Vectorized Matlab Codes for Linear Two-Dimensional Elasticity
Jonas Koko
2007-01-01
Full Text Available A vectorized Matlab implementation for the linear finite element is provided for the two-dimensional linear elasticity with mixed boundary conditions. Vectorization means that there is no loop over triangles. Numerical experiments show that our implementation is more efficient than the standard implementation with a loop over all triangles.
Mihai-Victor PRICOP
2010-09-01
Full Text Available The present paper introduces a numerical approach of static linear elasticity equations for anisotropic materials. The domain and boundary conditions are simple, to enhance an easy implementation of the finite difference scheme. SOR and gradient are used to solve the resulting linear system. The simplicity of the geometry is also useful for MPI parallelization of the code.
Wang, Wenjun; Li, Peng; Jin, Feng
2016-09-01
A novel two-dimensional linear elastic theory of magneto-electro-elastic (MEE) plates, considering both surface and nonlocal effects, is established for the first time based on Hamilton’s principle and the Lee plate theory. The equations derived are more general, suitable for static and dynamic analyses, and can also be reduced to the piezoelectric, piezomagnetic, and elastic cases. As a specific application example, the influences of the surface and nonlocal effects, poling directions, piezoelectric phase materials, volume fraction, damping, and applied magnetic field (i.e., constant applied magnetic field and time-harmonic applied magnetic field) on the magnetoelectric (ME) coupling effects are first investigated based on the established two-dimensional plate theory. The results show that the ME coupling coefficient has an obvious size-dependent characteristic owing to the surface effects, and the surface effects increase the ME coupling effects significantly when the plate thickness decreases to its critical thickness. Below this critical thickness, the size-dependent effect is obvious and must be considered. In addition, the output power density of a magnetic energy nanoharvester is also evaluated using the two-dimensional plate theory obtained, with the results showing that a relatively larger output power density can be achieved at the nanoscale. This study provides a mathematical tool which can be used to analyze the mechanical properties of nanostructures theoretically and numerically, as well as evaluating the size effect qualitatively and quantitatively.
Linear negative magnetoresistance in two-dimensional Lorentz gases
Schluck, J.; Hund, M.; Heckenthaler, T.; Heinzel, T.; Siboni, N. H.; Horbach, J.; Pierz, K.; Schumacher, H. W.; Kazazis, D.; Gennser, U.; Mailly, D.
2018-03-01
Two-dimensional Lorentz gases formed by obstacles in the shape of circles, squares, and retroreflectors are reported to show a pronounced linear negative magnetoresistance at small magnetic fields. For circular obstacles at low number densities, our results agree with the predictions of a model based on classical retroreflection. In extension to the existing theoretical models, we find that the normalized magnetoresistance slope depends on the obstacle shape and increases as the number density of the obstacles is increased. The peaks are furthermore suppressed by in-plane magnetic fields as well as by elevated temperatures. These results suggest that classical retroreflection can form a significant contribution to the magnetoresistivity of two-dimensional Lorentz gases, while contributions from weak localization cannot be excluded, in particular for large obstacle densities.
Linear and nonlinear viscous flow in two-dimensional fluids
Gravina, D.; Ciccotti, G.; Holian, B.L.
1995-01-01
We report on molecular dynamics simulations of shear viscosity η of a dense two-dimensional fluid as a function of the shear rate γ. We find an analytic dependence of η on γ, and do not find any evidence whatsoever of divergence in the Green-Kubo (GK) value that would be caused by the well-known long-time tail for the shear-stress autocorrelation function, as predicted by the mode-coupling theory. In accordance with the linear response theory, the GK value of η agrees remarkably well with nonequilibrium values at small shear rates. (c) 1995 The American Physical Society
Discrete elastic model for two-dimensional melting.
Lansac, Yves; Glaser, Matthew A; Clark, Noel A
2006-04-01
We present a network model for the study of melting and liquid structure in two dimensions, the first in which the presence and energy of topological defects (dislocations and disclinations) and of geometrical defects (elemental voids) can be independently controlled. Interparticle interaction is via harmonic springs and control is achieved by Monte Carlo moves which springs can either be orientationally "flipped" between particles to generate topological defects, or can be "popped" in force-free shape, to generate geometrical defects. With the geometrical defects suppressed the transition to the liquid phase occurs via disclination unbinding, as described by the Kosterlitz-Thouless-Halperin-Nelson-Young model and found in soft potential two-dimensional (2D) systems, such as the dipole-dipole potential [H. H. von Grünberg, Phys. Rev. Lett. 93, 255703 (2004)]. By contrast, with topological defects suppressed, a disordering transition, the Glaser-Clark condensation of geometrical defects [M. A. Glaser and N. A. Clark, Adv. Chem. Phys. 83, 543 (1993); M. A. Glaser, (Springer-Verlag, Berlin, 1990), Vol. 52, p. 141], produces a state that accurately characterizes the local liquid structure and first-order melting observed in hard-potential 2D systems, such as hard disk and the Weeks-Chandler-Andersen (WCA) potentials (M. A. Glaser and co-workers, see above). Thus both the geometrical and topological defect systems play a role in melting. The present work introduces a system in which the relative roles of topological and geometrical defects and their interactions can be explored. We perform Monte Carlo simulations of this model in the isobaric-isothermal ensemble, and present the phase diagram as well as various thermodynamic, statistical, and structural quantities as a function of the relative populations of geometrical and topological defects. The model exhibits a rich phase behavior including hexagonal and square crystals, expanded crystal, dodecagonal quasicrystal
FEAST: a two-dimensional non-linear finite element code for calculating stresses
Tayal, M.
1986-06-01
The computer code FEAST calculates stresses, strains, and displacements. The code is two-dimensional. That is, either plane or axisymmetric calculations can be done. The code models elastic, plastic, creep, and thermal strains and stresses. Cracking can also be simulated. The finite element method is used to solve equations describing the following fundamental laws of mechanics: equilibrium; compatibility; constitutive relations; yield criterion; and flow rule. FEAST combines several unique features that permit large time-steps in even severely non-linear situations. The features include a special formulation for permitting many finite elements to simultaneously cross the boundary from elastic to plastic behaviour; accomodation of large drops in yield-strength due to changes in local temperature and a three-step predictor-corrector method for plastic analyses. These features reduce computing costs. Comparisons against twenty analytical solutions and against experimental measurements show that predictions of FEAST are generally accurate to ± 5%
Wen Jihong; Yu, Dianlong; Wang Gang; Zhao Honggang; Liu Yaozong; Wen Xisen
2007-01-01
The directional propagation characteristics of elastic wave during pass bands in two-dimensional thin plate phononic crystals are analyzed by using the lumped-mass method to yield the phase constant surface. The directions and regions of wave propagation in phononic crystals for certain frequencies during pass bands are predicted with the iso-frequency contour lines of the phase constant surface, which are then validated with the harmonic responses of a finite two-dimensional thin plate phononic crystals with 16x16 unit cells. These results are useful for controlling the wave propagation in the pass bands of phononic crystals
Ravi Kanth, A.S.V.; Aruna, K.
2009-01-01
In this paper, we propose a reliable algorithm to develop exact and approximate solutions for the linear and nonlinear Schroedinger equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.
Farag, Marwa H.; Hoenders, Bernhard J.; Knoester, Jasper; Jansen, Thomas L. C.
2017-01-01
The effect of Gaussian dynamics on the line shapes in linear absorption and two-dimensional correlation spectroscopy is well understood as the second-order cumulant expansion provides exact spectra. Gaussian solvent dynamics can be well analyzed using slope line analysis of two-dimensional
Introduction to linear elasticity
Gould, Phillip L
2013-01-01
Introduction to Linear Elasticity, 3rd Edition, provides an applications-oriented grounding in the tensor-based theory of elasticity for students in mechanical, civil, aeronautical, and biomedical engineering, as well as materials and earth science. The book is distinct from the traditional text aimed at graduate students in solid mechanics by introducing the subject at a level appropriate for advanced undergraduate and beginning graduate students. The author's presentation allows students to apply the basic notions of stress analysis and move on to advanced work in continuum mechanics, plasticity, plate and shell theory, composite materials, viscoelasticity and finite method analysis. This book also: Emphasizes tensor-based approach while still distilling down to explicit notation Provides introduction to theory of plates, theory of shells, wave propagation, viscoelasticity and plasticity accessible to advanced undergraduate students Appropriate for courses following emerging trend of teaching solid mechan...
Jagla, E A
2004-01-01
I study the buckling transition under compression of a two-dimensional, hexagonal, regular elastic honeycomb. Under isotropic compression, the system buckles to a configuration consisting of a unit cell containing four of the original hexagons. This buckling pattern preserves the sixfold rotational symmetry of the original lattice but is chiral, and can be described as a combination of three different elemental distortions in directions rotated by 2π/3 from each other. Non-isotropic compression may induce patterns consisting of a single elemental distortion or a superposition of two of them. The numerical results compare very well with the outcome of a Landau theory of second-order phase transitions
Liu, Wei; Chen, Jiwei; Liu, Yongquan; Su, Xianyue
2012-01-01
In the present Letter, the multiple scattering theory (MST) for calculating the elastic wave band structure of two-dimensional phononic crystals (PCs) is extended to include the interface/surface stress effect at the nanoscale. The interface/surface elasticity theory is employed to describe the nonclassical boundary conditions at the interface/surface and the elastic Mie scattering matrix embodying the interface/surface stress effect is derived. Using this extended MST, the authors investigate the interface/surface stress effect on the elastic wave band structure of two-dimensional PCs, which is demonstrated to be significant when the characteristic size reduces to nanometers. -- Highlights: ► Multiple scattering theory including the interface/surface stress effect. ► Interface/surface elasticity theory to describe the nonclassical boundary conditions. ► Elastic Mie scattering matrix embodying the interface/surface stress effect. ► Interface/surface stress effect would be significant at the nanoscale.
Tracer particles in two-dimensional elastic networks diffuse logarithmically slow
Lizana, Ludvig; Ambjörnsson, Tobias; Lomholt, Michael A
2017-01-01
Several experiments on tagged molecules or particles in living systems suggest that they move anomalously slow—their mean squared displacement (MSD) increase slower than linearly with time. Leading models aimed at understanding these experiments predict that the MSD grows as a power law with a growth exponent that is smaller than unity. However, in some experiments the growth is so slow (fitted exponent ∼0.1–0.2) that they hint towards other mechanisms at play. In this paper, we theoretically demonstrate how in-plane collective modes excited by thermal fluctuations in a two dimensional membrane lead to logarithmic time dependence for the the tracer particle’s MSD. (paper)
Musa Danjuma SHEHU
2008-06-01
Full Text Available This paper lays emphasis on formulation of two dimensional differential games via optimal control theory and consideration of control systems whose dynamics is described by a system of Ordinary Differential equation in the form of linear equation under the influence of two controls U(. and V(.. Base on this, strategies were constructed. Hence we determine the optimal strategy for a control say U(. under a perturbation generated by the second control V(. within a given manifold M.
On oscillation and nonoscillation of two-dimensional linear differential systems
Lomtatidze, A.; Šremr, Jiří
2013-01-01
Roč. 20, č. 3 (2013), s. 573-600 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : two-dimensional system of linear ODE * oscillation * nonoscillation Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-3/gmj-2013-0025/gmj-2013-0025.xml?format=INT
On oscillation and nonoscillation of two-dimensional linear differential systems
Lomtatidze, A.; Šremr, Jiří
2013-01-01
Roč. 20, č. 3 (2013), s. 573-600 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : two-dimensional system of linear ODE * oscillation * nonoscillation Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-3/gmj-2013-0025/gmj-2013-0025. xml ?format=INT
Uniqueness theorems in linear elasticity
Knops, Robin John
1971-01-01
The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniquenes...
Driving performance of a two-dimensional homopolar linear DC motor
Wang, Y.; Yamaguchi, M.; Kano, Y. [Tokyo University of Agriculture and Technology, Tokyo (Japan)
1998-05-01
This paper presents a novel two-dimensional homopolar linear de motor (LDM) which can realize two-dimensional (2-D) motion. For position control purposes, two kinds of position detecting methods are proposed. The position in one position is detected by means of a capacitive sensor which makes the output of the sensor partially immune to the variation of the gap between electrodes. The position in the other direction is achieved by exploiting the position dependent property of the driving coil inductance, instead of using an independent sensor. The position control is implemented on the motor and 2-D tracking performance is analyzed. Experiments show that the motor demonstrates satisfactory driving performance, 2-D tracking error being within 5.5% when the angular frequency of reference signal is 3.14 rad./s. 7 refs., 17 figs., 2 tabs.
Transfer of optical signals around bends in two-dimensional linear photonic networks
Nikolopoulos, G M
2015-01-01
The ability to navigate light signals in two-dimensional networks of waveguide arrays is a prerequisite for the development of all-optical integrated circuits for information processing and networking. In this article, we present a theoretical analysis of bending losses in linear photonic lattices with engineered couplings, and discuss possible ways for their minimization. In contrast to previous work in the field, the lattices under consideration operate in the linear regime, in the sense that discrete solitons cannot exist. The present results suggest that the functionality of linear waveguide networks can be extended to operations that go beyond the recently demonstrated point-to-point transfer of signals, such as blocking, routing, logic functions, etc. (paper)
Improved implementation algorithms of the two-dimensional nonseparable linear canonical transform.
Ding, Jian-Jiun; Pei, Soo-Chang; Liu, Chun-Lin
2012-08-01
The two-dimensional nonseparable linear canonical transform (2D NSLCT), which is a generalization of the fractional Fourier transform and the linear canonical transform, is useful for analyzing optical systems. However, since the 2D NSLCT has 16 parameters and is very complicated, it is a great challenge to implement it in an efficient way. In this paper, we improved the previous work and propose an efficient way to implement the 2D NSLCT. The proposed algorithm can minimize the numerical error arising from interpolation operations and requires fewer chirp multiplications. The simulation results show that, compared with the existing algorithm, the proposed algorithms can implement the 2D NSLCT more accurately and the required computation time is also less.
Ma, Q.; Boulet, C.; Tipping, R. H.
2014-01-01
The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ^S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.
Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices
Luz, H. L. F. da; Gammal, A.; Abdullaev, F. Kh.; Salerno, M.; Tomio, Lauro
2010-01-01
The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.
Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices
da Luz, H. L. F.; Abdullaev, F. Kh.; Gammal, A.; Salerno, M.; Tomio, Lauro
2010-10-01
The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.
Two-Dimensional Linear Inversion of GPR Data with a Shifting Zoom along the Observation Line
Raffaele Persico
2017-09-01
Full Text Available Linear inverse scattering problems can be solved by regularized inversion of a matrix, whose calculation and inversion may require significant computing resources, in particular, a significant amount of RAM memory. This effort is dependent on the extent of the investigation domain, which drives a large amount of data to be gathered and a large number of unknowns to be looked for, when this domain becomes electrically large. This leads, in turn, to the problem of inversion of excessively large matrices. Here, we consider the problem of a ground-penetrating radar (GPR survey in two-dimensional (2D geometry, with antennas at an electrically short distance from the soil. In particular, we present a strategy to afford inversion of large investigation domains, based on a shifting zoom procedure. The proposed strategy was successfully validated using experimental radar data.
Quantum pump effect induced by a linearly polarized microwave in a two-dimensional electron gas.
Song, Juntao; Liu, Haiwen; Jiang, Hua
2012-05-30
A quantum pump effect is predicted in an ideal homogeneous two-dimensional electron gas (2DEG) that is normally irradiated by linearly polarized microwaves (MW). Without considering effects from spin-orbital coupling or the magnetic field, it is found that a polarized MW can continuously pump electrons from the longitudinal to the transverse direction, or from the transverse to the longitudinal direction, in the central irradiated region. The large pump current is obtained for both the low frequency limit and the high frequency case. Its magnitude depends on sample properties such as the size of the radiated region, the power and frequency of the MW, etc. Through the calculated results, the pump current should be attributed to the dominant photon-assisted tunneling processes as well as the asymmetry of the electron density of states with respect to the Fermi energy.
Two-dimensional linear and nonlinear Talbot effect from rogue waves.
Zhang, Yiqi; Belić, Milivoj R; Petrović, Milan S; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Lu, Keqing; Zhang, Yanpeng
2015-03-01
We introduce two-dimensional (2D) linear and nonlinear Talbot effects. They are produced by propagating periodic 2D diffraction patterns and can be visualized as 3D stacks of Talbot carpets. The nonlinear Talbot effect originates from 2D rogue waves and forms in a bulk 3D nonlinear medium. The recurrences of an input rogue wave are observed at the Talbot length and at the half-Talbot length, with a π phase shift; no other recurrences are observed. Differing from the nonlinear Talbot effect, the linear effect displays the usual fractional Talbot images as well. We also find that the smaller the period of incident rogue waves, the shorter the Talbot length. Increasing the beam intensity increases the Talbot length, but above a threshold this leads to a catastrophic self-focusing phenomenon which destroys the effect. We also find that the Talbot recurrence can be viewed as a self-Fourier transform of the initial periodic beam that is automatically performed during propagation. In particular, linear Talbot effect can be viewed as a fractional self-Fourier transform, whereas the nonlinear Talbot effect can be viewed as the regular self-Fourier transform. Numerical simulations demonstrate that the rogue-wave initial condition is sufficient but not necessary for the observation of the effect. It may also be observed from other periodic inputs, provided they are set on a finite background. The 2D effect may find utility in the production of 3D photonic crystals.
Akaishi, A; Shudo, A
2009-12-01
We investigate the stickiness of the two-dimensional piecewise linear map with a family of marginal unstable periodic orbits (FMUPOs), and show that a series of unstable periodic orbits accumulating to FMUPOs plays a significant role to give rise to the power law correlation of trajectories. We can explicitly specify the sticky zone in which unstable periodic orbits whose stability increases algebraically exist, and find that there exists a hierarchy in accumulating periodic orbits. In particular, the periodic orbits with linearly increasing stability play the role of fundamental cycles as in the hyperbolic systems, which allows us to apply the method of cycle expansion. We also study the recurrence time distribution, especially discussing the position and size of the recurrence region. Following the definition adopted in one-dimensional maps, we show that the recurrence time distribution has an exponential part in the short time regime and an asymptotic power law part. The analysis on the crossover time T(c)(*) between these two regimes implies T(c)(*) approximately -log[micro(R)] where micro(R) denotes the area of the recurrence region.
Rudianto, Indra; Sudarmaji
2018-04-01
We present an implementation of the spectral-element method for simulation of two-dimensional elastic wave propagation in fully heterogeneous media. We have incorporated most of realistic geological features in the model, including surface topography, curved layer interfaces, and 2-D wave-speed heterogeneity. To accommodate such complexity, we use an unstructured quadrilateral meshing technique. Simulation was performed on a GPU cluster, which consists of 24 core processors Intel Xeon CPU and 4 NVIDIA Quadro graphics cards using CUDA and MPI implementation. We speed up the computation by a factor of about 5 compared to MPI only, and by a factor of about 40 compared to Serial implementation.
Zafar, I.; Edirisinghe, E. A.; Acar, S.; Bez, H. E.
2007-02-01
Automatic vehicle Make and Model Recognition (MMR) systems provide useful performance enhancements to vehicle recognitions systems that are solely based on Automatic License Plate Recognition (ALPR) systems. Several car MMR systems have been proposed in literature. However these approaches are based on feature detection algorithms that can perform sub-optimally under adverse lighting and/or occlusion conditions. In this paper we propose a real time, appearance based, car MMR approach using Two Dimensional Linear Discriminant Analysis that is capable of addressing this limitation. We provide experimental results to analyse the proposed algorithm's robustness under varying illumination and occlusions conditions. We have shown that the best performance with the proposed 2D-LDA based car MMR approach is obtained when the eigenvectors of lower significance are ignored. For the given database of 200 car images of 25 different make-model classifications, a best accuracy of 91% was obtained with the 2D-LDA approach. We use a direct Principle Component Analysis (PCA) based approach as a benchmark to compare and contrast the performance of the proposed 2D-LDA approach to car MMR. We conclude that in general the 2D-LDA based algorithm supersedes the performance of the PCA based approach.
Large angle and high linearity two-dimensional laser scanner based on voice coil actuators
Wu, Xin; Chen, Sihai; Chen, Wei; Yang, Minghui; Fu, Wen
2011-10-01
A large angle and high linearity two-dimensional laser scanner with an in-house ingenious deflection angle detecting system is developed based on voice coil actuators direct driving mechanism. The specially designed voice coil actuators make the steering mirror moving at a sufficiently large angle. Frequency sweep method based on virtual instruments is employed to achieve the natural frequency of the laser scanner. The response shows that the performance of the laser scanner is limited by the mechanical resonances. The closed-loop controller based on mathematical model is used to reduce the oscillation of the laser scanner at resonance frequency. To design a qualified controller, the model of the laser scanner is set up. The transfer function of the model is identified with MATLAB according to the tested data. After introducing of the controller, the nonlinearity decreases from 13.75% to 2.67% at 50 Hz. The laser scanner also has other advantages such as large deflection mirror, small mechanical structure, and high scanning speed.
Elastic-plastic code in the static regime for two-dimensional structures
Giuliani, S.
1976-07-01
The finite-element computer code STEP-2D, which was conceived as a numerical tool for basic research in fracture mechanics presently under way in the Materials Division of JRC Ispra is described. The code employs 8-node isoparametric elements for calculating elastic-plastic stress and strain distributions in 2-D geometries. The von Mises yield criterion is used. Material strain hardening is described by means of either the isotropic or the so-called 'overlay' model. An incremental solution is employed in the plastic range. The program has been written in Fortran IV and compiled on an IBM 370-165
Voinovich, Peter; Merlen, Alain
2005-12-01
The effect of parametric wave phase conjugation (WPC) in application to ultrasound or acoustic waves in magnetostrictive solids has been addressed numerically by Ben Khelil et al. [J. Acoust. Soc. Am. 109, 75-83 (2001)] using 1-D unsteady formulation. Here the numerical method presented by Voinovich et al. [Shock waves 13(3), 221-230 (2003)] extends the analysis to the 2-D effects. The employed model describes universally elastic solids and liquids. A source term similar to Ben Khelil et al.'s accounts for the coupling between deformation and magnetostriction due to external periodic magnetic field. The compatibility between the isotropic constitutive law of the medium and the model of magnetostriction has been considered. Supplementary to the 1-D simulations, the present model involves longitudinal/transversal mode conversion at the sample boundaries and separate magnetic field coupling with dilatation and shear stress. The influence of those factors in a 2-D geometry on the potential output of a magneto-elastic wave phase conjugator is analyzed in this paper. The process under study includes propagation of a wave burst of a given frequency from a point source in a liquid into the active solid, amplification of the waves due to parametric resonance, and formation of time-reversed waves, their radiation into liquid, and focusing. The considered subject is particularly important for ultrasonic applications in acoustic imaging, nondestructive testing, or medical diagnostics and therapy.
Vâgberg, Daniel; Olsson, Peter; Teitel, S.
2017-01-01
We carry out constant volume simulations of steady-state, shear-driven flow in a simple model of athermal, bidisperse, soft-core, frictionless disks in two dimensions, using a dissipation law that gives rise to Bagnoldian rheology. Focusing on the small strain rate limit, we map out the rheological behavior as a function of particle packing fraction ϕ and a parameter Q that measures the elasticity of binary particle collisions. We find a Q*(ϕ ) that marks the clear crossover from a region characteristic of strongly inelastic collisions, Q Q* , and give evidence that Q*(ϕ ) diverges as ϕ →ϕJ , the shear-driven jamming transition. We thus conclude that the jamming transition at any value of Q behaves the same as the strongly inelastic case, provided one is sufficiently close to ϕJ. We further characterize the differing nature of collisions in the strongly inelastic vs weakly inelastic regions, and recast our results into the constitutive equation form commonly used in discussions of hard granular matter.
Krapchev, V.
1976-01-01
In the framework of the two-dimensional scalar quantum theory of the bag model of Chodos et al a definition of the physical field and a general scheme for constructing a physical state are given. Some of the difficulties associated with such an approach are exposed. Expressions for the physical current and the elastic form factor are given. The calculation of the latter is restricted at first to the approximation in which the mapping from a bag of changing shape to a fixed domain is realized only by a term which is a diagonal, bilinear function of the creation and annihilation operators. This is done for the case of a one-mode and an infinite-mode bag theory. By computing the form factor in an exact one-mode bag model it is shown that the logarithmic falloff of the asymptotic term is the same as the one in the approximation. On the basis of this a form for the asymptotic behavior of the form factor is suggested which may be correct for the general two-dimensional scalar bag theory
Non-linear elastic deformations
Ogden, R W
1997-01-01
Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.
