488 research outputs found
Development of an Optimization-Based Atomistic-to-Continuum Coupling Method
Atomistic-to-Continuum (AtC) coupling methods are a novel means of computing
the properties of a discrete crystal structure, such as those containing
defects, that combine the accuracy of an atomistic (fully discrete) model with
the efficiency of a continuum model. In this note we extend the
optimization-based AtC, formulated in arXiv:1304.4976 for linear,
one-dimensional problems to multi-dimensional settings and arbitrary
interatomic potentials. We conjecture optimal error estimates for the
multidimensional AtC, outline an implementation procedure, and provide
numerical results to corroborate the conjecture for a 1D Lennard-Jones system
with next-nearest neighbor interactions.Comment: 12 pages, 3 figure
Control of Flow Structure on a Semi-Circular Planform Wing
Active flow control is used to modify the lift, drag and pitching moments on a semicircular wing with aspect ratio, AR = 2, and chord Reynolds number is 68,000. The wing is mounted on a pitch/plunge sting mechanism that responds to the instantaneous loads and moments acting on the wing. The leading edge of the airfoil contains 16 spatially localized actuators that can be independently controlled. Smoke wire visualization, surface pressure and six-component force balance measurements are used to characterize the effects of openloop forcing. The lift coefficients on the steady wing are enhanced with the actuation, similar to the effect of dynamic stall vortex lift enhancement that occurs during a pitch up maneuver. Surface pressure measurements are being used to construct a flow model for use in feedback control. Progress toward the goal of designing a feedback controller to stabilize the flight of the model in an oscillatory freestream is discussed
Renormalization group approach to multiscale modelling in materials science
Dendritic growth, and the formation of material microstructure in general,
necessarily involves a wide range of length scales from the atomic up to sample
dimensions. The phase field approach of Langer, enhanced by optimal asymptotic
methods and adaptive mesh refinement, copes with this range of scales, and
provides an effective way to move phase boundaries. However, it fails to
preserve memory of the underlying crystallographic anisotropy, and thus is
ill-suited for problems involving defects or elasticity. The phase field
crystal (PFC) equation-- a conserving analogue of the Hohenberg-Swift equation
--is a phase field equation with periodic solutions that represent the atomic
density. It can natively model elasticity, the formation of solid phases, and
accurately reproduces the nonequilibrium dynamics of phase transitions in real
materials. However, the PFC models matter at the atomic scale, rendering it
unsuitable for coping with the range of length scales in problems of serious
interest. Here, we show that a computationally-efficient multiscale approach to
the PFC can be developed systematically by using the renormalization group or
equivalent techniques to derive appropriate coarse-grained coupled phase and
amplitude equations, which are suitable for solution by adaptive mesh
refinement algorithms
Approximation of Parametric Derivatives by the Empirical Interpolation Method
We introduce a general a priori convergence result for the approximation of parametric derivatives of parametrized functions. We consider the best approximations to parametric derivatives in a sequence of approximation spaces generated by a general approximation scheme, and we show that these approximations are convergent provided that the best approximation to the function itself is convergent. We also provide estimates for the convergence rates. We present numerical results with spaces generated by a particular approximation scheme—the Empirical Interpolation Method—to confirm the validity of the general theory
Singular Cucker-Smale Dynamics
The existing state of the art for singular models of flocking is overviewed,
starting from microscopic model of Cucker and Smale with singular communication
weight, through its mesoscopic mean-filed limit, up to the corresponding
macroscopic regime. For the microscopic Cucker-Smale (CS) model, the
collision-avoidance phenomenon is discussed, also in the presence of bonding
forces and the decentralized control. For the kinetic mean-field model, the
existence of global-in-time measure-valued solutions, with a special emphasis
on a weak atomic uniqueness of solutions is sketched. Ultimately, for the
macroscopic singular model, the summary of the existence results for the
Euler-type alignment system is provided, including existence of strong
solutions on one-dimensional torus, and the extension of this result to higher
dimensions upon restriction on the smallness of initial data. Additionally, the
pressureless Navier-Stokes-type system corresponding to particular choice of
alignment kernel is presented, and compared - analytically and numerically - to
the porous medium equation
Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations
Discontinuous Galerkin (DG) methods have a long history in computational
physics and engineering to approximate solutions of partial differential
equations due to their high-order accuracy and geometric flexibility. However,
DG is not perfect and there remain some issues. Concerning robustness, DG has
undergone an extensive transformation over the past seven years into its modern
form that provides statements on solution boundedness for linear and nonlinear
problems.
This chapter takes a constructive approach to introduce a modern incarnation
of the DG spectral element method for the compressible Navier-Stokes equations
in a three-dimensional curvilinear context. The groundwork of the numerical
scheme comes from classic principles of spectral methods including polynomial
approximations and Gauss-type quadratures. We identify aliasing as one
underlying cause of the robustness issues for classical DG spectral methods.
Removing said aliasing errors requires a particular differentiation matrix and
careful discretization of the advective flux terms in the governing equations.Comment: 85 pages, 2 figures, book chapte
The effect of materials' rheology on process energy consumption and melt thermal quality in polymer extrusion
YesPolymer extrusion is an important but an energy intensive method of processing polymeric materials. The rapid increase in demand of polymeric products has forced manufactures to rethink their processing efficiencies to manufacture good quality products with low-unit-cost. Here, analyzing the operational conditions has become a key strategy to achieve both energy and thermal efficiencies simultaneously. This study aims to explore the effects of polymers' rheology on the energy consumption and melt thermal quality (ie, a thermally homogeneous melt flow in both radial and axil directions) of extruders. Six commodity grades of polymers (LDPE, LLDPE, PP, PET, PS, and PMMA) were processed at different conditions in two types of continuous screw extruders. Total power, motor power, and melt temperature profiles were analyzed in an industrial scale single-screw extruder. Moreover, the active power (AP), mass throughput, torque, and power factor were measured in a laboratory scale twin-screw extruder. The results confirmed that the specific energy consumption for both single and twin screw extruders tends to decrease with the processing speed. However, this action deteriorates the thermal stability of the melt regardless the nature of the polymer. Rheological characterization results showed that the viscosity of LDPE and PS exhibited a normal shear thinning behavior. However, PMMA presented a shear thickening behavior at moderate-to-high shear rates, indicating the possible formation of entanglements. Overall, the findings of this work confirm that the materials' rheology has an appreciable correlation with the energy consumption in polymer extrusion and also most of the findings are in agreement with the previously reported investigations. Therefore, further research should be useful for identifying possible correlations between key process parameters and hence to further understand the processing behavior for wide range of machines, polymers, and operating conditions
Multidimensional Conservation Laws: Overview, Problems, and Perspective
Some of recent important developments are overviewed, several longstanding
open problems are discussed, and a perspective is presented for the
mathematical theory of multidimensional conservation laws. Some basic features
and phenomena of multidimensional hyperbolic conservation laws are revealed,
and some samples of multidimensional systems/models and related important
problems are presented and analyzed with emphasis on the prototypes that have
been solved or may be expected to be solved rigorously at least for some cases.
In particular, multidimensional steady supersonic problems and transonic
problems, shock reflection-diffraction problems, and related effective
nonlinear approaches are analyzed. A theory of divergence-measure vector fields
and related analytical frameworks for the analysis of entropy solutions are
discussed.Comment: 43 pages, 3 figure
Efeitos das condições de preparação e de modificação de superfície de membranas de PEUAPM na separação água/óleo
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