15,850 research outputs found
An approach to NLO QCD analysis of the semi-inclusive DIS data with modified Jacobi polynomial expansion method
It is proposed the modification of the Jacobi polynomial expansion method
(MJEM) which is based on the application of the truncated moments instead of
the full ones. This allows to reconstruct with a high precision the local quark
helicity distributions even for the narrow accessible for measurement Bjorken
region using as an input only four first moments extracted from the data in
NLO QCD. It is also proposed the variational (extrapolation) procedure allowing
to reconstruct the distributions outside the accessible Bjorken region
using the distributions obtained with MJEM in the accessible region. The
numerical calculations encourage one that the proposed variational
(extrapolation) procedure could be applied to estimate the full first
(especially important) quark moments
NLO QCD method of the polarized SIDIS data analysis
Method of polarized semi-inclusive deep inelastic scattering (SIDIS) data
analysis in the next to leading order (NLO) QCD is developed. Within the method
one first directly extracts in NLO few first truncated (available to
measurement) Mellin moments of the quark helicity distributions. Second, using
these moments as an input to the proposed modification of the Jacobi polynomial
expansion method (MJEM), one eventually reconstructs the local quark helicity
distributions themselves. All numerical tests demonstrate that MJEM allows us
to reproduce with the high precision the input local distributions even inside
the narrow Bjorken region accessible for experiment. It is of importance
that only four first input moments are sufficient to achieve a good quality of
reconstruction. The application of the method to the simulated SIDIS data on
the pion production is considered. The obtained results encourage one that the
proposed NLO method can be successfully applied to the SIDIS data analysis. The
analysis of HERMES data on pion production is performed. To this end the pion
difference asymmetries are constructed from the measured by HERMES standard
semi-inclusive spin asymmetries. The LO results of the valence distribution
reconstruction are in a good accordance with the respective leading order SMC
and HERMES results, while the NLO results are in agreement with the existing
NLO parametrizations on these quantities
Simple model of the static exchange-correlation kernel of a uniform electron gas with long-range electron-electron interaction
A simple approximate expression in real and reciprocal spaces is given for
the static exchange-correlation kernel of a uniform electron gas interacting
with the long-range part only of the Coulomb interaction. This expression
interpolates between the exact asymptotic behaviors of this kernel at small and
large wave vectors which in turn requires, among other thing, information from
the momentum distribution of the uniform electron gas with the same interaction
that have been calculated in the G0W0 approximation. This exchange-correlation
kernel as well as its complement analogue associated to the short-range part of
the Coulomb interaction are more local than the Coulombic exchange-correlation
kernel and constitute potential ingredients in approximations for recent
adiabatic connection fluctuation-dissipation and/or density functional theory
approaches of the electronic correlation problem based on a separate treatment
of long-range and short-range interaction effects.Comment: 14 pages, 14 figures, to be published in Phys. Rev.
Nucleon Charge and Magnetization Densities from Sachs Form Factors
Relativistic prescriptions relating Sachs form factors to nucleon charge and
magnetization densities are used to fit recent data for both the proton and the
neutron. The analysis uses expansions in complete radial bases to minimize
model dependence and to estimate the uncertainties in radial densities due to
limitation of the range of momentum transfer. We find that the charge
distribution for the proton is significantly broad than its magnetization
density and that the magnetization density is slightly broader for the neutron
than the proton. The neutron charge form factor is consistent with the Galster
parametrization over the available range of Q^2, but relativistic inversion
produces a softer radial density. Discrete ambiguities in the inversion method
are analyzed in detail. The method of Mitra and Kumari ensures compatibility
with pQCD and is most useful for extrapolating form factors to large Q^2.Comment: To appear in Phys. Rev. C. Two new figures and accompanying text have
been added and several discussions have been clarified with no significant
changes to the conclusions. Now contains 47 pages including 21 figures and 2
table
Generalized Parton Distributions from Hadronic Observables: Non-Zero Skewness
We propose a physically motivated parametrization for the unpolarized
generalized parton distributions, H and E, valid at both zero and non-zero
values of the skewness variable, \zeta. Our approach follows a previous
detailed study of the \zeta=0 case where H and E were determined using
constraints from simultaneous fits of the experimental data on both the nucleon
elastic form factors and the deep inelastic structure functions in the non
singlet sector. Additional constraints at \zeta \neq 0 are provided by lattice
calculations of the higher moments of generalized parton distributions. We
illustrate a method for extracting generalized parton distributions from
lattice moments based on a reconstruction using sets of orthogonal polynomials.