Kirillov, I.R.; Obukhov, D.M.
2005-01-01
One introduces a completely two-dimensional mathematical model to calculate characteristics of induction magnetohydrodynamic (MHD) machines with a cylindrical channel. On the basis of the numerical analysis one obtained a pattern of liquid metal flow in a electromagnetic pump at presence of the MHD-instability characterized by initiation of large-scale vortices propagating longitudinally and azimuthally. Comparison of the basic calculated characteristics of pump with the experiment shows their adequate qualitative and satisfactory quantitative coincidence [ru
Integrodifferential relations in linear elasticity
Kostin, Georgy V
2012-01-01
This work treats the elasticity of deformed bodies, including the resulting interior stresses and displacements.It also takes into account that some of constitutive relations can be considered in a weak form. To discuss this problem properly, the method of integrodifferential relations is used, and an advanced numerical technique for stress-strain analysis is presented and evaluated using various discretization techniques. The methods presented in this book are of importance for almost all elasticity problems in materials science and mechanical engineering.
Yan Zhizhong; Zhang Chuanzeng; Wang Yuesheng
2011-01-01
The band structures of in-plane elastic waves propagating in two-dimensional phononic crystals with one-dimensional random disorder and aperiodicity are analyzed in this paper. The localization of wave propagation is discussed by introducing the concept of the localization factor, which is calculated by the plane-wave-based transfer-matrix method. By treating the random disorder and aperiodicity as the deviation from the periodicity in a special way, three kinds of aperiodic phononic crystals that have normally distributed random disorder, Thue-Morse and Rudin-Shapiro sequence in one direction and translational symmetry in the other direction are considered and the band structures are characterized using localization factors. Besides, as a special case, we analyze the band gap properties of a periodic planar layered composite containing a periodic array of square inclusions. The transmission coefficients based on eigen-mode matching theory are also calculated and the results show the same behaviors as the localization factor does. In the case of random disorders, the localization degree of the normally distributed random disorder is larger than that of the uniformly distributed random disorder although the eigenstates are both localized no matter what types of random disorders, whereas, for the case of Thue-Morse and Rudin-Shapiro structures, the band structures of Thue-Morse sequence exhibit similarities with the quasi-periodic (Fibonacci) sequence not present in the results of the Rudin-Shapiro sequence.
Numerical solution of two-dimensional non-linear partial differential ...
linear partial differential equations using a hybrid method. The solution technique involves discritizing the non-linear system of partial differential equations (PDEs) to obtain a corresponding nonlinear system of algebraic difference equations to be ...
Oscillation of two-dimensional linear second-order differential systems
Kwong, M.K.; Kaper, H.G.
1985-01-01
This article is concerned with the oscillatory behavior at infinity of the solution y: [a, ∞) → R 2 of a system of two second-order differential equations, y''(t) + Q(t) y(t) = 0, t epsilon[a, ∞); Q is a continuous matrix-valued function on [a, ∞) whose values are real symmetric matrices of order 2. It is shown that the solution is oscillatory at infinity if the largest eigenvalue of the matrix integral/sub a//sup t/ Q(s) ds tends to infinity as t → ∞. This proves a conjecture of D. Hinton and R.T. Lewis for the two-dimensional case. Furthermore, it is shown that considerably weaker forms of the condition still suffice for oscillatory behavior at infinity. 7 references
Bezotosnyi, V V; Kumykov, Kh Kh
1998-01-01
A two-dimensional transient thermal model of an injection laser is developed. This model makes it possible to analyse the temperature profiles in pulsed and cw stripe lasers with an arbitrary width of the stripe contact, and also in linear laser-diode arrays. This can be done for any durations and repetition rates of the pump pulses. The model can also be applied to two-dimensional laser-diode arrays operating quasicontinuously. An analysis is reported of the influence of various structural parameters of a diode array on the thermal regime of a single laser. The temperature distributions along the cavity axis are investigated for different variants of mounting a crystal on a heat sink. It is found that the temperature drop along the cavity length in cw and quasi-cw laser diodes may exceed 20%. (lasers)
On the Dynamics of Two-Dimensional Capillary-Gravity Solitary Waves with a Linear Shear Current
Dali Guo
2014-01-01
Full Text Available The numerical study of the dynamics of two-dimensional capillary-gravity solitary waves on a linear shear current is presented in this paper. The numerical method is based on the time-dependent conformal mapping. The stability of different kinds of solitary waves is considered. Both depression wave and large amplitude elevation wave are found to be stable, while small amplitude elevation wave is unstable to the small perturbation, and it finally evolves to be a depression wave with tails, which is similar to the irrotational capillary-gravity waves.
Two-dimensional Fast ESPRIT Algorithm for Linear Array SAR Imaging
Zhao Yi-chao
2015-10-01
Full Text Available The linear array Synthetic Aperture Radar (SAR system is a popular research tool, because it can realize three-dimensional imaging. However, owning to limitations of the aircraft platform and actual conditions, resolution improvement is difficult in cross-track and along-track directions. In this study, a twodimensional fast Estimation of Signal Parameters by Rotational Invariance Technique (ESPRIT algorithm for linear array SAR imaging is proposed to overcome these limitations. This approach combines the Gerschgorin disks method and the ESPRIT algorithm to estimate the positions of scatterers in cross and along-rack directions. Moreover, the reflectivity of scatterers is obtained by a modified pairing method based on “region growing”, replacing the least-squares method. The simulation results demonstrate the applicability of the algorithm with high resolution, quick calculation, and good real-time response.
Electron-electron scattering in linear transport in two-dimensional systems
Hu, Ben Yu-Kuang; Flensberg, Karsten
1996-01-01
We describe a method for numerically incorporating electron-electron scattering in quantum wells for small deviations of the distribution function from equilibrium, within the framework of the Boltzmann equation. For a given temperature T and density n, a symmetric matrix needs to be evaluated only...... once, and henceforth it can be used to describe electron-electron scattering in any Boltzmann equation linear-response calculation for that particular T and n. Using this method, we calculate the distribution function and mobility for electrons in a quantum well, including full finite...
Spatiotemporal chaos in mixed linear-nonlinear two-dimensional coupled logistic map lattice
Zhang, Ying-Qian; He, Yi; Wang, Xing-Yuan
2018-01-01
We investigate a new spatiotemporal dynamics with mixing degrees of nonlinear chaotic maps for spatial coupling connections based on 2DCML. Here, the coupling methods are including with linear neighborhood coupling and the nonlinear chaotic map coupling of lattices, and the former 2DCML system is only a special case in the proposed system. In this paper the criteria such Kolmogorov-Sinai entropy density and universality, bifurcation diagrams, space-amplitude and snapshot pattern diagrams are provided in order to investigate the chaotic behaviors of the proposed system. Furthermore, we also investigate the parameter ranges of the proposed system which holds those features in comparisons with those of the 2DCML system and the MLNCML system. Theoretical analysis and computer simulation indicate that the proposed system contains features such as the higher percentage of lattices in chaotic behaviors for most of parameters, less periodic windows in bifurcation diagrams and the larger range of parameters for chaotic behaviors, which is more suitable for cryptography.
Anon.
1991-01-01
This chapter addresses the extension of previous work in one-dimensional (linear) error theory to two-dimensional error analysis. The topics of the chapter include the definition of two-dimensional error, the probability ellipse, the probability circle, elliptical (circular) error evaluation, the application to position accuracy, and the use of control systems (points) in measurements
Chacon-Madrid, Heber J; Murphy, Benjamin N; Pandis, Spyros N; Donahue, Neil M
2012-10-16
We use a two-dimensional volatility basis set (2D-VBS) box model to simulate secondary organic aerosol (SOA) mass yields of linear oxygenated molecules: n-tridecanal, 2- and 7-tridecanone, 2- and 7-tridecanol, and n-pentadecane. A hybrid model with explicit, a priori treatment of the first-generation products for each precursor molecule, followed by a generic 2D-VBS mechanism for later-generation chemistry, results in excellent model-measurement agreement. This strongly confirms that the 2D-VBS mechanism is a predictive tool for SOA modeling but also suggests that certain important first-generation products for major primary SOA precursors should be treated explicitly for optimal SOA predictions.
Two-dimensional linear variation displacement discontinuity method for three-layered elastic media
Shou, KJ
1999-09-01
Full Text Available of the double element can be written in the form Ua?s ? 1=2 Das ? Fas Ua?n ? 1=2 Dan ? Fan Ub?s ??1=2 Dbs ? Fbs Ub?s ??1=2 Dbs ? Fbs ?B:3? Substituting Eqs. (B.2) and (B.3) into Eq. (B.1), it can be shown that the unknown displacement disconti- nuities are given... and Mining Sciences 36 (1999) 719?729 2 66 4 Das Dan Dbs Dbn 3 77 5 ? 1 Ka ? Kb 2 66 4 Kb 010 0 Kb 01 Ka 0 ?10 0 Ka 0 ?1 3 77 5 2 66 4 2?Fbs ? Fas ? 2?Fbn ? Fan? Ebs ? Eas Ebn ? Ean 3 77 5 ?B:4? Coupling the above scheme to a general two-dimen- sional...
Discriminative Elastic-Net Regularized Linear Regression.
Zhang, Zheng; Lai, Zhihui; Xu, Yong; Shao, Ling; Wu, Jian; Xie, Guo-Sen
2017-03-01
In this paper, we aim at learning compact and discriminative linear regression models. Linear regression has been widely used in different problems. However, most of the existing linear regression methods exploit the conventional zero-one matrix as the regression targets, which greatly narrows the flexibility of the regression model. Another major limitation of these methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability. To this end, we present an elastic-net regularized linear regression (ENLR) framework, and develop two robust linear regression models which possess the following special characteristics. First, our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix. Second, a robust elastic-net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix. Third, the resulting optimization problem of ENLR has a closed-form solution in each iteration, which can be solved efficiently. Finally, rather than directly exploiting the projection matrix for recognition, our methods employ the transformed features as the new discriminate representations to make final image classification. Compared with the traditional linear regression model and some of its variants, our method is much more accurate in image classification. Extensive experiments conducted on publicly available data sets well demonstrate that the proposed framework can outperform the state-of-the-art methods. The MATLAB codes of our methods can be available at http://www.yongxu.org/lunwen.html.
Non-Linear Non Stationary Analysis of Two-Dimensional Time-Series Applied to GRACE Data, Phase II
National Aeronautics and Space Administration — The proposed innovative two-dimensional (2D) empirical mode decomposition (EMD) analysis was applied to NASA's Gravity Recovery and Climate Experiment (GRACE)...
Sengupta, Tapan K.; Sharma, Nidhi; Sengupta, Aditi
2018-05-01
An enstrophy-based non-linear instability analysis of the Navier-Stokes equation for two-dimensional (2D) flows is presented here, using the Taylor-Green vortex (TGV) problem as an example. This problem admits a time-dependent analytical solution as the base flow, whose instability is traced here. The numerical study of the evolution of the Taylor-Green vortices shows that the flow becomes turbulent, but an explanation for this transition has not been advanced so far. The deviation of the numerical solution from the analytical solution is studied here using a high accuracy compact scheme on a non-uniform grid (NUC6), with the fourth-order Runge-Kutta method. The stream function-vorticity (ψ, ω) formulation of the governing equations is solved here in a periodic square domain with four vortices at t = 0. Simulations performed at different Reynolds numbers reveal that numerical errors in computations induce a breakdown of symmetry and simultaneous fragmentation of vortices. It is shown that the actual physical instability is triggered by the growth of disturbances and is explained by the evolution of disturbance mechanical energy and enstrophy. The disturbance evolution equations have been traced by looking at (a) disturbance mechanical energy of the Navier-Stokes equation, as described in the work of Sengupta et al., "Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003), and (b) the creation of rotationality via the enstrophy transport equation in the work of Sengupta et al., "Diffusion in inhomogeneous flows: Unique equilibrium state in an internal flow," Comput. Fluids 88, 440-451 (2013).
Delrue, Steven; Aleshin, Vladislav; Truyaert, Kevin; Bou Matar, Olivier; Van Den Abeele, Koen
2018-01-01
Our study aims at the creation of a numerical toolbox that describes wave propagation in samples containing internal contacts (e.g. cracks, delaminations, debondings, imperfect intergranular joints) of known geometry with postulated contact interaction laws including friction. The code consists of two entities: the contact model and the solid mechanics module. Part I of the paper concerns an in-depth description of a constitutive model for realistic contacts or cracks that takes into account the roughness of the contact faces and the associated effects of friction and hysteresis. In the crack model, three different contact states can be recognized: contact loss, total sliding and partial slip. Normal (clapping) interactions between the crack faces are implemented using a quadratic stress-displacement relation, whereas tangential (friction) interactions were introduced using the Coulomb friction law for the total sliding case, and the Method of Memory Diagrams (MMD) in case of partial slip. In the present part of the paper, we integrate the developed crack model into finite element software in order to simulate elastic wave propagation in a solid material containing internal contacts or cracks. We therefore implemented the comprehensive crack model in MATLAB® and introduced it in the Structural Mechanics Module of COMSOL Multiphysics®. The potential of the approach for ultrasound based inspection of solids with cracks showing acoustic nonlinearity is demonstrated by means of an example of shear wave propagation in an aluminum sample containing a single crack with rough surfaces and friction. Copyright © 2017 Elsevier B.V. All rights reserved.
Maire, Pierre-Henri; Abgrall, Rémi; Breil, Jérôme; Loubère, Raphaël; Rebourcet, Bernard
2013-02-01
In this paper, we describe a cell-centered Lagrangian scheme devoted to the numerical simulation of solid dynamics on two-dimensional unstructured grids in planar geometry. This numerical method, utilizes the classical elastic-perfectly plastic material model initially proposed by Wilkins [M.L. Wilkins, Calculation of elastic-plastic flow, Meth. Comput. Phys. (1964)]. In this model, the Cauchy stress tensor is decomposed into the sum of its deviatoric part and the thermodynamic pressure which is defined by means of an equation of state. Regarding the deviatoric stress, its time evolution is governed by a classical constitutive law for isotropic material. The plasticity model employs the von Mises yield criterion and is implemented by means of the radial return algorithm. The numerical scheme relies on a finite volume cell-centered method wherein numerical fluxes are expressed in terms of sub-cell force. The generic form of the sub-cell force is obtained by requiring the scheme to satisfy a semi-discrete dissipation inequality. Sub-cell force and nodal velocity to move the grid are computed consistently with cell volume variation by means of a node-centered solver, which results from total energy conservation. The nominally second-order extension is achieved by developing a two-dimensional extension in the Lagrangian framework of the Generalized Riemann Problem methodology, introduced by Ben-Artzi and Falcovitz [M. Ben-Artzi, J. Falcovitz, Generalized Riemann Problems in Computational Fluid Dynamics, Cambridge Monogr. Appl. Comput. Math. (2003)]. Finally, the robustness and the accuracy of the numerical scheme are assessed through the computation of several test cases.
Raisee, M.; Hejazi, S.H.
2007-01-01
This paper presents comparisons between heat transfer predictions and measurements for developing turbulent flow through straight rectangular channels with sudden contractions at the mid-channel section. The present numerical results were obtained using a two-dimensional finite-volume code which solves the governing equations in a vertical plane located at the lateral mid-point of the channel. The pressure field is obtained with the well-known SIMPLE algorithm. The hybrid scheme was employed for the discretization of convection in all transport equations. For modeling of the turbulence, a zonal low-Reynolds number k-ε model and the linear and non-linear low-Reynolds number k-ε models with the 'Yap' and 'NYP' length-scale correction terms have been employed. The main objective of present study is to examine the ability of the above turbulence models in the prediction of convective heat transfer in channels with sudden contraction at a mid-channel section. The results of this study show that a sudden contraction creates a relatively small recirculation bubble immediately downstream of the channel contraction. This separation bubble influences the distribution of local heat transfer coefficient and increases the heat transfer levels by a factor of three. Computational results indicate that all the turbulence models employed produce similar flow fields. The zonal k-ε model produces the wrong Nusselt number distribution by underpredicting heat transfer levels in the recirculation bubble and overpredicting them in the developing region. The linear low-Re k-ε model, on the other hand, returns the correct Nusselt number distribution in the recirculation region, although it somewhat overpredicts heat transfer levels in the developing region downstream of the separation bubble. The replacement of the 'Yap' term with the 'NYP' term in the linear low-Re k-ε model results in a more accurate local Nusselt number distribution. Moreover, the application of the non-linear k
Wedellsborg, B.W.
1981-01-01
This paper presents a two-dimensional nonlinear analysis method applicable to floor, wall, and containment dome liner analysis for continuous line anchor liner systems. The procedure initially involve obtaining the strain input data for each load case at each liner panel from available load data. This load input is then mapped for the entire liner, and an optimum pattern of inward deflected liner panels is then selected for each particular load case in order to obtain maximum liner system response. In-plane axial and shear sresses are calculated at critical points, and safety factors based on ASME Section III Division 2 Criteria against postulated and actually observed failure modes are evaluated. Modifications on the ASME criteria on safety factors based on biaxial strain capacity are proposed. The method has been used for analyzing an actual containment liner system with welded continuous orthogonal line anchors. Complete two-dimensional liner displacement and stress response were obtained and mapped for each load case. The response indicated the existence of several potential high stress regions in the dome and wall liners, and new types of response modes were predicted. (orig./HP)
Isogeometric BDDC deluxe preconditioners for linear elasticity
Pavarino, L. F.
2018-03-14
Balancing Domain Decomposition by Constraints (BDDC) preconditioners have been shown to provide rapidly convergent preconditioned conjugate gradient methods for solving many of the very ill-conditioned systems of algebraic equations which often arise in finite element approximations of a large variety of problems in continuum mechanics. These algorithms have also been developed successfully for problems arising in isogeometric analysis. In particular, the BDDC deluxe version has proven very successful for problems approximated by Non-Uniform Rational B-Splines (NURBS), even those of high order and regularity. One main purpose of this paper is to extend the theory, previously fully developed only for scalar elliptic problems in the plane, to problems of linear elasticity in three dimensions. Numerical experiments supporting the theory are also reported. Some of these experiments highlight the fact that the development of the theory can help to decrease substantially the dimension of the primal space of the BDDC algorithm, which provides the necessary global component of these preconditioners, while maintaining scalability and good convergence rates.
Isogeometric BDDC deluxe preconditioners for linear elasticity
Pavarino, L. F.; Scacchi, S.; Widlund, O. B.; Zampini, Stefano
2018-01-01
Balancing Domain Decomposition by Constraints (BDDC) preconditioners have been shown to provide rapidly convergent preconditioned conjugate gradient methods for solving many of the very ill-conditioned systems of algebraic equations which often arise in finite element approximations of a large variety of problems in continuum mechanics. These algorithms have also been developed successfully for problems arising in isogeometric analysis. In particular, the BDDC deluxe version has proven very successful for problems approximated by Non-Uniform Rational B-Splines (NURBS), even those of high order and regularity. One main purpose of this paper is to extend the theory, previously fully developed only for scalar elliptic problems in the plane, to problems of linear elasticity in three dimensions. Numerical experiments supporting the theory are also reported. Some of these experiments highlight the fact that the development of the theory can help to decrease substantially the dimension of the primal space of the BDDC algorithm, which provides the necessary global component of these preconditioners, while maintaining scalability and good convergence rates.
Græsbøll, Rune; Janssen, Hans-Gerd; Christensen, Jan H.
2017-01-01
The linear solvent strength model was used to predict coverage in online comprehensive two-dimensional reversed-phase liquid chromatography. The prediction model uses a parallelogram to describe the separation space covered with peaks in a system with limited orthogonality. The corners of the par......The linear solvent strength model was used to predict coverage in online comprehensive two-dimensional reversed-phase liquid chromatography. The prediction model uses a parallelogram to describe the separation space covered with peaks in a system with limited orthogonality. The corners...... of the parallelogram are assumed to behave like chromatographic peaks and the position of these pseudo-compounds was predicted. A mix of 25 polycyclic aromatic compounds were used as a test. The precision of the prediction, span 0-25, was tested by varying input parameters, and was found to be acceptable with root...... factors were low, or when gradient conditions affected parameters not included in the model, e.g. second dimension gradient time affects the second dimension equilibration time. The concept shows promise as a tool for gradient optimization in online comprehensive two-dimensional liquid chromatography...
Non-linear theory of elasticity
Lurie, AI
2012-01-01
This book examines in detail the Theory of Elasticity which is a branch of the mechanics of a deformable solid. Special emphasis is placed on the investigation of the process of deformation within the framework of the generally accepted model of a medium which, in this case, is an elastic body. A comprehensive list of Appendices is included providing a wealth of references for more in depth coverage. The work will provide both a stimulus for future research in this field as well as useful reference material for many years to come.
On the structure on non-local conservation laws in the two-dimensional non-linear sigma-model
Zamolodchikov, Al.B.
1978-01-01
The non-local conserved charges are supposed to satisfy a special multiplicative law in the space of asymptotic states of the non-linear sigma-model. This supposition leads to factorization equations for two-particle scattering matrix elements and determines to some extent the action of these charges in the asymptotic space. Their conservation turns out to be consistent with the factorized S-matrix of the non-linear sigma-model. It is shown also that the factorized sine-Gordon S-matrix is consistent with a similar family of conservation laws
Siuly; Yin, Xiaoxia; Hadjiloucas, Sillas; Zhang, Yanchun
2016-04-01
This work provides a performance comparison of four different machine learning classifiers: multinomial logistic regression with ridge estimators (MLR) classifier, k-nearest neighbours (KNN), support vector machine (SVM) and naïve Bayes (NB) as applied to terahertz (THz) transient time domain sequences associated with pixelated images of different powder samples. The six substances considered, although have similar optical properties, their complex insertion loss at the THz part of the spectrum is significantly different because of differences in both their frequency dependent THz extinction coefficient as well as differences in their refractive index and scattering properties. As scattering can be unquantifiable in many spectroscopic experiments, classification solely on differences in complex insertion loss can be inconclusive. The problem is addressed using two-dimensional (2-D) cross-correlations between background and sample interferograms, these ensure good noise suppression of the datasets and provide a range of statistical features that are subsequently used as inputs to the above classifiers. A cross-validation procedure is adopted to assess the performance of the classifiers. Firstly the measurements related to samples that had thicknesses of 2mm were classified, then samples at thicknesses of 4mm, and after that 3mm were classified and the success rate and consistency of each classifier was recorded. In addition, mixtures having thicknesses of 2 and 4mm as well as mixtures of 2, 3 and 4mm were presented simultaneously to all classifiers. This approach provided further cross-validation of the classification consistency of each algorithm. The results confirm the superiority in classification accuracy and robustness of the MLR (least accuracy 88.24%) and KNN (least accuracy 90.19%) algorithms which consistently outperformed the SVM (least accuracy 74.51%) and NB (least accuracy 56.86%) classifiers for the same number of feature vectors across all studies
Dosoudilová, M.; Lomtatidze, Alexander; Šremr, Jiří
2015-01-01
Roč. 120, June (2015), s. 57-75 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : half-linear system * Hartman -Wintner theorem * Kamenev theorem Subject RIV: BA - General Mathematics Impact factor: 1.125, year: 2015 http://www.sciencedirect.com/science/article/pii/S0362546X15000620
Kiguradze, I.; Šremr, Jiří
2011-01-01
Roč. 74, č. 17 (2011), s. 6537-6552 ISSN 0362-546X Institutional research plan: CEZ:AV0Z10190503 Keywords : half-linear differential system * non-local boundary value problem * solvability Subject RIV: BA - General Mathematics Impact factor: 1.536, year: 2011 http://www.sciencedirect.com/science/article/pii/S0362546X11004573
A Linear Theory for Pretwisted Elastic Beams
Krenk, Steen
1983-01-01
contains a general system of differential equations and gives explicit solutions for homogenous extension, torsion, and bending. The theory accounts explicitly for the shear center, the elastic center, and the axis of pretwist. The resulting torsion-extension coupling is in agreement with a recent...
Asymptotic expansions for high-contrast linear elasticity
Poveda, Leonardo A.; Huepo, Sebastian; Calo, Victor M.; Galvis, Juan
2015-01-01
We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.
Asymptotic expansions for high-contrast linear elasticity
Poveda, Leonardo A.
2015-03-01
We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.
