the plainl1-regularized models as expected. In this paper we make a further use of the prior grouping information as well as possibly other prior information by considering a weightedl2,1model. Specifically, we propose a multistage convex relaxation procedure to alternatively estimate weights and solve the resulted weighted problem. The procedure of estimating weights makes better use of the prior grouping information and is implemented based on the iterative support detection (Wang and Yin, 2010). Comprehensive numerical experiments show that our approach brings significant recovery enhancements compared with the plainl2,1model, solved via the alternating direction method (ADM) (Deng et al., 2013), either in noiseless or in noisy environments.

Coupled finite element - hierarchical boundary element methods for dynamic soil-structure interaction in the frequency domain

SUMMARY This paper discusses the coupling of finite element and fast boundary element methods for the solution of dynamic soil–structure interaction problems in the frequency domain. The application of hierarchical matrices in the boundary element formulation allows considering much larger problems compared to classical methods. Three coupling methodologies are presented and their computational performance is assessed through numerical examples. It is demonstrated that the use of hierarchical matrices renders a direct coupling approach the least efficient, as it requires the assembly of a dynamic soil stiffness matrix. Iterative solution procedures are presented as well, and it is shown that the application of such schemes to dynamic soil–structure interaction problems in the frequency domain is not trivial, as convergence can hardly be achieved if no relaxation procedure is incorporated. Aitken's Δ2-method is therefore employed in sequential iterative schemes for the calculation of an optimized interface relaxation parameter, while a novel relaxation technique is proposed for parallel iterative algorithms. It is demonstrated that the efficiency of these algorithms strongly depends on the boundary conditions applied to each subdomain; the fastest convergence is observed if Neumann boundary conditions are imposed on the stiffest subdomain. The use of a dedicated solver for each subdomain hence results in a reduced computational effort. A monolithic coupling strategy, often used for the solution of fluid–structure interaction problems, is also introduced. The governing equations are simultaneously solved in this approach, while the assembly of a dynamic soil stiffness matrix is avoided. Copyright © 2013 John Wiley & Sons, Ltd.

미분게임 이론을 이용한 차량 전복 방지 제어기 설계

This study presents an approach for designing a vehicle rollover prevention controller using differential game theory and multi-level programming. The rollover prevention problem can be modeled as a non-cooperative zero-sum two-player differential game. A controller as an equilibrium solution of the differential game guarantees the worst-case performance against every possible steering input. To obtain an equilibrium solution to the differential game with a small amount of computational effort, a multi-level programming approach with a relaxation procedure is used. To cope with the loss of maneuverability caused by the active suspension, an electronic stability program (ESP) is adopted. Through simulations, the proposed method is shown to be effective in obtaining an equilibrium solution of the differential game.

Attraction sets in abstract attainability problems: Equivalent representations and basic properties

In this paper we use the following abbreviations: FB (filter base), MS (measurable space), AS (attraction set), DS (directed set), AD (attainability domain), GE (generalized element), s/s (subset), ApS (approximate solution), TS (topological space), and u/f (ultrafilter). We consider general questions connected with the asymptotic attainability; the latter is understood as the attainability of certain states under asymptotic constraints. One natural concrete variant of the problem which we consider below is related to the construction of the AD of a controlled system at a fixed time moment and the study of its properties. This concrete problem is not stable with respect to disturbances, in particular, for weakened constraints. One can treat weakened constraints (phase constraints, edge and intermediate ones) in this problem as asymptotic restrictions. Respectively, the limit of real AD which correspond to weakened constraints can be considered as an AS; from the practical point of view it plays the same role as a “regular ” AD does. Together with AD, with the strict and approximate fulfillment of constraints one can consider sheaves of trajectories of the controlled system and thus obtain sets in a functional space equipped with the corresponding topology. The latter can be generated by a metric, but this is not necessarily so (for example, in cases typical for control problems with continuous time, the topology of pointwise convergence is not metrizable). Therefore it is natural to consider logically similar problems on the attainability in TS, though this can require the application of more complex constructions for AS. This approach is used in the present paper. In addition, using such general statements of the problem, it is natural to assume asymptotic analogs of constraints which are not necessary connected with the weakening of some standard conditions. Really, weakening conditions of such a kind, we form a family of sets of feasible elements for each constraint weakened in a concrete way (generated by the set of mentioned conditions). From this moment we “deal” with the obtained family (really, this is a result of the relaxation procedure for the initial problem), using the minimal set of properties of sets that compose it. But this means that from the beginning we can assume that the family of s/s of the space of regular solutions (or controls) is given, not questioning how this family has been obtained (it is advisable to reduce the set of properties “to the minimum”). In particular, we do not tend to connect this family with a successive weakening of some “rigid ” conditions. In this case the question on the attainability in TS has an asymptotic character. Let us consider a very simple example of a static problem, fixing two finite-dimensional spaces R m and R n (m and n are natural numbers), and a bounded mapping f from R m to R n .F or de finiteness,

Stress relaxation of grouted entirely large diameter B-GFRP soil nail

One of the potential solutions to steel-corrosion-related problems is the usage of fiber reinforced polymer (FRP) as a replacement of steel bars. In the past few decades, researchers have conducted a large number of experimental and theoretical studies on the behavior of small size glass fiber reinforce polymer (GFRP) bars (diameter smaller than 20 mm). However, the behavior of large size GFRP bar is still not well understood. Particularly, few studies were conducted on the stress relaxation of grouted entirely large diameter GFRP soil nail. This paper investigates the effect of stress levels on the relaxation behavior of GFRP soil nail under sustained deformation ranging from 30% to 60% of its ultimate strain. In order to study the behavior of stress relaxation, two B-GFRP soil nail element specimens were developed and instrumented with fiber Bragg grating (FBG) strain sensors which were used to measure strains along the B-GFRP bars. The test results reveal that the behavior of stress relaxation of B-GFRP soil nail element subjected to pre-stress is significantly related to the elapsed time and the initial stress of relaxation procedure. The newly proposed model for evaluating stress relaxation ratio can substantially reflect the influences of the nature of B-GFRP bar and the property of grip body. The strain on the nail body can be redistributed automatically. Modulus reduction is not the single reason for the stress degradation.