The inclusion in our fit of data on Deeply Virtual Compton Scattering is also
discussed. Our method provides a step towards a model independent extraction of
generalized distributions from the data. It also provides an alternative to
double distributions based phenomenological models in that we are able to
satisfy the polynomiality condition by construction, using a combination of
experimental data and lattice, without resorting to any specific mathematical
construct.Comment: 29 pages, 8 figures; added references, changed text in several place
Curve Skeleton and Moments of Area Supported Beam Parametrization in Multi-Objective Compliance Structural Optimization
This work addresses the end-to-end virtual automation of structural optimization up to the derivation of a parametric geometry model that can be used for application areas such as additive manufacturing or the verification of the structural optimization result with the finite element method.
A holistic design in structural optimization can be achieved with the weighted sum method, which can be automatically parameterized with curve skeletonization and cross-section regression to virtually verify the result and control the local size for additive manufacturing.
is investigated in general. In this paper, a holistic design is understood as a design that considers various compliances as an objective function. This parameterization uses the automated determination of beam parameters by so-called curve skeletonization with subsequent cross-section shape parameter estimation based on moments of area, especially for multi-objective optimized shapes. An essential contribution is the linking of the parameterization with the results of the structural optimization, e.g., to include properties such as boundary conditions, load conditions, sensitivities or even density variables in the curve skeleton parameterization.
The parameterization focuses on guiding the skeletonization based on the information provided by the optimization and the finite element model. In addition, the cross-section detection considers circular, elliptical, and tensor product spline cross-sections that can be applied to various shape descriptors such as convolutional surfaces, subdivision surfaces, or constructive solid geometry. The shape parameters of these cross-sections are estimated using stiffness distributions, moments of area of 2D images, and convolutional neural networks with a tailored loss function to moments of area. Each final geometry is designed by extruding the cross-section along the appropriate curve segment of the beam and joining it to other beams by using only unification operations.
The focus of multi-objective structural optimization considering 1D, 2D and 3D elements is on cases that can be modeled using equations by the Poisson equation and linear elasticity. This enables the development of designs in application areas such as thermal conduction, electrostatics, magnetostatics, potential flow, linear elasticity and diffusion, which can be optimized in combination or individually. Due to the simplicity of the cases defined by the Poisson equation, no experts are required, so that many conceptual designs can be generated and reconstructed by ordinary users with little effort.
Specifically for 1D elements, a element stiffness matrices for tensor product spline cross-sections are derived, which can be used to optimize a variety of lattice structures and automatically convert them into free-form surfaces. For 2D elements, non-local trigonometric interpolation functions are used, which should significantly increase interpretability of the density distribution. To further improve the optimization, a parameter-free mesh deformation is embedded so that the compliances can be further reduced by locally shifting the node positions.