Osserman, Robert
2011-01-01
The basic component of several-variable calculus, two-dimensional calculus is vital to mastery of the broader field. This extensive treatment of the subject offers the advantage of a thorough integration of linear algebra and materials, which aids readers in the development of geometric intuition. An introductory chapter presents background information on vectors in the plane, plane curves, and functions of two variables. Subsequent chapters address differentiation, transformations, and integration. Each chapter concludes with problem sets, and answers to selected exercises appear at the end o
1979-02-01
tests were conducted on two geometrica lly similar models of each of two aerofoil sections -—t he NA CA 00/ 2 and the BGK- 1 sections -and covered a...and slotted-wall tes t sections are corrected for wind tunnel wall interference efJ~cts by the application of classical linearized theory. For the...solid wall results , these corrections appear to produce data which are very close to being free of the effects of interference. In the case of
Two dimensional untwisted (4,4), twisted (4,4-bar) and chiral supersymmetric non linear σ-models
Lhallabi, T.; Saidi, E.H.
1987-09-01
D=2 N=(4,4) harmonic superspace analysis is developed. The underlying untwisted (4,4) non linear σ-models are studied. A method of deriving chiral (4,0) and (0,4) models is presented. The Lagrange superparameter leading to the constraint specifying the hyperkahler manifold structure is predicted and its relation to the matter superfield is stated in a covariant way. A known construction is recovered. We show also that (4,4) model is not a direct sum of the chiral ones. Finally a twisted (4,4-bar) model is obtained. (author). 28 refs
Non-linear theory of elasticity and optimal design
Ratner, LW
2003-01-01
In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it
Wang, Wei; Sommer, Ephraim; De Sio, Antonietta; Gross, Petra; Vogelgesang, Ralf; Lienau, Christoph; Vasa, Parinda
2014-01-01
We analyze the linear optical reflectivity spectra of a prototypical, strongly coupled metal/molecular hybrid nanostructure by means of a new experimental approach, linear two-dimensional optical spectroscopy. White-light, broadband spectral interferometry is used to measure amplitude and spectral phase of the sample reflectivity or transmission with high precision and to reconstruct the time structure of the electric field emitted by the sample upon impulsive excitation. A numerical analysis of this time-domain signal provides a two-dimensional representation of the coherent optical response of the sample as a function of excitation and detection frequency. The approach is used to study a nanostructure formed by depositing a thin J-aggregated dye layer on a gold grating. In this structure, strong coupling between excitons and surface plasmon polaritons results in the formation of hybrid polariton modes. In the strong coupling regime, Lorentzian lineshape profiles of different polariton modes are observed at room temperature. This is taken as an indication that the investigated strongly coupled polariton excitations are predominantly homogeneously broadened at room temperature. This new approach presents a versatile, simple and highly precise addition to nonlinear optical spectroscopic techniques for the analysis of line broadening phenomena. (paper)
Susanti, Hesty; Suprijanto, Kurniadi, Deddy
2018-02-01
Needle visibility in ultrasound-guided technique has been a crucial factor for successful interventional procedure. It has been affected by several factors, i.e. puncture depth, insertion angle, needle size and material, and imaging technology. The influences of those factors made the needle not always well visible. 20 G needles of 15 cm length (Nano Line, facet) were inserted into water bath with variation of insertion angles and depths. Ultrasound measurements are performed with BK-Medical Flex Focus 800 using 12 MHz linear array and 5 MHz curved array in Ultrasound Guided Regional Anesthesia mode. We propose 3 criteria to evaluate needle visibility, i.e. maximum intensity, mean intensity, and the ratio between minimum and maximum intensity. Those criteria were then depicted into representative maps for practical purpose. The best criterion candidate for representing the needle visibility was criterion 1. Generally, the appearance pattern of the needle from this criterion was relatively consistent, i.e. for linear array, it was relatively poor visibility in the middle part of the shaft, while for curved array, it is relatively better visible toward the end of the shaft. With further investigations, for example with the use of tissue-mimicking phantom, the representative maps can be built for future practical purpose, i.e. as a tool for clinicians to ensure better needle placement in clinical application. It will help them to avoid the "dead" area where the needle is not well visible, so it can reduce the risks of vital structures traversing and the number of required insertion, resulting in less patient morbidity. Those simple criteria and representative maps can be utilized to evaluate general visibility patterns of the needle in vast range of needle types and sizes in different insertion media. This information is also important as an early investigation for future research of needle visibility improvement, i.e. the development of beamforming strategies and
Calculation of elastic-plastic strain ranges for fatigue analysis based on linear elastic stresses
Sauer, G.
1998-01-01
Fatigue analysis requires that the maximum strain ranges be known. These strain ranges are generally computed from linear elastic analysis. The elastic strain ranges are enhanced by a factor K e to obtain the total elastic-plastic strain range. The reliability of the fatigue analysis depends on the quality of this factor. Formulae for calculating the K e factor are proposed. A beam is introduced as a computational model for determining the elastic-plastic strains. The beam is loaded by the elastic stresses of the real structure. The elastic-plastic strains of the beam are compared with the beam's elastic strains. This comparison furnishes explicit expressions for the K e factor. The K e factor is tested by means of seven examples. (orig.)
On the use of elastic-plastic material characteristics for linear-elastic component assessments
Kussmaul, K.; Silcher, H.; Eisele, U.
1995-01-01
In this paper the procedure of safety assessment of components by fracture mechanics analysis as recommended in TECDOC 717 is applied to two standard specimens of ductile cast iron. It is shown that the use of a pseudo-elastic K IJ -value in linear elastic safety analysis may lead to non-conservative results, when elastic-plastic material behaviour can be expected. (author)
Khouri, T; Zeitler, U; Reichl, C; Wegscheider, W; Hussey, N E; Wiedmann, S; Maan, J C
2016-12-16
We report a high-field magnetotransport study of an ultrahigh mobility (μ[over ¯]≈25×10^{6} cm^{2} V^{-1} s^{-1}) n-type GaAs quantum well. We observe a strikingly large linear magnetoresistance (LMR) up to 33 T with a magnitude of order 10^{5}% onto which quantum oscillations become superimposed in the quantum Hall regime at low temperature. LMR is very often invoked as evidence for exotic quasiparticles in new materials such as the topological semimetals, though its origin remains controversial. The observation of such a LMR in the "simplest system"-with a free electronlike band structure and a nearly defect-free environment-excludes most of the possible exotic explanations for the appearance of a LMR and rather points to density fluctuations as the primary origin of the phenomenon. Both, the featureless LMR at high T and the quantum oscillations at low T follow the empirical resistance rule which states that the longitudinal conductance is directly related to the derivative of the transversal (Hall) conductance multiplied by the magnetic field and a constant factor α that remains unchanged over the entire temperature range. Only at low temperatures, small deviations from this resistance rule are observed beyond ν=1 that likely originate from a different transport mechanism for the composite fermions.
On the hyperbolicity condition in linear elasticity
Remigio Russo
1991-05-01
Full Text Available This talk, which is mainly expository and based on [2-5], discusses the hyperbolicity conditions in linear elastodynamics. Particular emphasis is devoted to the key role it plays in the uniqueness questions associated with the mixed boundary-initial value problem in unbounded domains.
On the 1/N expansion of the two-dimensional non-linear sigma-model: The vestige of chiral geometry
Flume, R.
1978-11-01
We investigate the functioning of the O(N)-symmetry of the non-linear two-dimensional sigma-model using the 1/N expansion. The mechanism of O(N)-symmetry restoration is made explicit. We show that the O(N) invariant operators are in a one to one correspondance with the (c-number) invariants of the classical model. We observe a phenomenon, important in the context of the symmetry restoration, which might be called 'transmutation of anomalies'. That is, an anomaly of the equations of motion appearing before a summation of graphs contributing to the leading order of 1/N as a short distance effect becomes, after the summation, a long-distance effect. (orig.) [de
Jain, Amit; Kuhls-Gilcrist, Andrew T; Gupta, Sandesh K; Bednarek, Daniel R; Rudin, Stephen
2010-03-01
The MTF, NNPS, and DQE are standard linear system metrics used to characterize intrinsic detector performance. To evaluate total system performance for actual clinical conditions, generalized linear system metrics (GMTF, GNNPS and GDQE) that include the effect of the focal spot distribution, scattered radiation, and geometric unsharpness are more meaningful and appropriate. In this study, a two-dimensional (2D) generalized linear system analysis was carried out for a standard flat panel detector (FPD) (194-micron pixel pitch and 600-micron thick CsI) and a newly-developed, high-resolution, micro-angiographic fluoroscope (MAF) (35-micron pixel pitch and 300-micron thick CsI). Realistic clinical parameters and x-ray spectra were used. The 2D detector MTFs were calculated using the new Noise Response method and slanted edge method and 2D focal spot distribution measurements were done using a pin-hole assembly. The scatter fraction, generated for a uniform head equivalent phantom, was measured and the scatter MTF was simulated with a theoretical model. Different magnifications and scatter fractions were used to estimate the 2D GMTF, GNNPS and GDQE for both detectors. Results show spatial non-isotropy for the 2D generalized metrics which provide a quantitative description of the performance of the complete imaging system for both detectors. This generalized analysis demonstrated that the MAF and FPD have similar capabilities at lower spatial frequencies, but that the MAF has superior performance over the FPD at higher frequencies even when considering focal spot blurring and scatter. This 2D generalized performance analysis is a valuable tool to evaluate total system capabilities and to enable optimized design for specific imaging tasks.
Horacio Hideki Yanasse
2013-01-01
Full Text Available Neste trabalho revemos alguns modelos lineares e não lineares inteiros para gerar padrões de corte bidimensionais guilhotinados de 2 estágios, incluindo os casos exato e não exato e restrito e irrestrito. Esses problemas são casos particulares do problema da mochila bidimensional. Apresentamos também novos modelos para gerar esses padrões de corte, baseados em adaptações ou extensões de modelos para gerar padrões de corte bidimensionais restritos 1-grupo. Padrões 2 estágios aparecem em diferentes processos de corte, como, por exemplo, em indústrias de móveis e de chapas de madeira. Os modelos são úteis para a pesquisa e o desenvolvimento de métodos de solução mais eficientes, explorando estruturas particulares, a decomposição do modelo, relaxações do modelo etc. Eles também são úteis para a avaliação do desempenho de heurísticas, já que permitem (pelo menos para problemas de tamanho moderado uma estimativa do gap de otimalidade de soluções obtidas por heurísticas. Para ilustrar a aplicação dos modelos, analisamos os resultados de alguns experimentos computacionais com exemplos da literatura e outros gerados aleatoriamente. Os resultados foram produzidos usando um software comercial conhecido e mostram que o esforço computacional necessário para resolver os modelos pode ser bastante diferente.In this work we review some linear and nonlinear integer models to generate two stage two-dimensional guillotine cutting patterns, including the constrained, non constrained, exact and non exact cases. These problems are particular cases of the two dimensional knapsack problems. We also present new models to generate these cutting patterns, based on adaptations and extensions of models that generate one-group constrained two dimensional cutting patterns. Two stage patterns arise in different cutting processes like, for instance, in the furniture industry and wooden hardboards. The models are useful for the research and
Deriglazov, A.A.; Ketov, S.V.
1991-01-01
The four-loop divergences of the (1,1) supersymmetric two-dimensional non-linear σ-model with a Wess-Zumino-Witten term are analyzed. All the four-loop 1/ε-divergences in the general case (and an overall coefficient at the total four-loop contribution to the β-function) are shown to be reducible to only structures proportional to ζ(3). We explicitly calculate non-derivative contributions to the four-loop β-function from logarithmically divergent graphs. As a by-product, we obtain the complete four-loop β-function for the supersymmetric Wess-Zumino-Witten model. We use the partial results for the general four-loop β-function to shed some light on the structure of the (α') 3 -corrections to the superstring effective-action with antisymmetric-tensor field coupling. An inconsistency of the supersymmetrical dimensional regularisation via dimensional reduction in the presence of torsion is discovered at four loops, unless the string interpretation for the σ-model is adopted. (orig.)
Quasi-two-dimensional holography
Kutzner, J.; Erhard, A.; Wuestenberg, H.; Zimpfer, J.
1980-01-01
The acoustical holography with numerical reconstruction by area scanning is memory- and time-intensive. With the experiences by the linear holography we tried to derive a scanning for the evaluating of the two-dimensional flaw-sizes. In most practical cases it is sufficient to determine the exact depth extension of a flaw, whereas the accuracy of the length extension is less critical. For this reason the applicability of the so-called quasi-two-dimensional holography is appropriate. The used sound field given by special probes is divergent in the inclined plane and light focussed in the perpendicular plane using cylindrical lenses. (orig.) [de
A Lagrangian meshfree method applied to linear and nonlinear elasticity.
Walker, Wade A
2017-01-01
The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code.
Non-linear elastic thermal stress analysis with phase changes
Amada, S.; Yang, W.H.
1978-01-01
The non-linear elastic, thermal stress analysis with temperature induced phase changes in the materials is presented. An infinite plate (or body) with a circular hole (or tunnel) is subjected to a thermal loading on its inner surface. The peak temperature around the hole reaches beyond the melting point of the material. The non-linear diffusion equation is solved numerically using the finite difference method. The material properties change rapidly at temperatures where the change of crystal structures and solid-liquid transition occur. The elastic stresses induced by the transient non-homogeneous temperature distribution are calculated. The stresses change remarkably when the phase changes occur and there are residual stresses remaining in the plate after one cycle of thermal loading. (Auth.)
A Galerkin approximation for linear elastic shallow shells
Figueiredo, I. N.; Trabucho, L.
1992-03-01
This work is a generalization to shallow shell models of previous results for plates by B. Miara (1989). Using the same basis functions as in the plate case, we construct a Galerkin approximation of the three-dimensional linearized elasticity problem, and establish some error estimates as a function of the thickness, the curvature, the geometry of the shell, the forces and the Lamé costants.
Yi, Xin; Gao, Huajian
2014-06-01
A fundamental understanding of cell-nanomaterial interaction is essential for biomedical diagnostics, therapeutics, and nanotoxicity. Here, we perform a theoretical analysis to investigate the phase diagram and morphological evolution of an elastic rod-shaped nanoparticle wrapped by a lipid membrane in two dimensions. We show that there exist five possible wrapping phases based on the stability of full wrapping, partial wrapping, and no wrapping states. The wrapping phases depend on the shape and size of the particle, adhesion energy, membrane tension, and bending rigidity ratio between the particle and membrane. While symmetric morphologies are observed in the early and late stages of wrapping, in between a soft rod-shaped nanoparticle undergoes a dramatic symmetry breaking morphological change while stiff and rigid nanoparticles experience a sharp reorientation. These results are of interest to the study of a range of phenomena including viral budding, exocytosis, as well as endocytosis or phagocytosis of elastic particles into cells.
Linear elastic properties derivation from microstructures representative of transport parameters.
Hoang, Minh Tan; Bonnet, Guy; Tuan Luu, Hoang; Perrot, Camille
2014-06-01
It is shown that three-dimensional periodic unit cells (3D PUC) representative of transport parameters involved in the description of long wavelength acoustic wave propagation and dissipation through real foam samples may also be used as a standpoint to estimate their macroscopic linear elastic properties. Application of the model yields quantitative agreement between numerical homogenization results, available literature data, and experiments. Key contributions of this work include recognizing the importance of membranes and properties of the base material for the physics of elasticity. The results of this paper demonstrate that a 3D PUC may be used to understand and predict not only the sound absorbing properties of porous materials but also their transmission loss, which is critical for sound insulation problems.
A reexamination of some puzzling results in linearized elasticity
University of North Carolina at Charlotte, Charlotte, NC 28223-0001, USA e-mail: jogc@mecheng.iisc.ernet.in; ..... ˆT (F) = C[ϵ] + o(∇u), where ϵ = [∇u+(∇u)T ]/2, and C = D ˆT (I) is the elasticity tensor, and one also linearizes the body force vector to get b = QT [ b∗ − ¨c. ] − ˙ × X − × ( × X) − 2 × v,. (5) where X is the position ...
Relating Cohesive Zone Model to Linear Elastic Fracture Mechanics
Wang, John T.
2010-01-01
The conditions required for a cohesive zone model (CZM) to predict a failure load of a cracked structure similar to that obtained by a linear elastic fracture mechanics (LEFM) analysis are investigated in this paper. This study clarifies why many different phenomenological cohesive laws can produce similar fracture predictions. Analytical results for five cohesive zone models are obtained, using five different cohesive laws that have the same cohesive work rate (CWR-area under the traction-separation curve) but different maximum tractions. The effect of the maximum traction on the predicted cohesive zone length and the remote applied load at fracture is presented. Similar to the small scale yielding condition for an LEFM analysis to be valid. the cohesive zone length also needs to be much smaller than the crack length. This is a necessary condition for a CZM to obtain a fracture prediction equivalent to an LEFM result.
Schroer, Bert; Freie Universitaet, Berlin
2005-02-01
It is not possible to compactly review the overwhelming literature on two-dimensional models in a meaningful way without a specific viewpoint; I have therefore tacitly added to the above title the words 'as theoretical laboratories for general quantum field theory'. I dedicate this contribution to the memory of J. A. Swieca with whom I have shared the passion of exploring 2-dimensional models for almost one decade. A shortened version of this article is intended as a contribution to the project 'Encyclopedia of mathematical physics' and comments, suggestions and critical remarks are welcome. (author)
Two-dimensional ferroelectrics
Blinov, L M; Fridkin, Vladimir M; Palto, Sergei P [A.V. Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow, Russian Federaion (Russian Federation); Bune, A V; Dowben, P A; Ducharme, Stephen [Department of Physics and Astronomy, Behlen Laboratory of Physics, Center for Materials Research and Analysis, University of Nebraska-Linkoln, Linkoln, NE (United States)
2000-03-31
The investigation of the finite-size effect in ferroelectric crystals and films has been limited by the experimental conditions. The smallest demonstrated ferroelectric crystals had a diameter of {approx}200 A and the thinnest ferroelectric films were {approx}200 A thick, macroscopic sizes on an atomic scale. Langmuir-Blodgett deposition of films one monolayer at a time has produced high quality ferroelectric films as thin as 10 A, made from polyvinylidene fluoride and its copolymers. These ultrathin films permitted the ultimate investigation of finite-size effects on the atomic thickness scale. Langmuir-Blodgett films also revealed the fundamental two-dimensional character of ferroelectricity in these materials by demonstrating that there is no so-called critical thickness; films as thin as two monolayers (1 nm) are ferroelectric, with a transition temperature near that of the bulk material. The films exhibit all the main properties of ferroelectricity with a first-order ferroelectric-paraelectric phase transition: polarization hysteresis (switching); the jump in spontaneous polarization at the phase transition temperature; thermal hysteresis in the polarization; the increase in the transition temperature with applied field; double hysteresis above the phase transition temperature; and the existence of the ferroelectric critical point. The films also exhibit a new phase transition associated with the two-dimensional layers. (reviews of topical problems)
Luescher, M.; Pohlmeyer, K.
1977-09-01
Finite energy solutions of the field equations of the non-linear sigma-model are shown to decay asymptotically into massless lumps. By means of a linear eigenvalue problem connected with the field equations we then find an infinite set of dynamical conserved charges. They, however, do not provide sufficient information to decode the complicated scattering of lumps. (orig.) [de
Luescher, M.
1977-12-01
Conserved non-local charges are shown to exist in the quantum non-linear sigma-model by a non-perturbative method. They imply the absence of particle production and the 'factorization equations' for the two particle S-matrix, which can then be calculated explicitly. (Auth.)
Morphology and linear-elastic moduli of random network solids.
Nachtrab, Susan; Kapfer, Sebastian C; Arns, Christoph H; Madadi, Mahyar; Mecke, Klaus; Schröder-Turk, Gerd E
2011-06-17
The effective linear-elastic moduli of disordered network solids are analyzed by voxel-based finite element calculations. We analyze network solids given by Poisson-Voronoi processes and by the structure of collagen fiber networks imaged by confocal microscopy. The solid volume fraction ϕ is varied by adjusting the fiber radius, while keeping the structural mesh or pore size of the underlying network fixed. For intermediate ϕ, the bulk and shear modulus are approximated by empirical power-laws K(phi)proptophin and G(phi)proptophim with n≈1.4 and m≈1.7. The exponents for the collagen and the Poisson-Voronoi network solids are similar, and are close to the values n=1.22 and m=2.11 found in a previous voxel-based finite element study of Poisson-Voronoi systems with different boundary conditions. However, the exponents of these empirical power-laws are at odds with the analytic values of n=1 and m=2, valid for low-density cellular structures in the limit of thin beams. We propose a functional form for K(ϕ) that models the cross-over from a power-law at low densities to a porous solid at high densities; a fit of the data to this functional form yields the asymptotic exponent n≈1.00, as expected. Further, both the intensity of the Poisson-Voronoi process and the collagen concentration in the samples, both of which alter the typical pore or mesh size, affect the effective moduli only by the resulting change of the solid volume fraction. These findings suggest that a network solid with the structure of the collagen networks can be modeled in quantitative agreement by a Poisson-Voronoi process. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Emergence of linear elasticity from the atomistic description of matter
Cakir, Abdullah, E-mail: acakir@ntu.edu.sg [Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University (Singapore); Pica Ciamarra, Massimo [Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University (Singapore); Dipartimento di Scienze Fisiche, CNR–SPIN, Università di Napoli Federico II, I-80126 Napoli (Italy)
2016-08-07
We investigate the emergence of the continuum elastic limit from the atomistic description of matter at zero temperature considering how locally defined elastic quantities depend on the coarse graining length scale. Results obtained numerically investigating different model systems are rationalized in a unifying picture according to which the continuum elastic limit emerges through a process determined by two system properties, the degree of disorder, and a length scale associated to the transverse low-frequency vibrational modes. The degree of disorder controls the emergence of long-range local shear stress and shear strain correlations, while the length scale influences the amplitude of the fluctuations of the local elastic constants close to the jamming transition.
Emergence of linear elasticity from the atomistic description of matter
Cakir, Abdullah; Pica Ciamarra, Massimo
2016-01-01
We investigate the emergence of the continuum elastic limit from the atomistic description of matter at zero temperature considering how locally defined elastic quantities depend on the coarse graining length scale. Results obtained numerically investigating different model systems are rationalized in a unifying picture according to which the continuum elastic limit emerges through a process determined by two system properties, the degree of disorder, and a length scale associated to the transverse low-frequency vibrational modes. The degree of disorder controls the emergence of long-range local shear stress and shear strain correlations, while the length scale influences the amplitude of the fluctuations of the local elastic constants close to the jamming transition.
Sznajd, J.
2016-12-01
The linear perturbation renormalization group (LPRG) is used to study the phase transition of the weakly coupled Ising chains with intrachain (J ) and interchain nearest-neighbor (J1) and next-nearest-neighbor (J2) interactions forming the triangular and rectangular lattices in a field. The phase diagrams with the frustration point at J2=-J1/2 for a rectangular lattice and J2=-J1 for a triangular lattice have been found. The LPRG calculations support the idea that the phase transition is always continuous except for the frustration point and is accompanied by a divergence of the specific heat. For the antiferromagnetic chains, the external field does not change substantially the shape of the phase diagram. The critical temperature is suppressed to zero according to the power law when approaching the frustration point with an exponent dependent on the value of the field.
Non-linear waves in heterogeneous elastic rods via homogenization
Quezada de Luna, Manuel
2012-03-01
We consider the propagation of a planar loop on a heterogeneous elastic rod with a periodic microstructure consisting of two alternating homogeneous regions with different material properties. The analysis is carried out using a second-order homogenization theory based on a multiple scale asymptotic expansion. © 2011 Elsevier Ltd. All rights reserved.
Self-organized defect strings in two-dimensional crystals.
Lechner, Wolfgang; Polster, David; Maret, Georg; Keim, Peter; Dellago, Christoph
2013-12-01
Using experiments with single-particle resolution and computer simulations we study the collective behavior of multiple vacancies injected into two-dimensional crystals. We find that the defects assemble into linear strings, terminated by dislocations with antiparallel Burgers vectors. We show that these defect strings propagate through the crystal in a succession of rapid one-dimensional gliding and rare rotations. While the rotation rate decreases exponentially with the number of defects in the string, the diffusion constant is constant for large strings. By monitoring the separation of the dislocations at the end points, we measure their effective interactions with high precision beyond their spontaneous formation and annihilation, and we explain the double-well form of the dislocation interaction in terms of continuum elasticity theory.
