Numerical comparison between Maxwell stress method and equivalent multipole approach for calculation of the dielectrophoretic force in octupolar cell traps

This work presents detailed numerical calculations of the dielectrophoretic force in octupolar traps designed for single-cell trapping. A trap with eight planar electrodes is studied for spherical and ellipsoidal particles using an indirect implementation of the boundary element method (BEM). Multipolar approximations of orders one to three are compared with the full Maxwell stress tensor (MST) calculation of the electrical force on spherical particles. Ellipsoidal particles are also studied, but in their case only the dipolar approximation is available for comparison with the MST solution. The results show that the full MST calculation is only required in the study of non-spherical particles.

Light-cone fluctuations and the renormalized stress tensor of a massless scalar field

We investigate the effects of light-cone fluctuations over the renormalized vacuum expectation value of the stress-energy tensor of a real massless minimally coupled scalar field defined in a (d+1)-dimensional flat space-time with topology R×Td. For modeling the influence of light-cone fluctuations over the quantum field, we consider a random Klein-Gordon equation. We study the case of centered Gaussian processes. After taking into account all the realizations of the random processes, we present the correction caused by random fluctuations. The averaged renormalized vacuum expectation value of the stress-energy associated with the scalar field is presented. © 2013 World Scientific Publishing Company.

Black hole evaporation and stress tensor correlations

General Relativity is one of the greatest scientific achievementes of the 20th century along with quantum theory. These two theories are extremely beautiful and they are well verified by experiments, but they are apparently incompatible. Hints towards understanding these problems can be derived studying Black Holes, some the most puzzling solutions of General Relativity. The main topic of this Master Thesis is the study of Black Holes, in particular the Physics of Hawking Radiation. After a short review of General Relativity, I study in detail the Schwarzschild solution with particular emphasis on the coordinates systems used and the mathematical proof of the classical laws of Black Hole "Thermodynamics". Then I introduce the theory of Quantum Fields in Curved Spacetime, from Bogolubov transformations to the Schwinger-De Witt expansion, useful for the renormalization of the stress energy tensor. After that I introduce a 2D model of gravitational collapse to study the Hawking radiation phenomenon. Particular emphasis is given to the analysis of the quantum states, from correlations to the physical implication of this quantum effect (e.g. Information Paradox, Black Hole Thermodynamics). Then I introduce the renormalized stress energy tensor. Using the Schwinger-De Witt expansion I renormalize this object and I compute it analytically in the various quantum states of interest. Moreover, I study the correlations between these objects. They are interesting because they are linked to the Hawking radiation experimental search in acoustic Black Hole models. In particular I find that there is a characteristic peak in correlations between points inside and outside the Black Hole region, which correpsonds to entangled excitations inside and outside the Black Hole. These peaks hopefully will be measurable soon in supersonic BEC.

Cálculo da força contra eletromotriz em máquinas síncronas com ímãs na superfície do rotor

O presente trabalho trata do cálculo da força contra eletromotriz em carga de uma máquina síncrona com ímãs na superfície do rotor (cuja forma de onda de força contra eletromotriz é não senoidal) sendo esta alimentada por correntes de fase cujas forma de onda são quadradas. Para conduzir esta investigação e calcular a força contra eletromotriz da máquina em estudo, faz-se uma revisão sobre o Método da Permeabilidade Fixa, método este que permite a linearização do ponto de operação da máquina. Dessa forma, as simulações são conduzidas por meio do método dos elementos finitos e do Método da Permeabilidade Fixa, levando-se em conta a forma de onda da corrente de alimentação. Atenção especial é dada ao modo que se analisa o fluxo concatenado e a forma de obtenção da força contra eletromotriz uma vez que as formas de onda do fluxo concatenado sofrem variações abruptas a cada 60º elétricos. Além destes parâmetros, analisa-se também cada uma das parcelas do torque eletromagnético, i.e., torque mútuo, torque de relutância e torque de borda, sendo realizado ao final do trabalho, uma comparação entre a soma da estimativa de cada parâmetro com o valor do torque eletromagnético obtido por meio de uma simulação não linear.

Numerical Solution of the Upper-Convected Maxwell Model for Three-Dimensional Free Surface Flows

This work presents a finite difference technique for simulating three-dimensional free surface flows governed by the Upper-Convected Maxwell (UCM) constitutive equation. A Marker-and-Cell approach is employed to represent the fluid free surface and formulations for calculating the non-Newtonian stress tensor on solid boundaries are developed. The complete free surface stress conditions are employed. The momentum equation is solved by an implicit technique while the UCM constitutive equation is integrated by the explicit Euler method. The resulting equations are solved by the finite difference method on a 3D-staggered grid. By using an exact solution for fully developed flow inside a pipe, validation and convergence results are provided. Numerical results include the simulation of the transient extrudate swell and the comparison between jet buckling of UCM and Newtonian fluids.