Finally, the proposed end-to-end optimization and parameterization is applied to verify a linear elasto-static optimization result for and to satisfy local size constraint for the manufacturing with selective laser melting of a heat transfer optimization result for a heat sink of a CPU. For the elasto-static case, the parameterization is adjusted until a certain criterion (displacement) is satisfied, while for the heat transfer case, the manufacturing constraints are satisfied by automatically changing the local size with the proposed parameterization. This heat sink is then manufactured without manual adjustment and experimentally validated to limit the temperature of a CPU to a certain level.:TABLE OF CONTENT III
I LIST OF ABBREVIATIONS V
II LIST OF SYMBOLS V
III LIST OF FIGURES XIII
IV LIST OF TABLES XVIII
1. INTRODUCTION 1
1.1 RESEARCH DESIGN AND MOTIVATION 6
1.2 RESEARCH THESES AND CHAPTER OVERVIEW 9
2. PRELIMINARIES OF TOPOLOGY OPTIMIZATION 12
2.1 MATERIAL INTERPOLATION 16
2.2 TOPOLOGY OPTIMIZATION WITH PARAMETER-FREE SHAPE OPTIMIZATION 17
2.3 MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION WITH THE WEIGHTED SUM METHOD 18
3. SIMULTANEOUS SIZE, TOPOLOGY AND PARAMETER-FREE SHAPE OPTIMIZATION OF WIREFRAMES WITH B-SPLINE CROSS-SECTIONS 21
3.1 FUNDAMENTALS IN WIREFRAME OPTIMIZATION 22
3.2 SIZE AND TOPOLOGY OPTIMIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 27
3.3 PARAMETER-FREE SHAPE OPTIMIZATION EMBEDDED IN SIZE OPTIMIZATION 32
3.4 WEIGHTED SUM SIZE AND TOPOLOGY OPTIMIZATION 36
3.5 CROSS-SECTION COMPARISON 39
4. NON-LOCAL TRIGONOMETRIC INTERPOLATION IN TOPOLOGY OPTIMIZATION 41
4.1 FUNDAMENTALS IN MATERIAL INTERPOLATIONS 43
4.2 NON-LOCAL TRIGONOMETRIC SHAPE FUNCTIONS 45
4.3 NON-LOCAL PARAMETER-FREE SHAPE OPTIMIZATION WITH TRIGONOMETRIC SHAPE FUNCTIONS 49
4.4 NON-LOCAL AND PARAMETER-FREE MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION 54
5. FUNDAMENTALS IN SKELETON GUIDED SHAPE PARAMETRIZATION IN TOPOLOGY OPTIMIZATION 58
5.1 SKELETONIZATION IN TOPOLOGY OPTIMIZATION 61
5.2 CROSS-SECTION RECOGNITION FOR IMAGES 66
5.3 SUBDIVISION SURFACES 67
5.4 CONVOLUTIONAL SURFACES WITH META BALL KERNEL 71
5.5 CONSTRUCTIVE SOLID GEOMETRY 73
6. CURVE SKELETON GUIDED BEAM PARAMETRIZATION OF TOPOLOGY OPTIMIZATION RESULTS 75
6.1 FUNDAMENTALS IN SKELETON SUPPORTED RECONSTRUCTION 76
6.2 SUBDIVISION SURFACE PARAMETRIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 78
6.3 CURVE SKELETONIZATION TAILORED TO TOPOLOGY OPTIMIZATION WITH PRE-PROCESSING 82
6.4 SURFACE RECONSTRUCTION USING LOCAL STIFFNESS DISTRIBUTION 86
7. CROSS-SECTION SHAPE PARAMETRIZATION FOR PERIODIC B-SPLINES 96
7.1 PRELIMINARIES IN B-SPLINE CONTROL GRID ESTIMATION 97
7.2 CROSS-SECTION EXTRACTION OF 2D IMAGES 101
7.3 TENSOR SPLINE PARAMETRIZATION WITH MOMENTS OF AREA 105
7.4 B-SPLINE PARAMETRIZATION WITH MOMENTS OF AREA GUIDED CONVOLUTIONAL NEURAL NETWORK 110
8. FULLY AUTOMATED COMPLIANCE OPTIMIZATION AND CURVE-SKELETON PARAMETRIZATION FOR A CPU HEAT SINK WITH SIZE CONTROL FOR SLM 115
8.1 AUTOMATED 1D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINED SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 118
8.2 AUTOMATED 2D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINT SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 120
8.3 USING THE HEAT SINK PROTOTYPES COOLING A CPU 123
9. CONCLUSION 127
10. OUTLOOK 131
LITERATURE 133
APPENDIX 147
A PREVIOUS STUDIES 147
B CROSS-SECTION PROPERTIES 149
C CASE STUDIES FOR THE CROSS-SECTION PARAMETRIZATION 155
D EXPERIMENTAL SETUP 15
Density of eigenvalues of random normal matrices
The relation between random normal matrices and conformal mappings discovered
by Wiegmann and Zabrodin is made rigorous by restricting normal matrices to
have spectrum in a bounded set. It is shown that for a suitable class of
potentials the asymptotic density of eigenvalues is uniform with support in the
interior domain of a simple smooth curve.Comment: 17 pages. Corrected versio
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