Two-dimensional strain gradient damage modeling: a variational approach
Placidi, Luca; Misra, Anil; Barchiesi, Emilio
2018-06-01
In this paper, we formulate a linear elastic second gradient isotropic two-dimensional continuum model accounting for irreversible damage. The failure is defined as the condition in which the damage parameter reaches 1, at least in one point of the domain. The quasi-static approximation is done, i.e., the kinetic energy is assumed to be negligible. In order to deal with dissipation, a damage dissipation term is considered in the deformation energy functional. The key goal of this paper is to apply a non-standard variational procedure to exploit the damage irreversibility argument. As a result, we derive not only the equilibrium equations but, notably, also the Karush-Kuhn-Tucker conditions. Finally, numerical simulations for exemplary problems are discussed as some constitutive parameters are varying, with the inclusion of a mesh-independence evidence. Element-free Galerkin method and moving least square shape functions have been employed.
Extreme non-linear elasticity and transformation optics
Gersborg, Allan Roulund; Sigmund, Ole
2010-01-01
realizations correspond to minimizers of elastic energy potentials for extreme values of the mechanical Poisson's ratio ν . For TE (Hz) polarized light an incompressible transformation ν = 1/2 is ideal and for TM (E z) polarized light one should use a compressible transformation with negative Poissons's ratio......Transformation optics is a powerful concept for designing novel optical components such as high transmission waveguides and cloaking devices. The selection of specific transformations is a non-unique problem. Here we reveal that transformations which allow for all dielectric and broadband optical...... ν = -1. For the TM polarization the mechanical analogy corresponds to a modified Liao functional known from the transformation optics literature. Finally, the analogy between ideal transformations and solid mechanical material models automates and broadens the concept of transformation optics...
Topological aspect of disclinations in two-dimensional crystals
Wei-Kai, Qi; Tao, Zhu; Yong, Chen; Ji-Rong, Ren
2009-01-01
By using topological current theory, this paper studies the inner topological structure of disclinations during the melting of two-dimensional systems. From two-dimensional elasticity theory, it finds that there are topological currents for topological defects in homogeneous equation. The evolution of disclinations is studied, and the branch conditions for generating, annihilating, crossing, splitting and merging of disclinations are given. (the physics of elementary particles and fields)
Designing Linear Feedback Controller for Elastic Inverted Pendulum with Tip Mass
Minh Hoang Nguyen
2016-12-01
Full Text Available This paper introduced a kind of cart and pole system. The pole in this system is not a solid beam but an elastic beam. The paper analyzed the dynamic equation of this complex system. Then, a linear feedback controller was designed to stabilize this model in order to keep the elastic beam balanced in the up-side position. The control results were proved to work well through simulation.
Pepi, John W.
2017-08-01
Thermally induced stress is readily calculated for linear elastic material properties using Hooke's law in which, for situations where expansion is constrained, stress is proportional to the product of the material elastic modulus and its thermal strain. When material behavior is nonlinear, one needs to make use of nonlinear theory. However, we can avoid that complexity in some situations. For situations in which both elastic modulus and coefficient of thermal expansion vary with temperature, solutions can be formulated using secant properties. A theoretical approach is thus presented to calculate stresses for nonlinear, neo-Hookean, materials. This is important for high acuity optical systems undergoing large temperature extremes.
Linear models of income patterns in consumer demand for foods and evaluation of its elasticity
Pavel Syrovátka
2005-01-01
Full Text Available The paper is focused on the use of the linear constructions for developing of Engel’s demand models in the field of the food-consumer demand. In the theoretical part of the paper, the linear approximations of this demand models are analysed on the bases of the linear interpolation. In the same part of this text, the hyperbolic elasticity function was defined for the linear Engel model. The behaviour of the hyperbolic elasticity function and its properties were consequently investigated too. The behaviour of the determined elasticity function was investigated according to the values of the intercept point and the direction parameter in the original linear Engel model. The obtained theoretical findings were tested using the real data of Czech Statistical Office. The developed linear Engel model was explicitly dynamised, because the achieved database was formed into the time series. With respect to the two variables definitions of the hyperbolic function in the theoretical part of the text, the determined dynamic model of the Engel demand for food was transformed into the form with parametric intercept point:ret* = At + 0.0946 · rmt*,where the values of absolute member are defined as:At = 1773.0973 + 9.3064 · t – 0.3023 · t2; (t = 1, 2, ... 32.The value of At in the parametric linear model of Engel consumer demand for food was during the observed period (1995–2002 always positive. Thus, the hyperbolic elasticity function achieved the elasticity coefficients from the interval:ηt ∈〈+0; +1.Within quantitative analysis of Engel demand for food in the Czech Republic during the given time period, it was founded, that income elasticity of food expenditures of the average Czech household was moved between +0.4080 and +0.4511. The Czech-household demand for food is thus income inelastic with the normal income reactions.
Two-dimensional NMR spectrometry
Farrar, T.C.
1987-01-01
This article is the second in a two-part series. In part one (ANALYTICAL CHEMISTRY, May 15) the authors discussed one-dimensional nuclear magnetic resonance (NMR) spectra and some relatively advanced nuclear spin gymnastics experiments that provide a capability for selective sensitivity enhancements. In this article and overview and some applications of two-dimensional NMR experiments are presented. These powerful experiments are important complements to the one-dimensional experiments. As in the more sophisticated one-dimensional experiments, the two-dimensional experiments involve three distinct time periods: a preparation period, t 0 ; an evolution period, t 1 ; and a detection period, t 2
A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation
Diosady, Laslo T.; Murman, Scott M.
2018-01-01
A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.
Two-dimensional metamaterial optics
Smolyaninov, I I
2010-01-01
While three-dimensional photonic metamaterials are difficult to fabricate, many new concepts and ideas in the metamaterial optics can be realized in two spatial dimensions using planar optics of surface plasmon polaritons. In this paper we review recent progress in this direction. Two-dimensional photonic crystals, hyperbolic metamaterials, and plasmonic focusing devices are demonstrated and used in novel microscopy and waveguiding schemes
The Simulation and Correction to the Brain Deformation Based on the Linear Elastic Model in IGS
MU Xiao-lan; SONG Zhi-jian
2004-01-01
@@ The brain deformation is a vital factor affecting the precision of the IGS and it becomes a hotspot to simulate and correct the brain deformation recently.The research organizations, which firstly resolved the brain deformation with the physical models, have the Image Processing and Analysis department of Yale University, Biomedical Modeling Lab of Vanderbilt University and so on. The former uses the linear elastic model; the latter uses the consolidation model.The linear elastic model only needs to drive the model using the surface displacement of exposed brain cortex,which is more convenient to be measured in the clinic.
Hysteresis and avalanches in two-dimensional foam rheology simulations
Jiang, Y.; Swart, P.J.; Saxena, A.; Asipauskas, M.; Glazier, J.A.
1999-01-01
Foams have unique rheological properties that range from solidlike to fluidlike. We study two-dimensional noncoarsening foams of different disorder under shear in a Monte Carlo simulation, using a driven large-Q Potts model. Simulations of periodic shear on an ordered foam show several different response regimes. At small strain amplitudes, bubbles deform and recover their shapes elastically, and the macroscopic response is that of a linear elastic cellular material. For increasing strain amplitude, the energy-strain curve starts to exhibit hysteresis before any topological rearrangements occur, indicating a macroscopic viscoelastic response. When the applied strain amplitude exceeds a critical value, the yield strain, topological rearrangements occur, the foam starts to flow, and we observe macroscopic irreversibility. We find that the dynamics of topological rearrangements depend sensitively on the structural disorder. Structural disorder decreases the yield strain; sufficiently high disorder changes the macroscopic response of a foam from a viscoelastic solid to a viscoelastic fluid. This wide-ranging dynamical response and the associated history effects of foams result from avalanchelike rearrangement events. The spatiotemporal statistics of rearrangement events do not display long-range correlations for ordered foams or at low shear rates, consistent with experimental observations. As the shear rate or structural disorder increases, the topological events become more correlated and their power spectra change from that of white noise toward 1/f noise. Intriguingly, the power spectra of the total stored energy also exhibit this 1/f trend. copyright 1999 The American Physical Society
Multisoliton formula for completely integrable two-dimensional systems
Chudnovsky, D.V.; Chudnovsky, G.V.
1979-01-01
For general two-dimensional completely integrable systems, the exact formulae for multisoliton type solutions are given. The formulae are obtained algebrically from solutions of two linear partial differential equations
Two-dimensional flexible nanoelectronics
Akinwande, Deji; Petrone, Nicholas; Hone, James
2014-12-01
2014/2015 represents the tenth anniversary of modern graphene research. Over this decade, graphene has proven to be attractive for thin-film transistors owing to its remarkable electronic, optical, mechanical and thermal properties. Even its major drawback--zero bandgap--has resulted in something positive: a resurgence of interest in two-dimensional semiconductors, such as dichalcogenides and buckled nanomaterials with sizeable bandgaps. With the discovery of hexagonal boron nitride as an ideal dielectric, the materials are now in place to advance integrated flexible nanoelectronics, which uniquely take advantage of the unmatched portfolio of properties of two-dimensional crystals, beyond the capability of conventional thin films for ubiquitous flexible systems.
Two-dimensional topological photonics
Khanikaev, Alexander B.; Shvets, Gennady
2017-12-01
Originating from the studies of two-dimensional condensed-matter states, the concept of topological order has recently been expanded to other fields of physics and engineering, particularly optics and photonics. Topological photonic structures have already overturned some of the traditional views on wave propagation and manipulation. The application of topological concepts to guided wave propagation has enabled novel photonic devices, such as reflection-free sharply bent waveguides, robust delay lines, spin-polarized switches and non-reciprocal devices. Discrete degrees of freedom, widely used in condensed-matter physics, such as spin and valley, are now entering the realm of photonics. In this Review, we summarize the latest advances in this highly dynamic field, with special emphasis on the experimental work on two-dimensional photonic topological structures.
Two-dimensional thermofield bosonization
Amaral, R.L.P.G.; Belvedere, L.V.; Rothe, K.D.
2005-01-01
The main objective of this paper was to obtain an operator realization for the bosonization of fermions in 1 + 1 dimensions, at finite, non-zero temperature T. This is achieved in the framework of the real-time formalism of Thermofield Dynamics. Formally, the results parallel those of the T = 0 case. The well-known two-dimensional Fermion-Boson correspondences at zero temperature are shown to hold also at finite temperature. To emphasize the usefulness of the operator realization for handling a large class of two-dimensional quantum field-theoretic problems, we contrast this global approach with the cumbersome calculation of the fermion-current two-point function in the imaginary-time formalism and real-time formalisms. The calculations also illustrate the very different ways in which the transmutation from Fermi-Dirac to Bose-Einstein statistics is realized
Two-dimensional critical phenomena
Saleur, H.
1987-09-01
Two dimensional critical systems are studied using transformation to free fields and conformal invariance methods. The relations between the two approaches are also studied. The analytical results obtained generally depend on universality hypotheses or on renormalization group trajectories which are not established rigorously, so numerical verifications, mainly using the transfer matrix approach, are presented. The exact determination of critical exponents; the partition functions of critical models on toruses; and results as the critical point is approached are discussed [fr
Two dimensional unstable scar statistics.
Warne, Larry Kevin; Jorgenson, Roy Eberhardt; Kotulski, Joseph Daniel; Lee, Kelvin S. H. (ITT Industries/AES Los Angeles, CA)
2006-12-01
This report examines the localization of time harmonic high frequency modal fields in two dimensional cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This paper examines the enhancements for these unstable orbits when the opposing mirrors are both convex and concave. In the latter case the construction includes the treatment of interior foci.
Silagadze, Z.K.
2007-01-01
Two-dimensional generalization of the original peak finding algorithm suggested earlier is given. The ideology of the algorithm emerged from the well-known quantum mechanical tunneling property which enables small bodies to penetrate through narrow potential barriers. We merge this 'quantum' ideology with the philosophy of Particle Swarm Optimization to get the global optimization algorithm which can be called Quantum Swarm Optimization. The functionality of the newborn algorithm is tested on some benchmark optimization problems
Niehuesbernd, Jörn; Müller, Clemens; Pantleon, Wolfgang
2013-01-01
. Consequently, the macroscopic elastic behavior results from the local elastic properties within the gradient. In the present investigation profiles produced by the linear flow splitting process were examined with respect to local and global elastic anisotropy, which develops during the complex forming process...
Non-linear buckling of an FGM truncated conical shell surrounded by an elastic medium
Sofiyev, A.H.; Kuruoglu, N.
2013-01-01
In this paper, the non-linear buckling of the truncated conical shell made of functionally graded materials (FGMs) surrounded by an elastic medium has been studied using the large deformation theory with von Karman–Donnell-type of kinematic non-linearity. A two-parameter foundation model (Pasternak-type) is used to describe the shell–foundation interaction. The FGM properties are assumed to vary continuously through the thickness direction. The fundamental relations, the modified Donnell type non-linear stability and compatibility equations of the FGM truncated conical shell resting on the Pasternak-type elastic foundation are derived. By using the Superposition and Galerkin methods, the non-linear stability equations for the FGM truncated conical shell is solved. Finally, influences of variations of Winkler foundation stiffness and shear subgrade modulus of the foundation, compositional profiles and shell characteristics on the dimensionless critical non-linear axial load are investigated. The present results are compared with the available data for a special case. -- Highlights: • Nonlinear buckling of FGM conical shell surrounded by elastic medium is studied. • Pasternak foundation model is used to describe the shell–foundation interaction. • Nonlinear basic equations are derived. • Problem is solved by using Superposition and Galerkin methods. • Influences of various parameters on the nonlinear critical load are investigated
Boundary value problems of the circular cylinders in the strain-gradient theory of linear elasticity
Kao, B.G.
1979-11-01
Three boundary value problems in the strain-gradient theory of linear elasticity are solved for circular cylinders. They are the twisting of circular cylinder, uniformly pressuring of concentric circular cylinder, and pure-bending of simply connected cylinder. The comparisons of these solutions with the solutions in classical elasticity and in couple-stress theory reveal the differences in the stress fields as well as the apparent stress fields due to the influences of the strain-gradient. These aspects of the strain-gradient theory could be important in modeling the failure behavior of structural materials
Compact solitary waves in linearly elastic chains with non-smooth on-site potential
Gaeta, Giuseppe [Dipartimento di Matematica, Universita di Milano, Via Saldini 50, 20133 Milan (Italy); Gramchev, Todor [Dipartimento di Matematica e Informatica, Universita di Cagliari, Via Ospedale 72, 09124 Cagliari (Italy); Walcher, Sebastian [Lehrstuhl A Mathematik, RWTH Aachen, 52056 Aachen (Germany)
2007-04-27
It was recently observed by Saccomandi and Sgura that one-dimensional chains with nonlinear elastic interaction and regular on-site potential can support compact solitary waves, i.e. travelling solitary waves with strictly compact support. In this paper, we show that the same applies to chains with linear elastic interaction and an on-site potential which is continuous but non-smooth at minima. Some different features arise; in particular, the speed of compact solitary waves is not uniquely fixed by the equation. We also discuss several generalizations of our findings.
Four-dimensional Hooke's law can encompass linear elasticity and inertia
Antoci, S.; Mihich, L.
1999-01-01
The question is examined whether the formally straightforward extension of Hooke's time-honoured stress-strain relation to the four dimensions of special and of general relativity can make physical sense. The four-dimensional Hooke law is found able to account for the inertia of matter; in the flat-space, slow-motion approximation the field equations for the displacement four-vector field ξ i can encompass both linear elasticity and inertia. In this limit one just recovers the equations of motion of the classical theory of elasticity
Two dimensional infinite conformal symmetry
Mohanta, N.N.; Tripathy, K.C.
1993-01-01
The invariant discontinuous (discrete) conformal transformation groups, namely the Kleinian and Fuchsian groups Gamma (with an arbitrary signature) of H (the Poincare upper half-plane l) and the unit disc Delta are explicitly constructed from the fundamental domain D. The Riemann surface with signatures of Gamma and conformally invariant automorphic forms (functions) with Peterson scalar product are discussed. The functor, where the category of complex Hilbert spaces spanned by the space of cusp forms constitutes the two dimensional conformal field theory. (Author) 7 refs
Two-dimensional liquid chromatography
Græsbøll, Rune
-dimensional separation space. Optimization of gradients in online RP×RP is more difficult than in normal HPLC as a result of the increased number of parameters and their influence on each other. Modeling the coverage of the compounds across the two-dimensional chromatogram as a result of a change in gradients could...... be used for optimization purposes, and reduce the time spend on optimization. In this thesis (chapter 6), and manuscript B, a measure of the coverage of the compounds in the twodimensional separation space is defined. It is then shown that this measure can be modeled for changes in the gradient in both...
Two-dimensional capillary origami
Brubaker, N.D., E-mail: nbrubaker@math.arizona.edu; Lega, J., E-mail: lega@math.arizona.edu
2016-01-08
We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid. - Highlights: • Full solution set of the two-dimensional capillary origami problem. • Fluid does not necessarily wet the entire plate. • Global energy approach provides exact differential equations satisfied by minimizers. • Bifurcation diagrams highlight three different regimes. • Conditions for spontaneous encapsulation are identified.
Two-dimensional capillary origami
Brubaker, N.D.; Lega, J.
2016-01-01
We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid. - Highlights: • Full solution set of the two-dimensional capillary origami problem. • Fluid does not necessarily wet the entire plate. • Global energy approach provides exact differential equations satisfied by minimizers. • Bifurcation diagrams highlight three different regimes. • Conditions for spontaneous encapsulation are identified.
Two dimensional solid state NMR
Kentgens, A.P.M.
1987-01-01
This thesis illustrates, by discussing some existing and newly developed 2D solid state experiments, that two-dimensional NMR of solids is a useful and important extension of NMR techniques. Chapter 1 gives an overview of spin interactions and averaging techniques important in solid state NMR. As 2D NMR is already an established technique in solutions, only the basics of two dimensional NMR are presented in chapter 2, with an emphasis on the aspects important for solid spectra. The following chapters discuss the theoretical background and applications of specific 2D solid state experiments. An application of 2D-J resolved NMR, analogous to J-resolved spectroscopy in solutions, to natural rubber is given in chapter 3. In chapter 4 the anisotropic chemical shift is mapped out against the heteronuclear dipolar interaction to obtain information about the orientation of the shielding tensor in poly-(oxymethylene). Chapter 5 concentrates on the study of super-slow molecular motions in polymers using a variant of the 2D exchange experiment developed by us. Finally chapter 6 discusses a new experiment, 2D nutation NMR, which makes it possible to study the quadrupole interaction of half-integer spins. 230 refs.; 48 figs.; 8 tabs
Two-dimensional turbulent convection
Mazzino, Andrea
2017-11-01
We present an overview of the most relevant, and sometimes contrasting, theoretical approaches to Rayleigh-Taylor and mean-gradient-forced Rayleigh-Bénard two-dimensional turbulence together with numerical and experimental evidences for their support. The main aim of this overview is to emphasize that, despite the different character of these two systems, especially in relation to their steadiness/unsteadiness, turbulent fluctuations are well described by the same scaling relationships originated from the Bolgiano balance. The latter states that inertial terms and buoyancy terms balance at small scales giving rise to an inverse kinetic energy cascade. The main difference with respect to the inverse energy cascade in hydrodynamic turbulence [R. H. Kraichnan, "Inertial ranges in two-dimensional turbulence," Phys. Fluids 10, 1417 (1967)] is that the rate of cascade of kinetic energy here is not constant along the inertial range of scales. Thanks to the absence of physical boundaries, the two systems here investigated turned out to be a natural physical realization of the Kraichnan scaling regime hitherto associated with the elusive "ultimate state of thermal convection" [R. H. Kraichnan, "Turbulent thermal convection at arbitrary Prandtl number," Phys. Fluids 5, 1374-1389 (1962)].
Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.
Preston, Leiph [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-08-01
Explosions within the earth nonlinearly deform the local media, but at typical seismological observation distances, the seismic waves can be considered linear. Although nonlinear algorithms can simulate explosions in the very near field well, these codes are computationally expensive and inaccurate at propagating these signals to great distances. A linearized wave propagation code, coupled to a nonlinear code, provides an efficient mechanism to both accurately simulate the explosion itself and to propagate these signals to distant receivers. To this end we have coupled Sandia's nonlinear simulation algorithm CTH to a linearized elastic wave propagation code for 2-D axisymmetric media (axiElasti) by passing information from the nonlinear to the linear code via time-varying boundary conditions. In this report, we first develop the 2-D axisymmetric elastic wave equations in cylindrical coordinates. Next we show how we design the time-varying boundary conditions passing information from CTH to axiElasti, and finally we demonstrate the coupling code via a simple study of the elastic radius.
Equivalency of two-dimensional algebras
Santos, Gildemar Carneiro dos; Pomponet Filho, Balbino Jose S.
2011-01-01
Full text: Let us consider a vector z = xi + yj over the field of real numbers, whose basis (i,j) satisfy a given algebra. Any property of this algebra will be reflected in any function of z, so we can state that the knowledge of the properties of an algebra leads to more general conclusions than the knowledge of the properties of a function. However structural properties of an algebra do not change when this algebra suffers a linear transformation, though the structural constants defining this algebra do change. We say that two algebras are equivalent to each other whenever they are related by a linear transformation. In this case, we have found that some relations between the structural constants are sufficient to recognize whether or not an algebra is equivalent to another. In spite that the basis transform linearly, the structural constants change like a third order tensor, but some combinations of these tensors result in a linear transformation, allowing to write the entries of the transformation matrix as function of the structural constants. Eventually, a systematic way to find the transformation matrix between these equivalent algebras is obtained. In this sense, we have performed the thorough classification of associative commutative two-dimensional algebras, and find that even non-division algebra may be helpful in solving non-linear dynamic systems. The Mandelbrot set was used to have a pictorial view of each algebra, since equivalent algebras result in the same pattern. Presently we have succeeded in classifying some non-associative two-dimensional algebras, a task more difficult than for associative one. (author)
Náhlík, Luboš; Šestáková, L.; Hutař, Pavel; Knésl, Zdeněk
2011-01-01
Roč. 452-453, - (2011), s. 445-448 ISSN 1013-9826 R&D Projects: GA AV ČR(CZ) KJB200410803; GA ČR GA101/09/1821 Institutional research plan: CEZ:AV0Z20410507 Keywords : generalized stress intensity factor * bimaterial interface * composite materials * strain energy density factor * fracture criterion * generalized linear elastic fracture mechanics Subject RIV: JL - Materials Fatigue, Friction Mechanics
Two-dimensional quantum repeaters
Wallnöfer, J.; Zwerger, M.; Muschik, C.; Sangouard, N.; Dür, W.
2016-11-01
The endeavor to develop quantum networks gave rise to a rapidly developing field with far-reaching applications such as secure communication and the realization of distributed computing tasks. This ultimately calls for the creation of flexible multiuser structures that allow for quantum communication between arbitrary pairs of parties in the network and facilitate also multiuser applications. To address this challenge, we propose a two-dimensional quantum repeater architecture to establish long-distance entanglement shared between multiple communication partners in the presence of channel noise and imperfect local control operations. The scheme is based on the creation of self-similar multiqubit entanglement structures at growing scale, where variants of entanglement swapping and multiparty entanglement purification are combined to create high-fidelity entangled states. We show how such networks can be implemented using trapped ions in cavities.
Pair Interaction of Dislocations in Two-Dimensional Crystals
Eisenmann, C.; Gasser, U.; Keim, P.; Maret, G.; von Grünberg, H. H.
2005-10-01
The pair interaction between crystal dislocations is systematically explored by analyzing particle trajectories of two-dimensional colloidal crystals measured by video microscopy. The resulting pair energies are compared to Monte Carlo data and to predictions derived from the standard Hamiltonian of the elastic theory of dislocations. Good agreement is found with respect to the distance and temperature dependence of the interaction potential, but not regarding the angle dependence where discrete lattice effects become important. Our results on the whole confirm that the dislocation Hamiltonian allows a quantitative understanding of the formation and interaction energies of dislocations in two-dimensional crystals.
Multigrid for the Galerkin least squares method in linear elasticity: The pure displacement problem
Yoo, Jaechil [Univ. of Wisconsin, Madison, WI (United States)
1996-12-31
Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we prove the convergence of a multigrid (W-cycle) method. This multigrid is robust in that the convergence is uniform as the parameter, v, goes to 1/2 Computational experiments are included.
Study of two-dimensional interchange turbulence
Sugama, Hideo; Wakatani, Masahiro.
