Existence of an optimal domain for the buckling load of a clamped plate with prescribed volume

We formulate the minimization of the buckling load of a clamped plate as a free boundary value problem with a penalization term for the volume constraint. As the penalization parameter becomes small, we show that the optimal shape problem with prescribed volume is solved. In addition, we discuss two different choices for the penalization term.

Optimization strategies for efficient high-resolution volcanic plume simulations with OpenFOAM

<p>In the last years, the interest in three-dimensional  physico-mathematical models for volcanic plumes has grown, motivated by the need of predicting accurately the dispersal patterns of volcanic ash in the atmosphere (to mitigate the risks for civil aviation and for the nearby inhabited regions) and pushed by improved remote sensing techniques and measurements. However, limitations due to the mesh resolution and numerical accuracy as well as the complexity entailed model formulations, have so far prevented a detailed study of turbulence in volcanic plumes at high resolution. Eruptive columns are indeed multiphase gas-particle turbulent flows, in which the largest (integral) scale is in the order of tens or hundreds of kilometers and the smallest scale is of the order of microns. Performing accurate numerical simulations of such phenomena remains therefore a challenging task.</p><p>Modern HPC resources and recent model developments enable the study of multiphase turbulent structures of volcanic plumes with an unprecedented level of detail. However, a number of issues of the present model implementation need to be addressed in order to efficiently use the computational resources of modern supercomputing machines. Here we present an overview of an optimization strategy that allows us to perform large parallel simulations of volcanic plumes using ASHEE, a numerical solver based on OpenFOAM and one of the target flagship codes of the project ChEESE (Centre of Excellence for Exascale in Solid Earth). Such optimizations include: mixed precision floating point operations to increase computational speed and reduce memory usage, optimal domain decomposition for better communication load balancing and asynchronous I/O to hide I/O costs. Scaling analysis and volcanic plume simulations are presented to demonstrate the improvement in both computational performances and computing capability.</p>

Automation and Management of Design Process of the Main Drive for an Innovative Fruits and Vegetables Washer

A new technique is described, used by the authors to automate the design process of the main drive of a new generation machine intended for industrial washing of fruits and vegetables. To solve the problem of multi-criteria design, the original approach is proposed that uses interconnected mathematical models describing the dynamic behavior, strength reliability and functional characteristics of the machine in a unified information space. The generalized mathematical model includes 12 controlled parameters, 16 functional constraints, and 3 quality criteria. A genetic algorithm was used to find the space of Pareto-optimal solutions. The situational approach was used to select the final rational solution from a set of solutions belonging to the Pareto-optimal domain. The rational design of option the washer found using the proposed approach is compared with the existing ones. The proposed design methodology can be recommended for the design of a wide range of similar mechanical structures.

Provider Perspectives on Latino Immigrants’ Access to Resources for Syndemic Health Issues

Introduction: Latino immigrants to the United States experience disproportionate impacts from the syndemic formed by substance abuse, violence victimization, HIV/AIDS, and mental health (SAVAME). This study characterizes resource access for Latino immigrants living in Philadelphia, as perceived by staff at Latino-serving organizations. Methods: An online cross-sectional survey of staff at key Latino-serving Philadelphia organizations assessed access to their organization and citywide access to each type of service (substance use, HIV/AIDS, domestic violence [DV], and mental health) for Latino immigrants. Descriptive statistics for organizational access indicators and citywide access scores across four syndemic domains (availability, accessibility, adequacy, and quality) and by syndemic condition were computed. Results: Organizational access and citywide access across HIV/AIDS (mean = 1.94, SD = 0.83), mental health (mean = 1.37, SD = 0.95), substance use (mean = 1.11, SD = 0.74), and DV (mean = 1.49, SD = 0.97) services were perceived as far from optimal. Domain scores were highest for accessibility (mean = 1.66, SD = 1.03), followed by quality (mean = 1.44, SD = 0.79), availability (mean = 1.41, SD = .81), and adequacy (mean = 1.24, SD = .75). Conclusion: Based on findings from a survey of staff working at Latino-serving organizations, this study highlights the lack of support and resources for Latino immigrants, in particular those related to mental health and substance use. Programs and interventions are needed to improve service delivery in Latino immigrant communities.

Universal functions for linear functions depending on two variables

We consider universal function’s construction for classes of sums of two arguments modulo 2. We constructed functions with optimal domain cardinality O(log n).

Hybrid Discontinuous Galerkin Discretisation and Domain Decomposition Preconditioners for the Stokes Problem

Solving the Stokes equation by an optimal domain decomposition method derived algebraically involves the use of nonstandard interface conditions whose discretisation is not trivial. For this reason the use of approximation methods such as hybrid discontinuous Galerkin appears as an appropriate strategy: on the one hand they provide the best compromise in terms of the number of degrees of freedom in between standard continuous and discontinuous Galerkin methods, and on the other hand the degrees of freedom used in the nonstandard interface conditions are naturally defined at the boundary between elements. In this paper, we introduce the coupling between a well chosen discretisation method (hybrid discontinuous Galerkin) and a novel and efficient domain decomposition method to solve the Stokes system. We present the detailed analysis of the hybrid discontinuous Galerkin method for the Stokes problem with nonstandard boundary conditions. The full stability and convergence analysis of the discretisation method is presented, and the results are corroborated by numerical experiments. In addition, the advantage of the new preconditioners over more classical choices is also supported by numerical experiments.

A Novel Computational Method of Processing Map for Ti-6Al-4V Alloy and Corresponding Microstructure Study

The Arrhenius-type constitutive equation is mostly used to describe flow behaviors of material. However, no processing map has been constructed directly according to it. In this study, a novel computational method was applied for establishing the processing map for Ti-6Al-4V alloy in the temperature and strain rate range of 800–1050 °C and 0.001–10 s−1, respectively. The processing map can be divided into four domains according to its graphic features. Among the four domains, the optimal domain is in the temperature and strain rate range of 850–925 °C and 0.001–0.1 s−1, where peak efficiency η is 0.54 and the main microstructural evolution is DRX (dynamic recrystallization). When the alloy is processed in the α + β phase field, the temperature and strain rate range of 800–850 °C and 3–10 s−1 should be avoided, where instability parameter ξ is negative and the microstructural feature is flow localization. When the alloy is processed in the β phase field, DRV (dynamic recovery) and slight DRX of β phase is the main microstructural characteristics in the range of 1000–1050 °C and 0.001–0.02 s−1. However, flow localization of β phase is the main microstructural feature in the range of 1000–1050 °C and 1–10 s−1, which should be avoided.

Shape optimization for the eigenfrequency of the plate

In this paper, we consider an eigenvalue problem for the biharmonic operator that describes the transverse vibrations of the plate. Under the imposed boundary conditions, the eigenvalues of this operator are indeed eigenfrequencies of the clamped plate. The domain of the plate is taken variable and the domain functional, involving an eigenfrequency, is studied. A new formula for an eigenfrequency is proved, the first variation of the functional with respect to the domain is calculated, and the necessary condition for an optimal shape is derived. New explicit formulas are obtained for the eigenfrequency in the optimal domain in some particular cases.