Application of the log-conformation tensor to three-dimensional time-dependent free surface flows

The numerical simulation of flows of highly elastic fluids has been the subject of intense research over the past decades with important industrial applications. Therefore, many efforts have been made to improve the convergence capabilities of the numerical methods employed to simulate viscoelastic fluid flows. An important contribution for the solution of the High-Weissenberg Number Problem has been presented by Fattal and Kupferman [J. Non-Newton. Fluid. Mech. 123 (2004) 281-285] who developed the matrix-logarithm of the conformation tensor technique, henceforth called log-conformation tensor. Its advantage is a better approximation of the large growth of the stress tensor that occur in some regions of the flow and it is doubly beneficial in that it ensures physically correct stress fields, allowing converged computations at high Weissenberg number flows. In this work we investigate the application of the log-conformation tensor to three-dimensional unsteady free surface flows. The log-conformation tensor formulation was applied to solve the Upper-Convected Maxwell (UCM) constitutive equation while the momentum equation was solved using a finite difference Marker-and-Cell type method. The resulting developed code is validated by comparing the log-conformation results with the analytic solution for fully developed pipe flows. To illustrate the stability of the log-conformation tensor approach in solving three-dimensional free surface flows, results from the simulation of the extrudate swell and jet buckling phenomena of UCM fluids at high Weissenberg numbers are presented. (C) 2012 Elsevier B.V. All rights reserved.

Fault delineation and stress orientations from the analysis of background, low magnitude seismicity in Southern Apennines (Italy)

The aim of this work was to show that refined analyses of background, low magnitude seismicity allow to delineate the main active faults and to accurately estimate the directions of the regional tectonic stress that characterize the Southern Apennines (Italy), a structurally complex area with high seismic potential. Thanks the presence in the area of an integrated dense and wide dynamic network, was possible to analyzed an high quality microearthquake data-set consisting of 1312 events that occurred from August 2005 to April 2011 by integrating the data recorded at 42 seismic stations of various networks. The refined seismicity location and focal mechanisms well delineate a system of NW-SE striking normal faults along the Apenninic chain and an approximately E-W oriented, strike-slip fault, transversely cutting the belt. The seismicity along the chain does not occur on a single fault but in a volume, delimited by the faults activated during the 1980 Irpinia M 6.9 earthquake, on sub-parallel predominant normal faults. Results show that the recent low magnitude earthquakes belongs to the background seismicity and they are likely generated along the major fault segments activated during the most recent earthquakes, suggesting that they are still active today thirty years after the mainshock occurrences. In this sense, this study gives a new perspective to the application of the high quality records of low magnitude background seismicity for the identification and characterization of active fault systems. The analysis of the stress tensor inversion provides two equivalent models to explain the microearthquake generation along both the NW-SE striking normal faults and the E- W oriented fault with a dominant dextral strike-slip motion, but having different geological interpretations. We suggest that the NW-SE-striking Africa-Eurasia convergence acts in the background of all these structures, playing a primary and unifying role in the seismotectonics of the whole region.

Static analysis of functionally graded cylindrical and conical shells or panels using the generalized unconstrained third order theory coupled with the stress recovery

A 2D Unconstrained Third Order Shear Deformation Theory (UTSDT) is presented for the evaluation of tangential and normal stresses in moderately thick functionally graded conical and cylindrical shells subjected to mechanical loadings. Several types of graded materials are investigated. The functionally graded material consists of ceramic and metallic constituents. A four parameter power law function is used. The UTSDT allows the presence of a finite transverse shear stress at the top and bottom surfaces of the graded shell. In addition, the initial curvature effect included in the formulation leads to the generalization of the present theory (GUTSDT). The Generalized Differential Quadrature (GDQ) method is used to discretize the derivatives in the governing equations, the external boundary conditions and the compatibility conditions. Transverse and normal stresses are also calculated by integrating the three dimensional equations of equilibrium in the thickness direction. In this way, the six components of the stress tensor at a point of the conical or cylindrical shell or panel can be given. The initial curvature effect and the role of the power law functions are shown for a wide range of functionally conical and cylindrical shells under various loading and boundary conditions. Finally, numerical examples of the available literature are worked out.

Representing microstates of static granular matter in a stress phase space

A stress phase space is proposed to compare the static packings of a granular system (microstates) that are compatible to a macrostate described by external stresses. The equivalent stress of each particle of a static packing can be obtained from the mechanical interaction forces, and the associated volume is given by the respective Voronoi cell. Therefore, particles can be located at different stress levels and grouped into categories or configurations, which are defined in base of the geometrical features of the local arrangement (in particular, of the number of forces that keep them force-balanced). They can be represented as points in a stress phase space. The nature of this space is analyzed in detail. The integration limits of the stress variables that avoid or limit tensile states and the capability of each configuration to represent specific stress states establish its main features. Furthermore, if some stress variables are used, instead of the usual components of the Cauchy stress tensor, then some symmetries can be found. Results obtained from molecular dynamics simulations are used to check this nature. Finally, some statistical ensembles are written in terms of the coordinates of this phase space. These require some assumptions that are made in base on continuum mechanics principles.