1990-04-01
An eddy viscosity model describing enstrophy transfer in two-dimensional turbulence is presented. This model is similar to that of Canuto et al. and provides an equation for the energy spectral function F(k) as a function of the energy input rate to the system per unit wavenumber, γ s (k). In the enstrophy-transfer inertial range, F(k)∝ k -3 is predicted by the model. The eddy viscosity model is applied to the interchange turbulence of a plasma in shearless magnetic field. Numerical simulation of the two-dimensional interchange turbulence demonstrates that the energy spectrum in the high wavenumber region is well described by this model. The turbulent transport driven by the interchange turbulence is expressed in terms of the Nusselt number Nu, the Rayleigh number Ra and Prantl number Pr in the same manner as that of thermal convection problem. When we use the linear growth rate for γ s (k), our theoretical model predicts that Nu ∝ (Ra·Pr) 1/2 for a constant background pressure gradient and Nu ∝ (Ra·Pr) 1/3 for a self-consistent background pressure profile with the stress-free slip boundary conditions. The latter agrees with our numerical result showing Nu ∝ Ra 1/3 . (author)
Exterior calculus and two-dimensional supersymmetric models
Sciuto, S.
1980-01-01
An important property of the calculus of differential forms on superspace is pointed out, and an economical way to treat the linear problem associated with certain supersymmetric two-dimensional models is discussed. A generalization of the super sine-Gordon model is proposed; its bosonic limit is a new model whose associate linear set has an SU(3) structure. (orig.)
Equilibrium: two-dimensional configurations
Anon.
1987-01-01
In Chapter 6, the problem of toroidal force balance is addressed in the simplest, nontrivial two-dimensional geometry, that of an axisymmetric torus. A derivation is presented of the Grad-Shafranov equation, the basic equation describing axisymmetric toroidal equilibrium. The solutions to equations provide a complete description of ideal MHD equilibria: radial pressure balance, toroidal force balance, equilibrium Beta limits, rotational transform, shear, magnetic wall, etc. A wide number of configurations are accurately modeled by the Grad-Shafranov equation. Among them are all types of tokamaks, the spheromak, the reversed field pinch, and toroidal multipoles. An important aspect of the analysis is the use of asymptotic expansions, with an inverse aspect ratio serving as the expansion parameter. In addition, an equation similar to the Grad-Shafranov equation, but for helically symmetric equilibria, is presented. This equation represents the leading-order description low-Beta and high-Beta stellarators, heliacs, and the Elmo bumpy torus. The solutions all correspond to infinitely long straight helices. Bending such a configuration into a torus requires a full three-dimensional calculation and is discussed in Chapter 7
Dynamics of pre-strained bi-material elastic systems linearized three-dimensional approach
Akbarov, Surkay D
2015-01-01
This book deals with dynamics of pre-stressed or pre-strained bi-material elastic systems consisting of stack of pre-stressed layers, stack of pre-stressed layers and pre-stressed half space (or half plane), stack of pre-stressed layers as well as absolute rigid foundation, pre-stressed compound solid and hollow cylinders and pre-stressed sandwich hollow cylinders. The problems considered in the book relate to the dynamics of a moving and oscillating moving load, forced vibration caused by linearly located or point located time-harmonic forces acting to the foregoing systems. Moreover, a considerable part of the book relate to the problems regarding the near surface, torsional and axisymmetric longitudinal waves propagation and dispersion in the noted above bi-material elastic systems. The book carries out the investigations within the framework of the piecewise homogeneous body model with the use of the Three-Dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies.
Force sensing using 3D displacement measurements in linear elastic bodies
Feng, Xinzeng; Hui, Chung-Yuen
2016-07-01
In cell traction microscopy, the mechanical forces exerted by a cell on its environment is usually determined from experimentally measured displacement by solving an inverse problem in elasticity. In this paper, an innovative numerical method is proposed which finds the "optimal" traction to the inverse problem. When sufficient regularization is applied, we demonstrate that the proposed method significantly improves the widely used approach using Green's functions. Motivated by real cell experiments, the equilibrium condition of a slowly migrating cell is imposed as a set of equality constraints on the unknown traction. Our validation benchmarks demonstrate that the numeric solution to the constrained inverse problem well recovers the actual traction when the optimal regularization parameter is used. The proposed method can thus be applied to study general force sensing problems, which utilize displacement measurements to sense inaccessible forces in linear elastic bodies with a priori constraints.
Lundsager, P.; Krenk, S.
1975-08-01
The static and dynamic response of a cylindrical/ spherical containment to a Boeing 720 impact is computed using 3 different linear elastic computer codes: FINEL, SAP and STARDYNE. Stress and displacement fields are shown together with time histories for a point in the impact zone. The main conclusions from this study are: - In this case the maximum dynamic load factors for stress and displacements were close to 1, but a static analysis alone is not fully sufficient. - More realistic load time histories should be considered. - The main effects seem to be local. The present study does not indicate general collapse from elastic stresses alone. - Further study of material properties at high rates is needed. (author)
Two dimensional generalizations of the Newcomb equation
Dewar, R.L.; Pletzer, A.
1989-11-01
The Bineau reduction to scalar form of the equation governing ideal, zero frequency linearized displacements from a hydromagnetic equilibrium possessing a continuous symmetry is performed in 'universal coordinates', applicable to both the toroidal and helical cases. The resulting generalized Newcomb equation (GNE) has in general a more complicated form than the corresponding one dimensional equation obtained by Newcomb in the case of circular cylindrical symmetry, but in this cylindrical case , the equation can be transformed to that of Newcomb. In the two dimensional case there is a transformation which leaves the form of the GNE invariant and simplifies the Frobenius expansion about a rational surface, especially in the limit of zero pressure gradient. The Frobenius expansions about a mode rational surface is developed and the connection with Hamiltonian transformation theory is shown. 17 refs
Geometrical aspects of solvable two dimensional models
Tanaka, K.
1989-01-01
It was noted that there is a connection between the non-linear two-dimensional (2D) models and the scalar curvature r, i.e., when r = -2 the equations of motion of the Liouville and sine-Gordon models were obtained. Further, solutions of various classical nonlinear 2D models can be obtained from the condition that the appropriate curvature two form Ω = 0, which suggests that these models are closely related. This relation is explored further in the classical version by obtaining the equations of motion from the evolution equations, the infinite number of conserved quantities, and the common central charge. The Poisson brackets of the solvable 2D models are specified by the Virasoro algebra. 21 refs
Spannenberg Jescica
2017-09-01
Full Text Available Fractional differentiation has adequate use for investigating real world scenarios related to geological formations associated with elasticity, heterogeneity, viscoelasticity, and the memory effect. Since groundwater systems exist in these geological formations, modelling groundwater recharge as a real world scenario is a challenging task to do because existing recharge estimation methods are governed by linear equations which make use of constant field parameters. This is inadequate because in reality these parameters are a function of both space and time. This study therefore concentrates on modifying the recharge equation governing the EARTH model, by application of the Eton approach. Accordingly, this paper presents a modified equation which is non-linear, and accounts for parameters in a way that it is a function of both space and time. To be more specific, herein, recharge and drainage resistance which are parameters within the equation, became a function of both space and time. Additionally, the study entailed solving the non-linear equation using an iterative method as well as numerical solutions by means of the Crank-Nicolson scheme. The numerical solutions were used alongside the Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu derivatives, so that account was taken for elasticity, heterogeneity, viscoelasticity, and the memory effect. In essence, this paper presents a more adequate model for recharge estimation.
Oscillations of a Beam on a Non-Linear Elastic Foundation under Periodic Loads
Donald Mark Santee
2006-01-01
Full Text Available The complexity of the response of a beam resting on a nonlinear elastic foundation makes the design of this structural element rather challenging. Particularly because, apparently, there is no algebraic relation for its load bearing capacity as a function of the problem parameters. Such an algebraic relation would be desirable for design purposes. Our aim is to obtain this relation explicitly. Initially, a mathematical model of a flexible beam resting on a non-linear elastic foundation is presented, and its non-linear vibrations and instabilities are investigated using several numerical methods. At a second stage, a parametric study is carried out, using analytical and semi-analytical perturbation methods. So, the influence of the various physical and geometrical parameters of the mathematical model on the non-linear response of the beam is evaluated, in particular, the relation between the natural frequency and the vibration amplitude and the first period doubling and saddle-node bifurcations. These two instability phenomena are the two basic mechanisms associated with the loss of stability of the beam. Finally Melnikov's method is used to determine an algebraic expression for the boundary that separates a safe from an unsafe region in the force parameters space. It is shown that this can be used as a basis for a reliable engineering design criterion.
Anisotropic mass density by two-dimensional acoustic metamaterials
Torrent, Daniel; Sanchez-Dehesa, Jose [Wave Phenomena Group, Department of Electronic Engineering, Polytechnic University of Valencia, C/Camino de Vera s/n, E-46022 Valencia (Spain)], E-mail: jsdehesa@upvnet.upv.es
2008-02-15
We show that specially designed two-dimensional arrangements of full elastic cylinders embedded in a nonviscous fluid or gas define (in the homogenization limit) a new class of acoustic metamaterials characterized by a dynamical effective mass density that is anisotropic. Here, analytic expressions for the dynamical mass density and the effective sound velocity tensors are derived in the long wavelength limit. Both show an explicit dependence on the lattice filling fraction, the elastic properties of cylinders relative to the background, their positions in the unit cell, and their multiple scattering interactions. Several examples of these metamaterials are reported and discussed.
The application of linear elastic fracture mechanics to thermally stressed welded components
Green, D.
1981-01-01
Linear Elastic Fracture Mechanics techniques are applied to components constructed from brittle materials and operating at low or ambient temperatures. It is argued that these techniques can justifiably be applied to components at high temperature provided that stresses are thermally induced, self-equilibrating and cyclic. Such loading conditions occur for example in an LMFBR and a simple welded detail containing a crevice is taken as an example. Theoretical and experimental estimates of crack growth in this component are compared and good agreement is shown. (author)
Franca, L.P.; Stenberg, R.
1989-06-01
Stability conditions are described to analyze a variational formulation emanating from a variational principle for linear isotropic elasticity. The variational principle is based on four dependent variables (namely, the strain tensor, augmented stress, pressure and displacement) and is shown to be valid for any compressibility including the incompressible limit. An improved convergence error analysis is established for a Galerkin-least-squares method based upon these four variables. The analysis presented establishes convergence for a wide choice of combinations of finite element interpolations. (author) [pt
On reconstruction of an unknown polygonal cavity in a linearized elasticity with one measurement
Ikehata, M; Itou, H
2011-01-01
In this paper we consider a reconstruction problem of an unknown polygonal cavity in a linearized elastic body. For this problem, an extraction formula of the convex hull of the unknown polygonal cavity is established by means of the enclosure method introduced by Ikehata. The advantages of our method are that it needs only a single set of boundary data and we do not require any a priori assumptions for the unknown polygonal cavity and any constraints on boundary data. The theoretical formula may have possibility of application in nondestructive evaluation.
Gabriela Queiroz de Melo Monteiro
2010-03-01
Full Text Available Linear polymerization shrinkage (LPS, flexural strength (FS and modulus of elasticity (ME of 7 dental composites (Filtek Z350™, Filtek Z250™/3M ESPE; Grandio™, Polofil Supra™/VOCO; TPH Spectrum™, TPH3™, Esthet-X™/Denstply were measured. For the measurement of LPS, composites were applied to a cylindrical metallic mold and polymerized (n = 8. The gap formed at the resin/mold interface was observed using scanning electron microscopy (1500×. For FS and ME, specimens were prepared according to the ISO 4049 specifications (n = 10. Statistical analysis of the data was performed with one-way ANOVA and the Tukey test. TPH Spectrum presented significantly higher LPS values (29.45 µm. Grandio had significantly higher mean values for FS (141.07 MPa and ME (13.91 GPa. The relationship between modulus of elasticity and polymerization shrinkage is the main challenge for maintenance of the adhesive interface, thus composites presenting high shrinkage values, associated with a high modulus of elasticity tend to disrupt the adhesive interface under polymerization.
Jessamine P Winer
2009-07-01
Full Text Available Most tissue cells grown in sparse cultures on linearly elastic substrates typically display a small, round phenotype on soft substrates and become increasingly spread as the modulus of the substrate increases until their spread area reaches a maximum value. As cell density increases, individual cells retain the same stiffness-dependent differences unless they are very close or in molecular contact. On nonlinear strain-stiffening fibrin gels, the same cell types become maximally spread even when the low strain elastic modulus would predict a round morphology, and cells are influenced by the presence of neighbors hundreds of microns away. Time lapse microscopy reveals that fibroblasts and human mesenchymal stem cells on fibrin deform the substrate by several microns up to five cell lengths away from their plasma membrane through a force limited mechanism. Atomic force microscopy and rheology confirm that these strains locally and globally stiffen the gel, depending on cell density, and this effect leads to long distance cell-cell communication and alignment. Thus cells are acutely responsive to the nonlinear elasticity of their substrates and can manipulate this rheological property to induce patterning.
Suarez Antola, R.
2004-12-01
The presence of cracks, voids or fields of pores, and their growth under applied forces or environmental actions, can produce a meaningful lowering in the proper frequencies of normal modes of mechanical vibration in machines and structures. A quite general expression for the square of modes proper frequency as a functional of displacement field, density field and elastic moduli fields is used as a starting point. The effect of defects on frequency are modeled as equivalent changes in density and elastic moduli fields, introducing the concept of region of influence of each defect. This region of influence is derived from the relation between the stress field of flawed components in machines or structures, and the elastic energy released from a suitable reference state, due to the presence of significant defects in the above mentioned mechanical components. An approximate analytical expression is obtained, which relates the relative variation in the square of mode s proper frequency with position, size, shape and orientation of defects in mode displacement field. Some simple mathematical models of machine and structural elements with cracks or fields of pores are considered as examples. The connections between the relative lowering in the square of mode s proper frequency and the stress intensity factor of a defect are discussed : the concept of region of influence of a defect is used as a bridge between (low frequency and low amplitude) vibration dynamics and linear elastic fracture mechanics. Some limitations of the present approach are discussed as well as the possibility of applying the region of influence of defects to the damping of normal modes of vibration
A New Theory of Non-Linear Thermo-Elastic Constitutive Equation of Isotropic Hyperelastic Materials
Li, Chen; Liao, Yufei
2018-03-01
Considering the influence of temperature and strain variables on materials. According to the relationship of conjugate stress-strain, a complete and irreducible non-linear constitutive equation of isotropic hyperelastic materials is derived and the constitutive equations of 16 types of isotropic hyperelastic materials are given we study the transformation methods and routes of 16 kinds of constitutive equations and the study proves that transformation of two forms of constitutive equation. As an example of application, the non-linear thermo-elastic constitutive equation of isotropic hyperelastic materials is combined with the natural vulcanized rubber experimental data in the existing literature base on MATLAB, The results show that the fitting accuracy is satisfactory.
DeLuca, R.
2006-03-01
Repeated elastic collisions of point particles on a finite frictionless linear track with perfectly reflecting endpoints are considered. The problem is analysed by means of an elementary linear algebra approach. It is found that, starting with a state consisting of a projectile particle in motion at constant velocity and a target particle at rest in a fixed known position, the points at which collisions occur on track, when plotted versus progressive numerals, corresponding to the collisions themselves, show periodic patterns for a rather large choice of values of the initial position x(0) and on the mass ratio r. For certain values of these parameters, however, only regular behaviour over a large number of collisions is detected.
Kim, Jin Kyu; Kim, Dong Keon
2016-01-01
A common approach for dynamic analysis in current practice is based on a discrete time-integration scheme. This approach can be largely attributed to the absence of a true variational framework for initial value problems. To resolve this problem, a new stationary variational principle was recently established for single-degree-of-freedom oscillating systems using mixed variables, fractional derivatives and convolutions of convolutions. In this mixed convolved action, all the governing differential equations and initial conditions are recovered from the stationarity of a single functional action. Thus, the entire description of linear elastic dynamical systems is encapsulated. For its practical application to structural dynamics, this variational formalism is systemically extended to linear elastic multidegree- of-freedom systems in this study, and a corresponding weak form is numerically implemented via a quadratic temporal finite element method. The developed numerical method is symplectic and unconditionally stable with respect to a time step for the underlying conservative system. For the forced-damped vibration, a three-story shear building is used as an example to investigate the performance of the developed numerical method, which provides accurate results with good convergence characteristics
Linear Elastic Waves - Series: Cambridge Texts in Applied Mathematics (No. 26)
Harris, John G.
2001-10-01
Wave propagation and scattering are among the most fundamental processes that we use to comprehend the world around us. While these processes are often very complex, one way to begin to understand them is to study wave propagation in the linear approximation. This is a book describing such propagation using, as a context, the equations of elasticity. Two unifying themes are used. The first is that an understanding of plane wave interactions is fundamental to understanding more complex wave interactions. The second is that waves are best understood in an asymptotic approximation where they are free of the complications of their excitation and are governed primarily by their propagation environments. The topics covered include reflection, refraction, the propagation of interfacial waves, integral representations, radiation and diffraction, and propagation in closed and open waveguides. Linear Elastic Waves is an advanced level textbook directed at applied mathematicians, seismologists, and engineers. Aimed at beginning graduate students Includes examples and exercises Has application in a wide range of disciplines
Kim, Jin Kyu [School of Architecture and Architectural Engineering, Hanyang University, Ansan (Korea, Republic of); Kim, Dong Keon [Dept. of Architectural Engineering, Dong A University, Busan (Korea, Republic of)
2016-09-15
A common approach for dynamic analysis in current practice is based on a discrete time-integration scheme. This approach can be largely attributed to the absence of a true variational framework for initial value problems. To resolve this problem, a new stationary variational principle was recently established for single-degree-of-freedom oscillating systems using mixed variables, fractional derivatives and convolutions of convolutions. In this mixed convolved action, all the governing differential equations and initial conditions are recovered from the stationarity of a single functional action. Thus, the entire description of linear elastic dynamical systems is encapsulated. For its practical application to structural dynamics, this variational formalism is systemically extended to linear elastic multidegree- of-freedom systems in this study, and a corresponding weak form is numerically implemented via a quadratic temporal finite element method. The developed numerical method is symplectic and unconditionally stable with respect to a time step for the underlying conservative system. For the forced-damped vibration, a three-story shear building is used as an example to investigate the performance of the developed numerical method, which provides accurate results with good convergence characteristics.
Solitary wave solutions of two-dimensional nonlinear Kadomtsev ...
Aly R Seadawy
2017-09-13
Sep 13, 2017 ... We considered the two-dimensional DASWs in colli- sionless, unmagnetized cold plasma consisting of dust fluid, ions and electrons. The dynamics of DASWs is governed by the normalized fluid equations of nonlin- ear continuity (1), nonlinear motion of system (2) and. (3) and linear Poisson equation (4) as.
Second invariant for two-dimensional classical super systems
Construction of superpotentials for two-dimensional classical super systems (for N. 2) is carried ... extensively used for the case of non-linear partial differential equation by various authors. [3,4–7,12 ..... found to be integrable just by accident.
Two-dimensional dissipation in third sound resonance
Buck, A.L.; Mochel, J.M.; Illinois Univ., Urbana
1981-01-01
The first determination of non-linear superflow dissipation in a truly two-dimensional helium film is reported. Superfluid velocities were measured using third sound resonance on a closed superfluid film. The predicted power law dissipation function, with exponent of approximately eight, is observed at three temperatures in a film of 0.58 mobile superfluid layers. (orig.)
Nonlinear dynamic characterization of two-dimensional materials
Davidovikj, D.; Alijani, F.; Cartamil Bueno, S.J.; van der Zant, H.S.J.; Amabili, M.; Steeneken, P.G.
2017-01-01
Owing to their atomic-scale thickness, the resonances of two-dimensional (2D) material membranes show signatures of nonlinearities at forces of only a few picoNewtons. Although the linear dynamics of membranes is well understood, the exact relation between the nonlinear response and the resonator's
Chudnovsky, A.; Dolgopolsky, A.; Kachanov, M.
1987-01-01
The elastic interactions of a two-dimensional configuration consisting of a crack with an array of microcracks located near the tip are studied. The general form of the solution is based on the potential representations and approximations of tractions on the microcracks by polynomials. In the second part, the technique is applied to two simple two-dimensional configurations involving one and two microcracks. The problems of stress shielding and stress amplification (the reduction or increase of the effective stress intensity factor due to the presence of microcracks) are discussed, and the refinements introduced by higher order polynomial approximations are illustrated.
Response statistics of rotating shaft with non-linear elastic restoring forces by path integration
Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael
2017-07-01
Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.
Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy
Paul, J.; Dey, P.; Karaiskaj, D., E-mail: karaiskaj@usf.edu [Department of Physics, University of South Florida, 4202 East Fowler Ave., Tampa, Florida 33620 (United States); Tokumoto, T.; Hilton, D. J. [Department of Physics, University of Alabama at Birmingham, Birmingham, Alabama 35294 (United States); Reno, J. L. [CINT, Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States)
2014-10-07
The dephasing of the Fermi edge singularity excitations in two modulation doped single quantum wells of 12 nm and 18 nm thickness and in-well carrier concentration of ∼4 × 10{sup 11} cm{sup −2} was carefully measured using spectrally resolved four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. Although the absorption at the Fermi edge is broad at this doping level, the spectrally resolved FWM shows narrow resonances. Two peaks are observed separated by the heavy hole/light hole energy splitting. Temperature dependent “rephasing” (S{sub 1}) 2DFT spectra show a rapid linear increase of the homogeneous linewidth with temperature. The dephasing rate increases faster with temperature in the narrower 12 nm quantum well, likely due to an increased carrier-phonon scattering rate. The S{sub 1} 2DFT spectra were measured using co-linear, cross-linear, and co-circular polarizations. Distinct 2DFT lineshapes were observed for co-linear and cross-linear polarizations, suggesting the existence of polarization dependent contributions. The “two-quantum coherence” (S{sub 3}) 2DFT spectra for the 12 nm quantum well show a single peak for both co-linear and co-circular polarizations.
Topology optimization of two-dimensional waveguides
Jensen, Jakob Søndergaard; Sigmund, Ole
2003-01-01
In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss.......In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss....
Interpolation problem for the solutions of linear elasticity equations based on monogenic functions
Grigor'ev, Yuri; Gürlebeck, Klaus; Legatiuk, Dmitrii
2017-11-01
Interpolation is an important tool for many practical applications, and very often it is beneficial to interpolate not only with a simple basis system, but rather with solutions of a certain differential equation, e.g. elasticity equation. A typical example for such type of interpolation are collocation methods widely used in practice. It is known, that interpolation theory is fully developed in the framework of the classical complex analysis. However, in quaternionic analysis, which shows a lot of analogies to complex analysis, the situation is more complicated due to the non-commutative multiplication. Thus, a fundamental theorem of algebra is not available, and standard tools from linear algebra cannot be applied in the usual way. To overcome these problems, a special system of monogenic polynomials the so-called Pseudo Complex Polynomials, sharing some properties of complex powers, is used. In this paper, we present an approach to deal with the interpolation problem, where solutions of elasticity equations in three dimensions are used as an interpolation basis.
CHILES, Singularity Strength of Linear Elastic Bodies by Finite Elements Method
Benzley, S.E.; Beisinger, Z.E.
1981-01-01
1 - Description of problem or function: CHILES is a finite element computer program that calculates the strength of singularities in linear elastic bodies. Plane stress, plane strain, and axisymmetric conditions are treated. Crack tip singularity problems are solved by this version of the code, but any type of integrable singularity may be properly modeled by modifying selected subroutines in the program. 2 - Method of solution: A generalized, quadrilateral finite element that includes a singular point at a corner node is incorporated in the code. The displacement formulation is used and inter-element compatibility is maintained so that monotone convergence is preserved. 3 - Restrictions on the complexity of the problem: CHILES allows three singular points to be modeled in the body being analyzed and each singular point may have coupled Mode I and II deformations. 1000 nodal points may be used
Zhu, Yongning; Wang, Yuting; Hellrung, Jeffrey; Cantarero, Alejandro; Sifakis, Eftychios; Teran, Joseph M.
2012-08-01
We present a cut cell method in R2 for enforcing Dirichlet and Neumann boundary conditions with nearly incompressible linear elastic materials in irregular domains. Virtual nodes on cut uniform grid cells are used to provide geometric flexibility in the domain boundary shape without sacrificing accuracy. We use a mixed formulation utilizing a MAC-type staggered grid with piecewise bilinear displacements centered at cell faces and piecewise constant pressures at cell centers. These discretization choices provide the necessary stability in the incompressible limit and the necessary accuracy in cut cells. Numerical experiments suggest second order accuracy in L∞. We target high-resolution problems and present a class of geometric multigrid methods for solving the discrete equations for displacements and pressures that achieves nearly optimal convergence rates independent of grid resolution.
Standard test method for linear-elastic plane-strain fracture toughness KIc of metallic materials
American Society for Testing and Materials. Philadelphia
2009-01-01
1.1 This test method covers the determination of fracture toughness (KIc) of metallic materials under predominantly linear-elastic, plane-strain conditions using fatigue precracked specimens having a thickness of 1.6 mm (0.063 in.) or greater subjected to slowly, or in special (elective) cases rapidly, increasing crack-displacement force. Details of test apparatus, specimen configuration, and experimental procedure are given in the Annexes. Note 1—Plane-strain fracture toughness tests of thinner materials that are sufficiently brittle (see 7.1) can be made using other types of specimens (1). There is no standard test method for such thin materials. 1.2 This test method is divided into two parts. The first part gives general recommendations and requirements for KIc testing. The second part consists of Annexes that give specific information on displacement gage and loading fixture design, special requirements for individual specimen configurations, and detailed procedures for fatigue precracking. Additional a...
Surek, T.; Kuon, L.G.; Luton, M.J.; Jones, J.J.
1975-01-01
For the case of linear elastic obstacles, the analysis of experimental plastic flow data is shown to have a particularly simple form when the pre-exponential factor is a single-valued function of the modulus-reduced stress. The analysis permits the separation of the stress and temperature dependence of the strain rate into those of the pre-exponential factor and the activation free energy. As a consequence, the true values of the activation enthalpy, volume and entropy also are obtained. The approach is applied to four sets of experimental data, including Zr, and the results for the pre-exponential term are examined for self-consistency in view of the assumed functional dependence
First-order system least squares for the pure traction problem in planar linear elasticity
Cai, Z.; Manteuffel, T.; McCormick, S.; Parter, S.
1996-12-31
This talk will develop two first-order system least squares (FOSLS) approaches for the solution of the pure traction problem in planar linear elasticity. Both are two-stage algorithms that first solve for the gradients of displacement, then for the displacement itself. One approach, which uses L{sup 2} norms to define the FOSLS functional, is shown under certain H{sup 2} regularity assumptions to admit optimal H{sup 1}-like performance for standard finite element discretization and standard multigrid solution methods that is uniform in the Poisson ratio for all variables. The second approach, which is based on H{sup -1} norms, is shown under general assumptions to admit optimal uniform performance for displacement flux in an L{sup 2} norm and for displacement in an H{sup 1} norm. These methods do not degrade as other methods generally do when the material properties approach the incompressible limit.
Topology optimization of two-dimensional elastic wave barriers
Van Hoorickx, C.; Sigmund, Ole; Schevenels, M.
2016-01-01
harmonic sources at a frequency in a given range, a uniform reduction of the response over a frequency range is pursued. The minimal insertion loss over the frequency range of interest is maximized. The resulting design contains features at depth leading to a reduction of the insertion loss at the lowest...... frequencies and features close to the surface leading to a reduction at the highest frequencies. For broadband sources, the average insertion loss in a frequency range is optimized. This leads to designs that especially reduce the response at high frequencies. The designs optimized for the frequency averaged...
Two-dimensional transport of tokamak plasmas
Hirshman, S.P.; Jardin, S.C.
1979-01-01
A reduced set of two-fluid transport equations is obtained from the conservation equations describing the time evolution of the differential particle number, entropy, and magnetic fluxes in an axisymmetric toroidal plasma with nested magnetic surfaces. Expanding in the small ratio of perpendicular to parallel mobilities and thermal conductivities yields as solubility constraints one-dimensional equations for the surface-averaged thermodynamic variables and magnetic fluxes. Since Ohm's law E +u x B =R', where R' accounts for any nonideal effects, only determines the particle flow relative to the diffusing magnetic surfaces, it is necessary to solve a single two-dimensional generalized differential equation, (partial/partialt) delpsi. (delp - J x B) =0, to find the absolute velocity of a magnetic surface enclosing a fixed toroidal flux. This equation is linear but nonstandard in that it involves flux surface averages of the unknown velocity. Specification of R' and the cross-field ion and electron heat fluxes provides a closed system of equations. A time-dependent coordinate transformation is used to describe the diffusion of plasma quantities through magnetic surfaces of changing shape
Terlain, Anne
1984-01-01
The 2D (two-dimensional) phase transitions and orientational order in N 2 O, CO 2 , C 2 N 2 and C 2 D 2 films physi-sorbed on the (0001) face of graphite or lamellar halides, were studied experimentally by adsorption isotherm measurements and neutron diffraction. The thermodynamic functions derived from sets of isotherms suggest that crystal monolayers of N 2 O, CO 2 , and C 2 N 2 adsorbed on graphite are orientationally ordered and that the quadrupolar interaction stabilizes the 2D crystal with respect to the 2D liquid. This stabilization leads to an increase in the 2D triple point temperature, T 2t as compared with the 2D critical temperature T 2c . For C 2 N 2 this stabilization is so pronounced that T 2t becomes virtually higher than T 2c , and the phase diagram qualitatively different, having no gas-liquid coexistence domain. From a neutron diffraction experiment we have determined the crystal structure of the C 2 N 2 monolayer. It supports our interpretation of the monolayer phase diagram. In N 2 O, CO 2 , C 2 N 2 films adsorbed on graphite the molecules lie flat on the surface and their orientational order hence differs from that in the bulk crystals resulting in a loss of adsorbate-adsorbate interaction energy. Beyond a given film thickness this loss will not be compensated by the adsorbate-substrate interaction and the film will stop growing. For most of the films studied a partial wetting transition is observed at which the film thickness increases discontinuously with temperature. Although C 2 N 2 and C 2 D 2 monolayers on graphite have comparable adsorption energies, only C 2 D 2 is adsorbed on lamellar halides. This adsorption is possible only because the monolayer has a large entropy due to orientational disorder. For C 2 N 2 , which has a higher moment of inertia, such an orientational disorder cannot exist. (author) [fr
On the hyperporous non-linear elasticity model for fusion-relevant pebble beds
Di Maio, P.A.; Giammusso, R.; Vella, G.
2010-01-01
Packed pebble beds are particular granular systems composed of a large amount of small particles, arranged in irregular lattices and surrounded by a gas filling interstitial spaces. Due to their heterogeneous structure, pebble beds have non-linear and strongly coupled thermal and mechanical behaviours whose constitutive models seem limited, being not suitable for fusion-relevant design-oriented applications. Within the framework of the modelling activities promoted for the lithiated ceramics and beryllium pebble beds foreseen in the Helium-Cooled Pebble Bed breeding blanket concept of DEMO, at the Department of Nuclear Engineering of the University of Palermo (DIN) a thermo-mechanical constitutive model has been set-up assuming that pebble beds can be considered as continuous, homogeneous and isotropic media. The present paper deals with the DIN non-linear elasticity constitutive model, based on the assumption that during the reversible straining of a pebble bed its effective logarithmic bulk modulus depends on the equivalent pressure according to a modified power law and its effective Poisson modulus remains constant. In these hypotheses the functional dependence of the effective tangential and secant bed deformation moduli on either the equivalent pressure or the volumetric strain have been derived in a closed analytical form. A procedure has been, then, defined to assess the model parameters for a given pebble bed from its oedometric test results and it has been applied to both polydisperse lithium orthosilicate and single size beryllium pebble beds.
TWO-DIMENSIONAL APPROXIMATION OF EIGENVALUE PROBLEMS IN SHELL THEORY: FLEXURAL SHELLS
无
2000-01-01
The eigenvalue problem for a thin linearly elastic shell, of thickness 2e, clamped along its lateral surface is considered. Under the geometric assumption on the middle surface of the shell that the space of inextensional displacements is non-trivial, the authors obtain, as ε→0,the eigenvalue problem for the two-dimensional"flexural shell"model if the dimension of the space is infinite. If the space is finite dimensional, the limits of the eigenvalues could belong to the spectra of both flexural and membrane shells. The method consists of rescaling the variables and studying the problem over a fixed domain. The principal difficulty lies in obtaining suitable a priori estimates for the scaled eigenvalues.
Piezoelectricity in Two-Dimensional Materials
Wu, Tao; Zhang, Hua
2015-01-01
Powering up 2D materials: Recent experimental studies confirmed the existence of piezoelectricity - the conversion of mechanical stress into electricity - in two-dimensional single-layer MoS2 nanosheets. The results represent a milestone towards
Construction of two-dimensional quantum chromodynamics
Klimek, S.; Kondracki, W.
1987-12-01
We present a sketch of the construction of the functional measure for the SU(2) quantum chromodynamics with one generation of fermions in two-dimensional space-time. The method is based on a detailed analysis of Wilson loops.
Development of Two-Dimensional NMR
Home; Journals; Resonance – Journal of Science Education; Volume 20; Issue 11. Development of Two-Dimensional NMR: Strucure Determination of Biomolecules in Solution. Anil Kumar. General Article Volume 20 Issue 11 November 2015 pp 995-1002 ...
Phase transitions in two-dimensional systems
Salinas, S.R.A.
1983-01-01
Some experiences are related using synchrotron radiation beams, to characterize solid-liquid (fusion) and commensurate solid-uncommensurate solid transitions in two-dimensional systems. Some ideas involved in the modern theories of two-dimensional fusion are shortly exposed. The systems treated consist of noble gases (Kr,Ar,Xe) adsorbed in the basal plane of graphite and thin films formed by some liquid crystal shells. (L.C.) [pt
Jiang, Yi; Li, Guoyang; Qian, Lin-Xue; Liang, Si; Destrade, Michel; Cao, Yanping
2015-10-01
We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus [Formula: see text] varies from 1.8 to 3.2 kPa, the stiffening parameter [Formula: see text] of the hyperelastic Demiray-Fung model from 0.13 to 0.73, and the third- [Formula: see text] and fourth-order [Formula: see text] constants of weakly nonlinear elasticity from [Formula: see text]1.3 to [Formula: see text]20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired [Formula: see text] test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery.
Garcia, R.D.M.
1984-01-01
A new technique for generating the isotropic and linearly anisotropic componets of elastic and discrete inelastic transfer matrices is proposed. The technique allows certain angular integrals to be expressed in terms of functions that can be computed by recursion relations or series expansions alternatively to the use of numerical quadratures. (Author) [pt
De Beer, Morris
2008-07-01
Full Text Available - wave and ρ the material density. The elastic moduli P-wave modulus, M, is defined so that M = K + 4µ / 3 and M can then be determined by Equation 11, with a known speed Vp P MV 2 ρ = (11) It should however also... gas (such as air within compacted road materials), the adiabatic bulk modulus KS is approximately given by pKS κ= (4) Where: κ is the adiabatic index, (sometimes calledγ ); p is the pressure. In a fluid (such as moisture...
Transport behavior of water molecules through two-dimensional nanopores
Zhu, Chongqin; Li, Hui; Meng, Sheng
2014-01-01
Water transport through a two-dimensional nanoporous membrane has attracted increasing attention in recent years thanks to great demands in water purification and desalination applications. However, few studies have been reported on the microscopic mechanisms of water transport through structured nanopores, especially at the atomistic scale. Here we investigate the microstructure of water flow through two-dimensional model graphene membrane containing a variety of nanopores of different size by using molecular dynamics simulations. Our results clearly indicate that the continuum flow transits to discrete molecular flow patterns with decreasing pore sizes. While for pores with a diameter ≥15 Å water flux exhibits a linear dependence on the pore area, a nonlinear relationship between water flux and pore area has been identified for smaller pores. We attribute this deviation from linear behavior to the presence of discrete water flow, which is strongly influenced by the water-membrane interaction and hydrogen bonding between water molecules
Nematic Equilibria on a Two-Dimensional Annulus
Lewis, A. H.; Aarts, D. G. A. L.; Howell, P. D.; Majumdar, A.
2017-01-01
We study planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, in the Oseen–Frank theoretical framework. We analyze a radially invariant defect-free state and compute analytic stability criteria for this state in terms of the elastic anisotropy, annular aspect ratio, and anchoring strength. In the strong anchoring case, we define and characterize a new spiral-like equilibrium which emerges as the defect-free state loses stability. In the weak anchoring case, we compute stability diagrams that quantify the response of the defect-free state to radial and azimuthal perturbations. We study sector equilibria on sectors of an annulus, including the effects of weak anchoring and elastic anisotropy, giving novel insights into the correlation between preferred numbers of boundary defects and the geometry. We numerically demonstrate that these sector configurations can approximate experimentally observed equilibria with boundary defects.
Nematic Equilibria on a Two-Dimensional Annulus
Lewis, A. H.
2017-01-16
We study planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, in the Oseen–Frank theoretical framework. We analyze a radially invariant defect-free state and compute analytic stability criteria for this state in terms of the elastic anisotropy, annular aspect ratio, and anchoring strength. In the strong anchoring case, we define and characterize a new spiral-like equilibrium which emerges as the defect-free state loses stability. In the weak anchoring case, we compute stability diagrams that quantify the response of the defect-free state to radial and azimuthal perturbations. We study sector equilibria on sectors of an annulus, including the effects of weak anchoring and elastic anisotropy, giving novel insights into the correlation between preferred numbers of boundary defects and the geometry. We numerically demonstrate that these sector configurations can approximate experimentally observed equilibria with boundary defects.
Acoustic metamaterials for new two-dimensional sonic devices
Torrent, Daniel; Sanchez-Dehesa, Jose [Wave Phenomena Group, Department of Electronic Engineering, Polytechnic University of Valencia, C/Camino de Vera sn, E-46022 Valencia (Spain)
2007-09-15
It has been shown that two-dimensional arrays of rigid or fluidlike cylinders in a fluid or a gas define, in the limit of large wavelengths, a class of acoustic metamaterials whose effective parameters (sound velocity and density) can be tailored up to a certain limit. This work goes a step further by considering arrays of solid cylinders in which the elastic properties of cylinders are taken into account. We have also treated mixtures of two different elastic cylinders. It is shown that both effects broaden the range of acoustic parameters available for designing metamaterials. For example, it is predicted that metamaterials with perfect matching of impedance with air are now possible by using aerogel and rigid cylinders equally distributed in a square lattice. As a potential application of the proposed metamaterial, we present a gradient index lens for airborne sound (i.e. a sonic Wood lens) whose functionality is demonstrated by multiple scattering simulations.
Two-dimensional simulation of the MHD stability, (1)
Kurita, Gen-ichi; Amano, Tsuneo.
1976-03-01
The two-dimensional computer code has been prepared to study MHD stability of an axisymmetric toroidal plasma with and without the surrounding vacuum region. It also includes the effect of magnetic surfaces with non-circular cross sections. The linearized equations of motion are solved as an initial value problem. The results by computer simulation are compared with those by the theory for the cylindrical plasma; they are in good agreement. (auth.)
Bal, Guillaume; Bellis, Cédric; Imperiale, Sébastien; Monard, François
2014-01-01
Within the framework of linear elasticity we assume the availability of internal full-field measurements of the continuum deformations of a non-homogeneous isotropic solid. The aim is the quantitative reconstruction of the associated moduli. A simple gradient system for the sought constitutive parameters is derived algebraically from the momentum equation, whose coefficients are expressed in terms of the measured displacement fields and their spatial derivatives. Direct integration of this system is discussed to finally demonstrate the inexpediency of such an approach when dealing with noisy data. Upon using polluted measurements, an alternative variational formulation is deployed to invert for the physical parameters. Analysis of this latter inversion procedure provides existence and uniqueness results while the reconstruction stability with respect to the measurements is investigated. As the inversion procedure requires differentiating the measurements twice, a numerical differentiation scheme based on an ad hoc regularization then allows an optimally stable reconstruction of the sought moduli. Numerical results are included to illustrate and assess the performance of the overall approach. (paper)
Kim, Dae-Hyeong; Song, Jizhou; Choi, Won Mook; Kim, Hoon-Sik; Kim, Rak-Hwan; Liu, Zhuangjian; Huang, Yonggang Y; Hwang, Keh-Chih; Zhang, Yong-wei; Rogers, John A
2008-12-02
Electronic systems that offer elastic mechanical responses to high-strain deformations are of growing interest because of their ability to enable new biomedical devices and other applications whose requirements are impossible to satisfy with conventional wafer-based technologies or even with those that offer simple bendability. This article introduces materials and mechanical design strategies for classes of electronic circuits that offer extremely high stretchability, enabling them to accommodate even demanding configurations such as corkscrew twists with tight pitch (e.g., 90 degrees in approximately 1 cm) and linear stretching to "rubber-band" levels of strain (e.g., up to approximately 140%). The use of single crystalline silicon nanomaterials for the semiconductor provides performance in stretchable complementary metal-oxide-semiconductor (CMOS) integrated circuits approaching that of conventional devices with comparable feature sizes formed on silicon wafers. Comprehensive theoretical studies of the mechanics reveal the way in which the structural designs enable these extreme mechanical properties without fracturing the intrinsically brittle active materials or even inducing significant changes in their electrical properties. The results, as demonstrated through electrical measurements of arrays of transistors, CMOS inverters, ring oscillators, and differential amplifiers, suggest a valuable route to high-performance stretchable electronics.
Ateş, Filiz; Hug, François; Bouillard, Killian; Jubeau, Marc; Frappart, Thomas; Couade, Mathieu; Bercoff, Jeremy; Nordez, Antoine
2015-08-01
Muscle shear elastic modulus is linearly related to muscle torque during low-level contractions (torque over the entire range of isometric contraction and (ii) the influence of the size of the region of interest (ROI) used to average the shear modulus value. Ten healthy males performed two incremental isometric little finger abductions. The joint torque produced by Abductor Digiti Minimi was considered as an index of muscle torque and elastic modulus. A high coefficient of determination (R(2)) (range: 0.86-0.98) indicated that the relationship between elastic modulus and torque can be accurately modeled by a linear regression over the entire range (0% to 100% of MVC). The changes in shear elastic modulus as a function of torque were highly repeatable. Lower R(2) values (0.89±0.13 for 1/16 of ROI) and significantly increased absolute errors were observed when the shear elastic modulus was averaged over smaller ROI, half, 1/4 and 1/16 of the full ROI) than the full ROI (mean size: 1.18±0.24cm(2)). It suggests that the ROI should be as large as possible for accurate measurement of muscle shear modulus. Copyright © 2015 Elsevier Ltd. All rights reserved.
Phason elasticity and surface roughening
Tang Leihan; Jaric, M.V.
1990-01-01
The phason elasticity of two-dimensional (2D) equilibrium quasicrystals is discussed in analogy with surface roughening phenomena. Taking a Penrose tiling model as an example, we show that the phason elastic energy is linear in the phason strain at zero temperature (T = 0), but becomes quadratic at any T > 0 and sufficiently small strain. Heuristic and real-space renormalization group arguments are given for the thermal roughening of the hyper-surface which represents quasicrystal tiling. Monte Carlo method is applied to illustrate the logarithmically diverging phason fluctuations and power-law diffraction intensities at T > 0. For three-dimensional systems, we present arguments which suggest a finite temperature transition between two quasicrystal phases, characterized by linear and quadratic phason elastic energy, respectively. (author). 17 refs, 12 figs
Two-dimensional nuclear magnetic resonance spectroscopy
Bax, A.; Lerner, L.
1986-01-01
Great spectral simplification can be obtained by spreading the conventional one-dimensional nuclear magnetic resonance (NMR) spectrum in two independent frequency dimensions. This so-called two-dimensional NMR spectroscopy removes spectral overlap, facilitates spectral assignment, and provides a wealth of additional information. For example, conformational information related to interproton distances is available from resonance intensities in certain types of two-dimensional experiments. Another method generates 1 H NMR spectra of a preselected fragment of the molecule, suppressing resonances from other regions and greatly simplifying spectral appearance. Two-dimensional NMR spectroscopy can also be applied to the study of 13 C and 15 N, not only providing valuable connectivity information but also improving sensitivity of 13 C and 15 N detection by up to two orders of magnitude. 45 references, 10 figures
Two-dimensional x-ray diffraction
He, Bob B
2009-01-01
Written by one of the pioneers of 2D X-Ray Diffraction, this useful guide covers the fundamentals, experimental methods and applications of two-dimensional x-ray diffraction, including geometry convention, x-ray source and optics, two-dimensional detectors, diffraction data interpretation, and configurations for various applications, such as phase identification, texture, stress, microstructure analysis, crystallinity, thin film analysis and combinatorial screening. Experimental examples in materials research, pharmaceuticals, and forensics are also given. This presents a key resource to resea
Equivalence of two-dimensional gravities
Mohammedi, N.
1990-01-01
The authors find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL(2,R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2 + 1 dimensional gravity. The authors present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given
Streit, R.D.
1981-01-01
The failure evaluation of Pressurized Water Reactor (PWR) primary coolant loop pipe is often based on a plastic limit load criterion; i.e., failure occurs when the stress on the pipe section exceeds the material flow stress. However, in addition the piping system must be safe against crack propagation at stresses less than those leading to plastic instability. In this paper, elastic, elastic-plastic, and fully-plastic failure models are evaluated, and the requirements for piping integrity based on these models are compared. The model yielding the 'more' critical criteria for the given geometry and loading conditions defines the appropriate failure criterion. The pipe geometry and loading used in this study was choosen based on an evaluation of a guillotine break in a PWR primary coolant loop. It is assumed that the piping may contain cracks. Since a deep circumferential crack, can lead to a guillotine pipe break without prior leaking and thus without warning it is the focus of the failure model comparison study. The hot leg pipe, a 29 in. I.D. by 2.5 in. wall thickness stainless pipe, was modeled in this investigation. Cracks up to 90% through the wall were considered. The loads considered in this evaluation result from the internal pressure, dead weight, and seismic stresses. For the case considered, the internal pressure contributes the most to the failure loading. The maximum moment stress due to the dead weight and seismic moments are simply added to the pressure stress. Thus, with the circumferential crack geometry and uniform pressure stress, the problem is axisymmetric. It is analyzed using NIKE2D--an implicit, finite deformation, finite element code for analyzing two-dimensional elastic-plastic problems. (orig./GL)
Poincare' maps of impulsed oscillators and two-dimensional dynamics
Lupini, R.; Lenci, S.; Gardini, L.; Urbino Univ.
1996-01-01
The Poincare' map of one-dimensional linear oscillators subject to periodic, non-linear and time-delayed impulses is shown to reduce to a family of plane maps with possible non-uniqueness of the inverse. By restricting the analysis to a convenient form of the impulse function, a variety of interesting dynamical behaviours in this family are pointed out, including multistability and homoclinic bifurcations. Critical curves of two-dimensional endomorphisms are used to identify the structure of absorbing areas and their bifurcations
Analytical simulation of two dimensional advection dispersion ...
The study was designed to investigate the analytical simulation of two dimensional advection dispersion equation of contaminant transport. The steady state flow condition of the contaminant transport where inorganic contaminants in aqueous waste solutions are disposed of at the land surface where it would migrate ...
Analytical Simulation of Two Dimensional Advection Dispersion ...
ADOWIE PERE
ABSTRACT: The study was designed to investigate the analytical simulation of two dimensional advection dispersion equation of contaminant transport. The steady state flow condition of the contaminant transport where inorganic contaminants in aqueous waste solutions are disposed of at the land surface where it would ...
Sums of two-dimensional spectral triples
Christensen, Erik; Ivan, Cristina
2007-01-01
construct a sum of two dimensional modules which reflects some aspects of the topological dimensions of the compact metric space, but this will only give the metric back approximately. At the end we make an explicit computation of the last module for the unit interval in. The metric is recovered exactly...
Stability of two-dimensional vorticity filaments
Elhmaidi, D.; Provenzale, A.; Lili, T.; Babiano, A.
2004-01-01
We discuss the results of a numerical study on the stability of two-dimensional vorticity filaments around a circular vortex. We illustrate how the stability of the filaments depends on the balance between the strain associated with the far field of the vortex and the local vorticity of the filament, and we discuss an empirical criterion for filament stability
Two-Dimensional Motions of Rockets
Kang, Yoonhwan; Bae, Saebyok
2007-01-01
We analyse the two-dimensional motions of the rockets for various types of rocket thrusts, the air friction and the gravitation by using a suitable representation of the rocket equation and the numerical calculation. The slope shapes of the rocket trajectories are discussed for the three types of rocket engines. Unlike the projectile motions, the…
Two-dimensional microstrip detector for neutrons
Oed, A [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)
1997-04-01
Because of their robust design, gas microstrip detectors, which were developed at ILL, can be assembled relatively quickly, provided the prefabricated components are available. At the beginning of 1996, orders were received for the construction of three two-dimensional neutron detectors. These detectors have been completed. The detectors are outlined below. (author). 2 refs.