Yield criterion of porous materials subjected to complex stress states

Finite-element simulations are used to obtain many thousands of yield points for porous materials with arbitrary void-volume fractions with spherical voids arranged in simple cubic, body-centred cubic and face-centred cubic three-dimensional arrays. Multi-axial stress states are explored. We show that the data may be fitted by a yield function which is similar to the Gurson-Tvergaard-Needleman (GTN) form, but which also depends on the determinant of the stress tensor, and all additional parameters may be expressed in terms of standard GTN-like parameters. The dependence of these parameters on the void-volume fraction is found. (c) 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

New constraints on micro-seismicity and stress state in the western part of the North Anatolian Fault Zone : Observations from a dense seismic array

Major funding was provided by the UK Natural Environment Research Council (NERC) under grant NE/I028017/1 and partially supported by Boğaziçi University Research Fund (BAP) under grant 6922. We would like to thank all the project members from the University of Leeds, Boğaziçi University, Kandilli Observatory, Aberdeen University and Sakarya University. I would also like to thank Prof. Ali Pinar and Dr. Kıvanç Kekovalı for their valuable comments. Some of the figures were generated by GMT software (Wessel and Smith, 1995).

New constraints on micro-seismicity and stress state in the western part of the North Anatolian Fault Zone : Observations from a dense seismic array

Major funding was provided by the UK Natural Environment Research Council (NERC) under grant NE/I028017/1 and partially supported by Boğaziçi University Research Fund (BAP) under grant 6922. We would like to thank all the project members from the University of Leeds, Boğaziçi University, Kandilli Observatory, Aberdeen University and Sakarya University. I would also like to thank Prof. Ali Pinar and Dr. Kıvanç Kekovalı for their valuable comments. Some of the figures were generated by GMT software (Wessel and Smith, 1995).

A positional FEM Formulation for geometrical non-linear analysis of shells

This work presents a fully non-linear finite element formulation for shell analysis comprising linear strain variation along the thickness of the shell and geometrically exact description for curved triangular elements. The developed formulation assumes positions and generalized unconstrained vectors as the variables of the problem, not displacements and finite rotations. The full 3D Saint-Venant-Kirchhoff constitutive relation is adopted and, to avoid locking, the rate of thickness variation enhancement is introduced. As a consequence, the second Piola-Kirchhoff stress tensor and the Green strain measure are employed to derive the specific strain energy potential. Curved triangular elements with cubic approximation are adopted using simple notation. Selected numerical simulations illustrate and confirm the objectivity, accuracy, path independence and applicability of the proposed technique.

Acoustic Simulation of a Special Switched Reluctance Drive by Means of Field-Circuit Coupling and Multiphysics Simulation

The approach presented in this paper consists of an energy-based field-circuit coupling in combination with multi-physics simulation of the acoustic radiation of electrical machines. The proposed method is applied to a special switched reluctance motor with asymmetric pole geometry to improve the start-up torque. The pole shape has been optimized, subject to low torque ripple, in a previous study. The proposed approach here is used to analyze the impact of the optimization on the overall acoustic behavior. The field-circuit coupling is based on a temporary lumped-parameter model of the magnetic part incorporated into a circuit simulation based on the modified nodal analysis. The harmonic force excitation is calculated by means of stress tensor computation, and it is transformed to a mechanical mesh by mapping techniques. The structural dynamic problem is solved in the frequency domain using a finite-element modal analysis and superposition. The radiation characteristic is obtained from boundary element acoustic simulation. Simulation results of both rotor types are compared, and measurements of the drive are presented.

High-Frequency Suspended Sediment Flux Measurements in a Small Estuary

In small estuaries, the predictions of scalar dispersion can rarely be predicted accurately because of a lack of fundamental understanding of the turbulence structure. Herein detailed turbulence measurements and suspended sediment concentrations were conducted simultaneously and continuously at high-frequency for 50 hours per investigation in a small subtropical estuary with semi-diurnal tides. The data analyses provided an unique characterisation of the turbulent mixing processes and suspended sediment fluxes. The turbulence was neither homogeneous nor isotropic, and it was not a Gaussian process. The integral time scales for turbulence and suspended sediment concentration were about equal during flood tides, but differed significantly during ebb tides. The field experiences showed that the turbulence measurements must be conducted at high-frequency to characterise the small eddies and the viscous dissipation process, while a continuous sampling was necessary to characterise the time-variations of the instantaneous velocity field, Reynolds stress tensor and suspended sediment flux during the tidal cycles.