Conformal invariance and two-dimensional physics
Zuber, J.B.
1993-01-01
Actually, physicists and mathematicians are very interested in conformal invariance: geometric transformations which keep angles. This symmetry is very important for two-dimensional systems as phase transitions, string theory or node mathematics. In this article, the author presents the conformal invariance and explains its usefulness
Matching Two-dimensional Gel Electrophoresis' Spots
Dos Anjos, António; AL-Tam, Faroq; Shahbazkia, Hamid Reza
2012-01-01
This paper describes an approach for matching Two-Dimensional Electrophoresis (2-DE) gels' spots, involving the use of image registration. The number of false positive matches produced by the proposed approach is small, when compared to academic and commercial state-of-the-art approaches. This ar...
Two-dimensional membranes in motion
Davidovikj, D.
2018-01-01
This thesis revolves around nanomechanical membranes made of suspended two - dimensional materials. Chapters 1-3 give an introduction to the field of 2D-based nanomechanical devices together with an overview of the underlying physics and the measurementtools used in subsequent chapters. The research
Extended Polymorphism of Two-Dimensional Material
Yoshida, Masaro; Ye, Jianting; Zhang, Yijin; Imai, Yasuhiko; Kimura, Shigeru; Fujiwara, Akihiko; Nishizaki, Terukazu; Kobayashi, Norio; Nakano, Masaki; Iwasa, Yoshihiro
When controlling electronic properties of bulk materials, we usually assume that the basic crystal structure is fixed. However, in two-dimensional (2D) materials, atomic structure or to functionalize their properties. Various polymorphs can exist in transition metal dichalcogenides (TMDCs) from
Piezoelectricity in Two-Dimensional Materials
Wu, Tao
2015-02-25
Powering up 2D materials: Recent experimental studies confirmed the existence of piezoelectricity - the conversion of mechanical stress into electricity - in two-dimensional single-layer MoS2 nanosheets. The results represent a milestone towards embedding low-dimensional materials into future disruptive technologies. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA.
Yuan, Rong [Univ. of California, Berkeley, CA (United States)
2007-01-01
Linear elastic fracture mechanics is widely used in industry because it established simple and explicit relationships between the permissible loading conditions and the critical crack size that is allowed in a structure. Stress intensity factors are the above-mentioned functional expressions that relate load with crack size through geometric functions or weight functions. Compliance functions are to determine the crack/flaw size in a structure when optical inspection is inconvenient. As a result, geometric functions, weight functions and compliance functions have been intensively studied to determine the stress intensity factor expressions for different geometries. However, the relations between these functions have received less attention. This work is therefore to investigate the intrinsic relationships between these functions. Theoretical derivation was carried out and the results were verified on single-edge cracked plate under tension and bending. It is found out that the geometric function is essentially the non-dimensional weight function at the loading point. The compliance function is composed of two parts: a varying part due to crack extension and a constant part from the intact structure if no crack exists. The derivative of the compliance function at any location is the product of the geometric function and the weight function at the evaluation point. Inversely, the compliance function can be acquired by the integration of the product of the geometric function and the weight function with respect to the crack size. The integral constant is just the unchanging compliance from the intact structure. Consequently, a special application of the relations is to obtain the compliance functions along a crack once the geometric function and weight functions are known. Any of the three special functions can be derived once the other two functions are known. These relations may greatly simplify the numerical process in obtaining either geometric functions, weight
D. A. Fetisov
2015-01-01
Full Text Available The controllability conditions are well known if we speak about linear stationary systems: a linear stationary system is controllable if and only if the dimension of the state vector is equal to the rank of the controllability matrix. The concept of the controllability matrix is extended to affine systems, but relations between affine systems controllability and properties of this matrix are more complicated. Various controllability conditions are set for affine systems, but they deal as usual either with systems of some special form or with controllability in some small neighborhood of the concerned point. An affine system is known to be controllable if the system is equivalent to a system of a canonical form, which is defined and regular in the whole space of states. In this case, the system is said to be feedback linearizable in the space of states. However there are examples, which illustrate that a system can be controllable even if it is not feedback linearizable in any open subset in the space of states. In this article we deal with such systems.Affine systems with two-dimensional control are considered. The system in question is assumed to be equivalent to a system of a quasicanonical form with two-dimensional zero dynamics which is defined and regular in the whole space of states. Therefore the controllability of the original system is equivalent to the controllability of the received system of a quasicanonical form. In this article the sufficient condition for an available solution of the terminal problem is proven for systems of a quasicanonical form with two-dimensional control and two-dimensional zero dynamics. The condition is valid in the case of an arbitrary time interval and arbitrary initial and finite states of the system. Therefore the controllability condition is set for systems of a quasicanonical form with two-dimensional control and two-dimensional zero dynamics. An example is given which illustrates how the proved
Two-dimensional confinement of heavy fermions
Shishido, Hiroaki; Shibauchi, Takasada; Matsuda, Yuji; Terashima, Takahito
2010-01-01
Metallic systems with the strongest electron correlations are realized in certain rare-earth and actinide compounds whose physics are dominated by f-electrons. These materials are known as heavy fermions, so called because the effective mass of the conduction electrons is enhanced via correlation effects up to as much as several hundreds times the free electron mass. To date the electronic structure of all heavy-fermion compounds is essentially three-dimensional. Here we report on the first realization of a two-dimensional heavy-fermion system, where the dimensionality is adjusted in a controllable fashion by fabricating heterostructures using molecular beam epitaxy. The two-dimensional heavy fermion system displays striking deviations from the standard Fermi liquid low-temperature electronic properties. (author)
Two-dimensional sensitivity calculation code: SENSETWO
Yamauchi, Michinori; Nakayama, Mitsuo; Minami, Kazuyoshi; Seki, Yasushi; Iida, Hiromasa.
1979-05-01
A SENSETWO code for the calculation of cross section sensitivities with a two-dimensional model has been developed, on the basis of first order perturbation theory. It uses forward neutron and/or gamma-ray fluxes and adjoint fluxes obtained by two-dimensional discrete ordinates code TWOTRAN-II. The data and informations of cross sections, geometry, nuclide density, response functions, etc. are transmitted to SENSETWO by the dump magnetic tape made in TWOTRAN calculations. The required input for SENSETWO calculations is thus very simple. The SENSETWO yields as printed output the cross section sensitivities for each coarse mesh zone and for each energy group, as well as the plotted output of sensitivity profiles specified by the input. A special feature of the code is that it also calculates the reaction rate with the response function used as the adjoint source in TWOTRAN adjoint calculation and the calculated forward flux from the TWOTRAN forward calculation. (author)
Two-dimensional ranking of Wikipedia articles
Zhirov, A. O.; Zhirov, O. V.; Shepelyansky, D. L.
2010-10-01
The Library of Babel, described by Jorge Luis Borges, stores an enormous amount of information. The Library exists ab aeterno. Wikipedia, a free online encyclopaedia, becomes a modern analogue of such a Library. Information retrieval and ranking of Wikipedia articles become the challenge of modern society. While PageRank highlights very well known nodes with many ingoing links, CheiRank highlights very communicative nodes with many outgoing links. In this way the ranking becomes two-dimensional. Using CheiRank and PageRank we analyze the properties of two-dimensional ranking of all Wikipedia English articles and show that it gives their reliable classification with rich and nontrivial features. Detailed studies are done for countries, universities, personalities, physicists, chess players, Dow-Jones companies and other categories.
Toward two-dimensional search engines
Ermann, L; Shepelyansky, D L; Chepelianskii, A D
2012-01-01
We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of ingoing links, while CheiRank orders nodes proportionally to a number of outgoing links. In this way, the ranking of nodes becomes two dimensional which paves the way for the development of two-dimensional search engines of a new type. Statistical properties of information flow on the PageRank–CheiRank plane are analyzed for networks of British, French and Italian universities, Wikipedia, Linux Kernel, gene regulation and other networks. A special emphasis is done for British universities networks using the large database publicly available in the UK. Methods of spam links control are also analyzed. (paper)
Acoustic phonon emission by two dimensional plasmons
Mishonov, T.M.
1990-06-01
Acoustic wave emission of the two dimensional plasmons in a semiconductor or superconductor microstructure is investigated by using the phenomenological deformation potential within the jellium model. The plasmons are excited by the external electromagnetic (e.m.) field. The power conversion coefficient of e.m. energy into acoustic wave energy is also estimated. It is shown, the coherent transformation has a sharp resonance at the plasmon frequency of the two dimensional electron gas (2DEG). The incoherent transformation of the e.m. energy is generated by ohmic dissipation of 2DEG. The method proposed for coherent phonon beam generation can be very effective for high mobility 2DEG and for thin superconducting layers if the plasmon frequency ω is smaller than the superconducting gap 2Δ. (author). 21 refs, 1 fig
Confined catalysis under two-dimensional materials
Li, Haobo; Xiao, Jianping; Fu, Qiang; Bao, Xinhe
2017-01-01
Small spaces in nanoreactors may have big implications in chemistry, because the chemical nature of molecules and reactions within the nanospaces can be changed significantly due to the nanoconfinement effect. Two-dimensional (2D) nanoreactor formed under 2D materials can provide a well-defined model system to explore the confined catalysis. We demonstrate a general tendency for weakened surface adsorption under the confinement of graphene overlayer, illustrating the feasible modulation of su...
Two-Dimensional Extreme Learning Machine
Bo Jia
2015-01-01
(BP networks. However, like many other methods, ELM is originally proposed to handle vector pattern while nonvector patterns in real applications need to be explored, such as image data. We propose the two-dimensional extreme learning machine (2DELM based on the very natural idea to deal with matrix data directly. Unlike original ELM which handles vectors, 2DELM take the matrices as input features without vectorization. Empirical studies on several real image datasets show the efficiency and effectiveness of the algorithm.
Superintegrability on the two dimensional hyperboloid
Akopyan, E.; Pogosyan, G.S.; Kalnins, E.G.; Miller, W. Jr
1998-01-01
This work is devoted to the investigation of the quantum mechanical systems on the two dimensional hyperboloid which admit separation of variables in at least two coordinate systems. Here we consider two potentials introduced in a paper of C.P.Boyer, E.G.Kalnins and P.Winternitz, which haven't been studied yet. An example of an interbasis expansion is given and the structure of the quadratic algebra generated by the integrals of motion is carried out
Two-dimensional Kagome photonic bandgap waveguide
Nielsen, Jens Bo; Søndergaard, Thomas; Libori, Stig E. Barkou
2000-01-01
The transverse-magnetic photonic-bandgap-guidance properties are investigated for a planar two-dimensional (2-D) Kagome waveguide configuration using a full-vectorial plane-wave-expansion method. Single-moded well-localized low-index guided modes are found. The localization of the optical modes...... is investigated with respect to the width of the 2-D Kagome waveguide, and the number of modes existing for specific frequencies and waveguide widths is mapped out....
Mechanical exfoliation of two-dimensional materials
Gao, Enlai; Lin, Shao-Zhen; Qin, Zhao; Buehler, Markus J.; Feng, Xi-Qiao; Xu, Zhiping
2018-06-01
Two-dimensional materials such as graphene and transition metal dichalcogenides have been identified and drawn much attention over the last few years for their unique structural and electronic properties. However, their rise begins only after these materials are successfully isolated from their layered assemblies or adhesive substrates into individual monolayers. Mechanical exfoliation and transfer are the most successful techniques to obtain high-quality single- or few-layer nanocrystals from their native multi-layer structures or their substrate for growth, which involves interfacial peeling and intralayer tearing processes that are controlled by material properties, geometry and the kinetics of exfoliation. This procedure is rationalized in this work through theoretical analysis and atomistic simulations. We propose a criterion to assess the feasibility for the exfoliation of two-dimensional sheets from an adhesive substrate without fracturing itself, and explore the effects of material and interface properties, as well as the geometrical, kinetic factors on the peeling behaviors and the torn morphology. This multi-scale approach elucidates the microscopic mechanism of the mechanical processes, offering predictive models and tools for the design of experimental procedures to obtain single- or few-layer two-dimensional materials and structures.
A non-linear elastic constitutive framework for replicating plastic deformation in solids.
Roberts, Scott Alan; Schunk, Peter Randall
2014-02-01
Ductile metals and other materials typically deform plastically under large applied loads; a behavior most often modeled using plastic deformation constitutive models. However, it is possible to capture some of the key behaviors of plastic deformation using only the framework for nonlinear elastic mechanics. In this paper, we develop a phenomenological, hysteretic, nonlinear elastic constitutive model that captures many of the features expected of a plastic deformation model. This model is based on calculating a secant modulus directly from a materials stress-strain curve. Scalar stress and strain values are obtained in three dimensions by using the von Mises invariants. Hysteresis is incorporated by tracking an additional history variable and assuming an elastic unloading response. This model is demonstrated in both single- and multi-element simulations under varying strain conditions.
Seismic isolation of buildings on two dimensional phononic crystal foundation
Han, Lin; Li, Xiao-mei; Zhang, Yan
2017-11-01
In order to realize the seismic isolation of buildings, we establish the two dimensional phononic crystal (PC) foundation which has the cell with the size close to the regular concrete test specimens, and is composed of the concrete base, rubber coating and lead cylindrical core. We study the in-plane band gap (BG) characteristics in it, through the analysis of the frequency dispersion relation and frequency response result. To lower the start BG frequency to the seismic frequency range, we also study the influences of material parameters (the elastic modulus of coating and density of cylindrical core) and geometry parameters (the thickness of coating, radius of cylindrical core and lattice constant) on BG ranges. The study could help to design the PC foundation for seismic isolation of building.
Inverse radiative transfer problems in two-dimensional heterogeneous media
Tito, Mariella Janette Berrocal
2001-01-01
The analysis of inverse problems in participating media where emission, absorption and scattering take place has several relevant applications in engineering and medicine. Some of the techniques developed for the solution of inverse problems have as a first step the solution of the direct problem. In this work the discrete ordinates method has been used for the solution of the linearized Boltzmann equation in two dimensional cartesian geometry. The Levenberg - Marquardt method has been used for the solution of the inverse problem of internal source and absorption and scattering coefficient estimation. (author)
All or nothing: On the small fluctuations of two-dimensional string theoretic black holes
Gilbert, Gerald [Univ. of Maryland, College Park, MD (United States); Raiten, Eric [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
1992-10-01
A comprehensive analysis of small fluctuations about two-dimensional string-theoretic and string-inspired black holes is presented. It is shown with specific examples that two-dimensional black holes behave in a radically different way from all known black holes in four dimensions. For both the SL(2,R)/U(1) black hole and the two-dimensional black hole coupled to a massive dilaton with constant field strength, it is shown that there are a {\\it continuous infinity} of solutions to the linearized equations of motion, which are such that it is impossible to ascertain the classical linear response. It is further shown that the two-dimensional black hole coupled to a massive, linear dilaton admits {\\it no small fluctuations at all}. We discuss possible implications of our results for the Callan-Giddings-Harvey-Strominger black hole.
Vector (two-dimensional) magnetic phenomena
Enokizono, Masato
2002-01-01
In this paper, some interesting phenomena were described from the viewpoint of two-dimensional magnetic property, which is reworded with the vector magnetic property. It shows imperfection of conventional magnetic property and some interested phenomena were discovered, too. We found magnetic materials had the strong nonlinearity both magnitude and spatial phase due to the relationship between the magnetic field strength H-vector and the magnetic flux density B-vector. Therefore, magnetic properties should be defined as the vector relationship. Furthermore, the new Barukhausen signal was observed under rotating flux. (Author)
Two-dimensional Semiconductor-Superconductor Hybrids
Suominen, Henri Juhani
This thesis investigates hybrid two-dimensional semiconductor-superconductor (Sm-S) devices and presents a new material platform exhibiting intimate Sm-S coupling straight out of the box. Starting with the conventional approach, we investigate coupling superconductors to buried quantum well....... To overcome these issues we integrate the superconductor directly into the semiconducting material growth stack, depositing it in-situ in a molecular beam epitaxy system under high vacuum. We present a number of experiments on these hybrid heterostructures, demonstrating near unity interface transparency...
Optimized two-dimensional Sn transport (BISTRO)
Palmiotti, G.; Salvatores, M.; Gho, C.
1990-01-01
This paper reports on an S n two-dimensional transport module developed for the French fast reactor code system CCRR to optimize algorithms in order to obtain the best performance in terms of computational time. A form of diffusion synthetic acceleration was adopted, and a special effort was made to solve the associated diffusion equation efficiently. The improvements in the algorithms, along with the use of an efficient programming language, led to a significant gain in computational time with respect to the DOT code
Binding energy of two-dimensional biexcitons
Singh, Jai; Birkedal, Dan; Vadim, Lyssenko
1996-01-01
Using a model structure for a two-dimensional (2D) biexciton confined in a quantum well, it is shown that the form of the Hamiltonian of the 2D biexciton reduces into that of an exciton. The binding energies and Bohr radii of a 2D biexciton in its various internal energy states are derived...... analytically using the fractional dimension approach. The ratio of the binding energy of a 2D biexciton to that of a 2D exciton is found to be 0.228, which agrees very well with the recent experimental value. The results of our approach are compared with those of earlier theories....
Airy beams on two dimensional materials
Imran, Muhammad; Li, Rujiang; Jiang, Yuyu; Lin, Xiao; Zheng, Bin; Dehdashti, Shahram; Xu, Zhiwei; Wang, Huaping
2018-05-01
We propose that quasi-transverse-magnetic (quasi-TM) Airy beams can be supported on two dimensional (2D) materials. By taking graphene as a typical example, the solution of quasi-TM Airy beams is studied under the paraxial approximation. The analytical field intensity in a bilayer graphene-based planar plasmonic waveguide is confirmed by the simulation results. Due to the tunability of the chemical potential of graphene, the self-accelerating behavior of the quasi-TM Airy beam can be steered effectively. 2D materials thus provide a good platform to investigate the propagation of Airy beams.
Two-dimensional heat flow apparatus
McDougall, Patrick; Ayars, Eric
2014-06-01
We have created an apparatus to quantitatively measure two-dimensional heat flow in a metal plate using a grid of temperature sensors read by a microcontroller. Real-time temperature data are collected from the microcontroller by a computer for comparison with a computational model of the heat equation. The microcontroller-based sensor array allows previously unavailable levels of precision at very low cost, and the combination of measurement and modeling makes for an excellent apparatus for the advanced undergraduate laboratory course.
Angela Mihai, L.; Goriely, Alain
2013-01-01
Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects
Decoherence in two-dimensional quantum walks
Oliveira, A. C.; Portugal, R.; Donangelo, R.
2006-01-01
We analyze the decoherence in quantum walks in two-dimensional lattices generated by broken-link-type noise. In this type of decoherence, the links of the lattice are randomly broken with some given constant probability. We obtain the evolution equation for a quantum walker moving on two-dimensional (2D) lattices subject to this noise, and we point out how to generalize for lattices in more dimensions. In the nonsymmetric case, when the probability of breaking links in one direction is different from the probability in the perpendicular direction, we have obtained a nontrivial result. If one fixes the link-breaking probability in one direction, and gradually increases the probability in the other direction from 0 to 1, the decoherence initially increases until it reaches a maximum value, and then it decreases. This means that, in some cases, one can increase the noise level and still obtain more coherence. Physically, this can be explained as a transition from a decoherent 2D walk to a coherent 1D walk
Two-Dimensional Theory of Scientific Representation
A Yaghmaie
2013-03-01
Full Text Available Scientific representation is an interesting topic for philosophers of science, many of whom have recently explored it from different points of view. There are currently two competing approaches to the issue: cognitive and non-cognitive, and each of them claims its own merits over the other. This article tries to provide a hybrid theory of scientific representation, called Two-Dimensional Theory of Scientific Representation, which has the merits of the two accounts and is free of their shortcomings. To do this, we will argue that although scientific representation needs to use the notion of intentionality, such a notion is defined and realized in a simply structural form contrary to what cognitive approach says about intentionality. After a short introduction, the second part of the paper is devoted to introducing theories of scientific representation briefly. In the third part, the structural accounts of representation will be criticized. The next step is to introduce the two-dimensional theory which involves two key components: fixing and structural fitness. It will be argued that fitness is an objective and non-intentional relation, while fixing is intentional.
Tahara, Masaki [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503 (Japan); Kim, Hee Young, E-mail: heeykim@ims.tsukuba.ac.jp [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Inamura, Tomonari; Hosoda, Hideki [Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503 (Japan); Miyazaki, Shuichi, E-mail: miyazaki@ims.tsukuba.ac.jp [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Center of Excellence for Advanced Materials Research, King Abdulaziz University, P.O. Box 80203, Jeddah 21589 (Saudi Arabia); School of Materials Science and Engineering and ERI, Gyeongsang National University, 900 Gazwadong, Jinju, Gyeongnam 660-701 (Korea, Republic of)
2013-11-15
Highlights: ► {110}{sub β}〈11{sup ¯}0〉{sub β} transverse type lattice modulation is confirmed in β phase. ► Nanosized modulated region (nanodomain) distributes homogeneously and randomly. ► Nanodomains act as obstacles against the long-ranged martensitic transformation. ► The origin of non-linear elastic deformation behavior is the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation. -- Abstract: In order to clarify the effect of interstitial atoms on the non-linear elastic deformation behavior of the Ti–Nb alloy, the microstructure of (Ti–26Nb)–1.0O alloy was closely investigated by transmission electron microscope (TEM) and in situ X-ray diffraction (XRD) measurements. The 〈1 1 0〉{sub β}* rel rods and {1 1 1}{sub β}* rel planes were observed in a reciprocal space for the (Ti–26Nb)–1.0O alloy. Their origin was {110}{sub β}〈11{sup ¯}0〉{sub β} transverse type lattice modulation generated by oxygen atoms. Nanosized modulated domain structure (nanodomain) distributed homogeneously and randomly in the β phase and acted as obstacles for the long-ranged martensitic transformation in the (Ti–26Nb)–1.0O alloy. The non-linear elastic strain of the (Ti–26Nb)–1.0O alloy was generated by the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation.
Tahara, Masaki; Kim, Hee Young; Inamura, Tomonari; Hosoda, Hideki; Miyazaki, Shuichi
2013-01-01
Highlights: ► {110} β 〈11 ¯ 0〉 β transverse type lattice modulation is confirmed in β phase. ► Nanosized modulated region (nanodomain) distributes homogeneously and randomly. ► Nanodomains act as obstacles against the long-ranged martensitic transformation. ► The origin of non-linear elastic deformation behavior is the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation. -- Abstract: In order to clarify the effect of interstitial atoms on the non-linear elastic deformation behavior of the Ti–Nb alloy, the microstructure of (Ti–26Nb)–1.0O alloy was closely investigated by transmission electron microscope (TEM) and in situ X-ray diffraction (XRD) measurements. The 〈1 1 0〉 β * rel rods and {1 1 1} β * rel planes were observed in a reciprocal space for the (Ti–26Nb)–1.0O alloy. Their origin was {110} β 〈11 ¯ 0〉 β transverse type lattice modulation generated by oxygen atoms. Nanosized modulated domain structure (nanodomain) distributed homogeneously and randomly in the β phase and acted as obstacles for the long-ranged martensitic transformation in the (Ti–26Nb)–1.0O alloy. The non-linear elastic strain of the (Ti–26Nb)–1.0O alloy was generated by the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation
Thermal expansion of two-dimensional itinerant nearly ferromagnetic metal
Konno, R; Hatayama, N; Takahashi, Y; Nakano, H
2009-01-01
Thermal expansion of two-dimensional itinerant nearly ferromagnetic metal is investigated according to the recent theoretical development of magneto-volume effect for the three-dimensional weak ferromagnets. We particularly focus on the T 2 -linear thermal expansion of magnetic origin at low temperatures, so far disregarded by conventional theories. As the effect of thermal spin fluctuations we have found that the T-linear thermal expansion coefficient shows strong enhancement by assuming the double Lorentzian form of the non-interacting dynamical susceptibility justified in the small wave-number and low frequency region. It grows faster in proportional to y -1/2 as we approach the magnetic instability point than two-dimensional nearly antiferromagnetic metals with ln(1/y s ) dependence, where y and y s are the inverses of the reduced uniform and staggered magnetic susceptibilities, respectively. Our result is consistent with the Grueneisen's relation between the thermal expansion coefficient and the specific heat at low temperatures. In 2-dimensional electron gas we find that the thermal expansion coefficient is divergent with a finite y when the higher order term of non-interacting dynamical susceptibility is taken into account.
Two dimensional kinetic analysis of electrostatic harmonic plasma waves
Fonseca-Pongutá, E. C.; Ziebell, L. F.; Gaelzer, R. [Instituto de Física, UFRGS, 91501-970 Porto Alegre, RS (Brazil); Yoon, P. H. [IPST, University of Maryland, College Park, Maryland 20742 (United States); SSR, Kyung Hee University, Yongin, Gyeonggi 446-701 (Korea, Republic of)
2016-06-15
Electrostatic harmonic Langmuir waves are virtual modes excited in weakly turbulent plasmas, first observed in early laboratory beam-plasma experiments as well as in rocket-borne active experiments in space. However, their unequivocal presence was confirmed through computer simulated experiments and subsequently theoretically explained. The peculiarity of harmonic Langmuir waves is that while their existence requires nonlinear response, their excitation mechanism and subsequent early time evolution are governed by essentially linear process. One of the unresolved theoretical issues regards the role of nonlinear wave-particle interaction process over longer evolution time period. Another outstanding issue is that existing theories for these modes are limited to one-dimensional space. The present paper carries out two dimensional theoretical analysis of fundamental and (first) harmonic Langmuir waves for the first time. The result shows that harmonic Langmuir wave is essentially governed by (quasi)linear process and that nonlinear wave-particle interaction plays no significant role in the time evolution of the wave spectrum. The numerical solutions of the two-dimensional wave spectra for fundamental and harmonic Langmuir waves are also found to be consistent with those obtained by direct particle-in-cell simulation method reported in the literature.
Two-dimensional MoS2 electromechanical actuators
Hung, Nguyen T.; Nugraha, Ahmad R. T.; Saito, Riichiro
2018-02-01
We investigate the electromechanical properties of two-dimensional MoS2 monolayers with 1H, 1T, and 1T‧ structures as a function of charge doping by using density functional theory. We find isotropic elastic moduli in the 1H and 1T structures, while the 1T‧ structure exhibits an anisotropic elastic modulus. Moreover, the 1T structure is shown to have a negative Poisson’s ratio, while Poisson’s ratios of the 1H and 1T‧ are positive. By charge doping, the monolayer MoS2 shows a reversible strain and work density per cycle ranging from -0.68% to 2.67% and from 4.4 to 36.9 MJ m-3, respectively, making them suitable for applications in electromechanical actuators. We also examine the stress generated in the MoS2 monolayers and we find that 1T and 1T‧ MoS2 monolayers have relatively better performance than 1H MoS2 monolayer. We argue that such excellent electromechanical performance originate from the electrical conductivity of the metallic 1T and semimetallic 1T‧ structures and also from their high Young’s modulus of about 150-200 GPa.
Some Differential Geometric Relations in the Elastic Shell
Xiaoqin Shen
2016-01-01
Full Text Available The theory of the elastic shells is one of the most important parts of the theory of solid mechanics. The elastic shell can be described with its middle surface; that is, the three-dimensional elastic shell with equal thickness comprises a series of overlying surfaces like middle surface. In this paper, the differential geometric relations between elastic shell and its middle surface are provided under the curvilinear coordinate systems, which are very important for forming two-dimensional linear and nonlinear elastic shell models. Concretely, the metric tensors, the determinant of metric matrix field, the Christoffel symbols, and Riemann tensors on the three-dimensional elasticity are expressed by those on the two-dimensional middle surface, which are featured by the asymptotic expressions with respect to the variable in the direction of thickness of the shell. Thus, the novelty of this work is that we can further split three-dimensional mechanics equations into two-dimensional variation problems. Finally, two kinds of special shells, hemispherical shell and semicylindrical shell, are provided as the examples.
Discrete formulation for two-dimensional multigroup neutron diffusion equations
Vosoughi, Naser E-mail: vosoughi@mehr.sharif.edu; Salehi, Ali A.; Shahriari, Majid
2003-02-01
The objective of this paper is to introduce a new numerical method for neutronic calculation in a reactor core. This method can produce the final finite form of the neutron diffusion equation by classifying the neutronic variables and using two kinds of cell complexes without starting from the conventional differential form of the neutron diffusion equation. The method with linear interpolation produces the same convergence as the linear continuous finite element method. The quadratic interpolation is proven; the convergence order depends on the shape of the dual cell. The maximum convergence order is achieved by choosing the dual cell based on two Gauss' points. The accuracy of the method was examined with a well-known IAEA two-dimensional benchmark problem. The numerical results demonstrate the effectiveness of the new method.
Discrete formulation for two-dimensional multigroup neutron diffusion equations
Vosoughi, Naser; Salehi, Ali A.; Shahriari, Majid
2003-01-01
The objective of this paper is to introduce a new numerical method for neutronic calculation in a reactor core. This method can produce the final finite form of the neutron diffusion equation by classifying the neutronic variables and using two kinds of cell complexes without starting from the conventional differential form of the neutron diffusion equation. The method with linear interpolation produces the same convergence as the linear continuous finite element method. The quadratic interpolation is proven; the convergence order depends on the shape of the dual cell. The maximum convergence order is achieved by choosing the dual cell based on two Gauss' points. The accuracy of the method was examined with a well-known IAEA two-dimensional benchmark problem. The numerical results demonstrate the effectiveness of the new method
Two-dimensional simulation of sintering process
Vasconcelos, Vanderley de; Pinto, Lucio Carlos Martins; Vasconcelos, Wander L.
1996-01-01
The results of two-dimensional simulations are directly applied to systems in which one of the dimensions is much smaller than the others, and to sections of three dimensional models. Moreover, these simulations are the first step of the analysis of more complex three-dimensional systems. In this work, two basic features of the sintering process are studied: the types of particle size distributions related to the powder production processes and the evolution of geometric parameters of the resultant microstructures during the solid-state sintering. Random packing of equal spheres is considered in the sintering simulation. The packing algorithm does not take into account the interactive forces between the particles. The used sintering algorithm causes the densification of the particle set. (author)
Pressure of two-dimensional Yukawa liquids
Feng, Yan; Wang, Lei; Tian, Wen-de; Goree, J; Liu, Bin
2016-01-01
A simple analytic expression for the pressure of a two-dimensional Yukawa liquid is found by fitting results from a molecular dynamics simulation. The results verify that the pressure can be written as the sum of a potential term which is a simple multiple of the Coulomb potential energy at a distance of the Wigner–Seitz radius, and a kinetic term which is a multiple of the one for an ideal gas. Dimensionless coefficients for each of these terms are found empirically, by fitting. The resulting analytic expression, with its empirically determined coefficients, is plotted as isochores, or curves of constant area. These results should be applicable to monolayer dusty plasmas. (paper)
Two dimensional nanomaterials for flexible supercapacitors.
Peng, Xu; Peng, Lele; Wu, Changzheng; Xie, Yi
2014-05-21
Flexible supercapacitors, as one of most promising emerging energy storage devices, are of great interest owing to their high power density with great mechanical compliance, making them very suitable as power back-ups for future stretchable electronics. Two-dimensional (2D) nanomaterials, including the quasi-2D graphene and inorganic graphene-like materials (IGMs), have been greatly explored to providing huge potential for the development of flexible supercapacitors with higher electrochemical performance. This review article is devoted to recent progresses in engineering 2D nanomaterials for flexible supercapacitors, which survey the evolution of electrode materials, recent developments in 2D nanomaterials and their hybrid nanostructures with regulated electrical properties, and the new planar configurations of flexible supercapacitors. Furthermore, a brief discussion on future directions, challenges and opportunities in this fascinating area is also provided.
Two-dimensional materials for ultrafast lasers
Wang Fengqiu
2017-01-01
As the fundamental optical properties and novel photophysics of graphene and related two-dimensional (2D) crystals are being extensively investigated and revealed, a range of potential applications in optical and optoelectronic devices have been proposed and demonstrated. Of the many possibilities, the use of 2D materials as broadband, cost-effective and versatile ultrafast optical switches (or saturable absorbers) for short-pulsed lasers constitutes a rapidly developing field with not only a good number of publications, but also a promising prospect for commercial exploitation. This review primarily focuses on the recent development of pulsed lasers based on several representative 2D materials. The comparative advantages of these materials are discussed, and challenges to practical exploitation, which represent good future directions of research, are laid out. (paper)
Two-dimensional phase fraction charts
Morral, J.E.
1984-01-01
A phase fraction chart is a graphical representation of the amount of each phase present in a system as a function of temperature, composition or other variable. Examples are phase fraction versus temperature charts used to characterize specific alloys and as a teaching tool in elementary texts, and Schaeffler diagrams used to predict the amount of ferrite in stainless steel welds. Isothermal-transformation diagrams (TTT diagrams) are examples that give phase (or microconstituent) amount versus temperature and time. The purpose of this communication is to discuss the properties of two-dimensional phase fraction charts in more general terms than have been reported before. It is shown that they can represent multi-component, multiphase equilibria in a way which is easier to read and which contains more information than the isotherms and isopleths of multi-component phase diagrams
Two-dimensional motions of rockets
Kang, Yoonhwan; Bae, Saebyok
2007-01-01
We analyse the two-dimensional motions of the rockets for various types of rocket thrusts, the air friction and the gravitation by using a suitable representation of the rocket equation and the numerical calculation. The slope shapes of the rocket trajectories are discussed for the three types of rocket engines. Unlike the projectile motions, the descending parts of the trajectories tend to be gentler and straighter slopes than the ascending parts for relatively large launching angles due to the non-vanishing thrusts. We discuss the ranges, the maximum altitudes and the engine performances of the rockets. It seems that the exponential fuel exhaustion can be the most potent engine for the longest and highest flights
Two dimensional NMR studies of polysaccharides
Byrd, R.A.; Egan, W.; Summers, M.F.
1987-01-01
Polysaccharides are very important components in the immune response system. Capsular polysaccharides and lipopolysaccharides occupy cell surface sites of bacteria, play key roles in recognition and some have been used to develop vaccines. Consequently, the ability to determine chemical structures of these systems is vital to an understanding of their immunogenic action. The authors have been utilizing recently developed two-dimensional homonuclear and heteronuclear correlation spectroscopy for unambiguous assignment and structure determination of a number of polysaccharides. In particular, the 1 H-detected heteronuclear correlation experiments are essential to the rapid and sensitive determination of these structures. Linkage sites are determined by independent polarization transfer experiments and multiple quantum correlation experiments. These methods permit the complete structure determination on very small amounts of the polysaccharides. They present the results of a number of structural determinations and discuss the limits of these experiments in terms of their applications to polysaccharides
Two-Dimensional Homogeneous Fermi Gases
Hueck, Klaus; Luick, Niclas; Sobirey, Lennart; Siegl, Jonas; Lompe, Thomas; Moritz, Henning
2018-02-01
We report on the experimental realization of homogeneous two-dimensional (2D) Fermi gases trapped in a box potential. In contrast to harmonically trapped gases, these homogeneous 2D systems are ideally suited to probe local as well as nonlocal properties of strongly interacting many-body systems. As a first benchmark experiment, we use a local probe to measure the density of a noninteracting 2D Fermi gas as a function of the chemical potential and find excellent agreement with the corresponding equation of state. We then perform matter wave focusing to extract the momentum distribution of the system and directly observe Pauli blocking in a near unity occupation of momentum states. Finally, we measure the momentum distribution of an interacting homogeneous 2D gas in the crossover between attractively interacting fermions and bosonic dimers.
Two-dimensional electroacoustic waves in silicene
Zhukov, Alexander V.; Bouffanais, Roland; Konobeeva, Natalia N.; Belonenko, Mikhail B.
2018-01-01
In this letter, we investigate the propagation of two-dimensional electromagnetic waves in a piezoelectric medium built upon silicene. Ultrashort optical pulses of Gaussian form are considered to probe this medium. On the basis of Maxwell's equations supplemented with the wave equation for the medium's displacement vector, we obtain the effective governing equation for the vector potential associated with the electromagnetic field, as well as the component of the displacement vector. The dependence of the pulse shape on the bandgap in silicene and the piezoelectric coefficient of the medium was analyzed, thereby revealing a nontrivial triadic interplay between the characteristics of the pulse dynamics, the electronic properties of silicene, and the electrically induced mechanical vibrations of the medium. In particular, we uncovered the possibility for an amplification of the pulse amplitude through the tuning of the piezoelectric coefficient. This property could potentially offer promising prospects for the development of amplification devices for the optoelectronics industry.
Versatile two-dimensional transition metal dichalcogenides
Canulescu, Stela; Affannoukoué, Kévin; Döbeli, Max
), a strategy for the fabrication of 2D heterostructures must be developed. Here we demonstrate a novel approach for the bottom-up synthesis of TMDC monolayers, namely Pulsed Laser Deposition (PLD) combined with a sulfur evaporation beam. PLD relies on the use of a pulsed laser (ns pulse duration) to induce...... material transfer from a solid source (such as a sintered target of MoS2) to a substrate (such as Si or sapphire). The deposition rate in PLD is typically much less than a monolayer per pulse, meaning that the number of MLs can be controlled by a careful selection of the number of laser pulses......Two-dimensional transition metal dichalcogenides (2D-TMDCs), such as MoS2, have emerged as a new class of semiconducting materials with distinct optical and electrical properties. The availability of 2D-TMDCs with distinct band gaps allows for unlimited combinations of TMDC monolayers (MLs...
Two-dimensional heterostructures for energy storage
Gogotsi, Yury G. [Drexel Univ., Philadelphia, PA (United States); Pomerantseva, Ekaterina [Drexel Univ., Philadelphia, PA (United States)
2017-06-12
Two-dimensional (2D) materials provide slit-shaped ion diffusion channels that enable fast movement of lithium and other ions. However, electronic conductivity, the number of intercalation sites, and stability during extended cycling are also crucial for building high-performance energy storage devices. While individual 2D materials, such as graphene, show some of the required properties, none of them can offer all properties needed to maximize energy density, power density, and cycle life. Here we argue that stacking different 2D materials into heterostructured architectures opens an opportunity to construct electrodes that would combine the advantages of the individual building blocks while eliminating the associated shortcomings. We discuss characteristics of common 2D materials and provide examples of 2D heterostructured electrodes that showed new phenomena leading to superior electrochemical performance. As a result, we also consider electrode fabrication approaches and finally outline future steps to create 2D heterostructured electrodes that could greatly expand current energy storage technologies.
Two-dimensional fourier transform spectrometer
DeFlores, Lauren; Tokmakoff, Andrei
2013-09-03
The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.
DESTRUCTION CRITERION IN MODEL OF NON-LINEAR ELASTIC PLASTIC MEDIUM
O. L. Shved
2014-01-01
Full Text Available The paper considers a destruction criterion in a specific phenomenological model of elastic plastic medium which significantly differs from the known criteria. In case of vector interpretation of rank-2 symmetric tensors yield surface in the Cauchy stress space is formed by closed piecewise concave surfaces of its deviator sections with due account of experimental data. Section surface is determined by normal vector which is selected from two private vectors of criterial “deviator” operator. Such selection is not always possible in the case of anisotropy growth. It is expected that destruction can only start when a process point in the stress space is located in the current deviator section of the yield surface. It occurs when a critical point appears in the section, and a private value of an operator becomes N-fold in the point that determines the private vector corresponding to the normal vector. Unique and reasonable selection of the normal vector becomes impossible in the critical point and an yield criteria loses its significance in the point.When the destruction initiation is determined there is a possibility of a special case due to the proposed conic form of the yield surface. The deviator section degenerates into the point at the yield surface peak. Criterion formulation at the surface peak lies in the fact that there is no physically correct solution while using a state equation in regard to elastic distortion measures with a fixed tensor of elastic turn. Such usage of the equation is always possible for the rest points of the yield surface and it is considered as an obligatory condition for determination of the deviator section. A critical point is generally absent at any deviator section of the yield surface for isotropic material. A limiting value of the mean stress has been calculated at uniform tension.
Geometric method for stability of non-linear elastic thin shells
Ivanova, Jordanka
2002-01-01
PREFACE This book deals with the new developments and applications of the geometric method to the nonlinear stability problem for thin non-elastic shells. There are no other published books on this subject except the basic ones of A. V. Pogorelov (1966,1967,1986), where variational principles defined over isometric surfaces, are postulated, and applied mainly to static and dynamic problems of elastic isotropic thin shells. A. V. Pogorelov (Harkov, Ukraine) was the first to provide in his monographs the geometric construction of the deformed shell surface in a post-critical stage and deriving explicitely the asymptotic formulas for the upper and lower critical loads. In most cases, these formulas were presented in a closed analytical form, and confirmed by experimental data. The geometric method by Pogorelov is one of the most important analytical methods developed during the last century. Its power consists in its ability to provide a clear geometric picture of the postcritical form of a deformed shell surfac...
Homogenization of Winkler-Steklov spectral conditions in three-dimensional linear elasticity
Gómez, D.; Nazarov, S. A.; Pérez, M. E.
2018-04-01
We consider a homogenization Winkler-Steklov spectral problem that consists of the elasticity equations for a three-dimensional homogeneous anisotropic elastic body which has a plane part of the surface subject to alternating boundary conditions on small regions periodically placed along the plane. These conditions are of the Dirichlet type and of the Winkler-Steklov type, the latter containing the spectral parameter. The rest of the boundary of the body is fixed, and the period and size of the regions, where the spectral parameter arises, are of order ɛ . For fixed ɛ , the problem has a discrete spectrum, and we address the asymptotic behavior of the eigenvalues {β _k^ɛ }_{k=1}^{∞} as ɛ → 0. We show that β _k^ɛ =O(ɛ ^{-1}) for each fixed k, and we observe a common limit point for all the rescaled eigenvalues ɛ β _k^ɛ while we make it evident that, although the periodicity of the structure only affects the boundary conditions, a band-gap structure of the spectrum is inherited asymptotically. Also, we provide the asymptotic behavior for certain "groups" of eigenmodes.
Chimera patterns in two-dimensional networks of coupled neurons
Schmidt, Alexander; Kasimatis, Theodoros; Hizanidis, Johanne; Provata, Astero; Hövel, Philipp
2017-03-01
We discuss synchronization patterns in networks of FitzHugh-Nagumo and leaky integrate-and-fire oscillators coupled in a two-dimensional toroidal geometry. A common feature between the two models is the presence of fast and slow dynamics, a typical characteristic of neurons. Earlier studies have demonstrated that both models when coupled nonlocally in one-dimensional ring networks produce chimera states for a large range of parameter values. In this study, we give evidence of a plethora of two-dimensional chimera patterns of various shapes, including spots, rings, stripes, and grids, observed in both models, as well as additional patterns found mainly in the FitzHugh-Nagumo system. Both systems exhibit multistability: For the same parameter values, different initial conditions give rise to different dynamical states. Transitions occur between various patterns when the parameters (coupling range, coupling strength, refractory period, and coupling phase) are varied. Many patterns observed in the two models follow similar rules. For example, the diameter of the rings grows linearly with the coupling radius.
Electronic Transport in Two-Dimensional Materials
Sangwan, Vinod K.; Hersam, Mark C.
2018-04-01
Two-dimensional (2D) materials have captured the attention of the scientific community due to the wide range of unique properties at nanometer-scale thicknesses. While significant exploratory research in 2D materials has been achieved, the understanding of 2D electronic transport and carrier dynamics remains in a nascent stage. Furthermore, because prior review articles have provided general overviews of 2D materials or specifically focused on charge transport in graphene, here we instead highlight charge transport mechanisms in post-graphene 2D materials, with particular emphasis on transition metal dichalcogenides and black phosphorus. For these systems, we delineate the intricacies of electronic transport, including band structure control with thickness and external fields, valley polarization, scattering mechanisms, electrical contacts, and doping. In addition, electronic interactions between 2D materials are considered in the form of van der Waals heterojunctions and composite films. This review concludes with a perspective on the most promising future directions in this fast-evolving field.
Stress distribution in two-dimensional silos
Blanco-Rodríguez, Rodolfo; Pérez-Ángel, Gabriel
2018-01-01
Simulations of a polydispersed two-dimensional silo were performed using molecular dynamics, with different numbers of grains reaching up to 64 000, verifying numerically the model derived by Janssen and also the main assumption that the walls carry part of the weight due to the static friction between grains with themselves and those with the silo's walls. We vary the friction coefficient, the radii dispersity, the silo width, and the size of grains. We find that the Janssen's model becomes less relevant as the the silo width increases since the behavior of the stresses becomes more hydrostatic. Likewise, we get the normal and tangential stress distribution on the walls evidencing the existence of points of maximum stress. We also obtained the stress matrix with which we observe zones of concentration of load, located always at a height around two thirds of the granular columns. Finally, we observe that the size of the grains affects the distribution of stresses, increasing the weight on the bottom and reducing the normal stress on the walls, as the grains are made smaller (for the same total mass of the granulate), giving again a more hydrostatic and therefore less Janssen-type behavior for the weight of the column.
Asymptotics for Two-dimensional Atoms
Nam, Phan Thanh; Portmann, Fabian; Solovej, Jan Philip
2012-01-01
We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E^{\\TF}(\\lambd......We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E......^{\\TF}(\\lambda)$ is given by a Thomas-Fermi type variational problem and $c^{\\rm H}\\approx -2.2339$ is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when $Z\\to \\infty$, which is contrary to the expected behavior of three-dimensional atoms....
Seismic isolation of two dimensional periodic foundations
Yan, Y.; Mo, Y. L.; Laskar, A.; Cheng, Z.; Shi, Z.; Menq, F.; Tang, Y.
2014-01-01
Phononic crystal is now used to control acoustic waves. When the crystal goes to a larger scale, it is called periodic structure. The band gaps of the periodic structure can be reduced to range from 0.5 Hz to 50 Hz. Therefore, the periodic structure has potential applications in seismic wave reflection. In civil engineering, the periodic structure can be served as the foundation of upper structure. This type of foundation consisting of periodic structure is called periodic foundation. When the frequency of seismic waves falls into the band gaps of the periodic foundation, the seismic wave can be blocked. Field experiments of a scaled two dimensional (2D) periodic foundation with an upper structure were conducted to verify the band gap effects. Test results showed the 2D periodic foundation can effectively reduce the response of the upper structure for excitations with frequencies within the frequency band gaps. When the experimental and the finite element analysis results are compared, they agree well with each other, indicating that 2D periodic foundation is a feasible way of reducing seismic vibrations.
Two-dimensional topological photonic systems
Sun, Xiao-Chen; He, Cheng; Liu, Xiao-Ping; Lu, Ming-Hui; Zhu, Shi-Ning; Chen, Yan-Feng
2017-09-01
The topological phase of matter, originally proposed and first demonstrated in fermionic electronic systems, has drawn considerable research attention in the past decades due to its robust transport of edge states and its potential with respect to future quantum information, communication, and computation. Recently, searching for such a unique material phase in bosonic systems has become a hot research topic worldwide. So far, many bosonic topological models and methods for realizing them have been discovered in photonic systems, acoustic systems, mechanical systems, etc. These discoveries have certainly yielded vast opportunities in designing material phases and related properties in the topological domain. In this review, we first focus on some of the representative photonic topological models and employ the underlying Dirac model to analyze the edge states and geometric phase. On the basis of these models, three common types of two-dimensional topological photonic systems are discussed: 1) photonic quantum Hall effect with broken time-reversal symmetry; 2) photonic topological insulator and the associated pseudo-time-reversal symmetry-protected mechanism; 3) time/space periodically modulated photonic Floquet topological insulator. Finally, we provide a summary and extension of this emerging field, including a brief introduction to the Weyl point in three-dimensional systems.
Turbulent equipartitions in two dimensional drift convection
Isichenko, M.B.; Yankov, V.V.
1995-01-01
Unlike the thermodynamic equipartition of energy in conservative systems, turbulent equipartitions (TEP) describe strongly non-equilibrium systems such as turbulent plasmas. In turbulent systems, energy is no longer a good invariant, but one can utilize the conservation of other quantities, such as adiabatic invariants, frozen-in magnetic flux, entropy, or combination thereof, in order to derive new, turbulent quasi-equilibria. These TEP equilibria assume various forms, but in general they sustain spatially inhomogeneous distributions of the usual thermodynamic quantities such as density or temperature. This mechanism explains the effects of particle and energy pinch in tokamaks. The analysis of the relaxed states caused by turbulent mixing is based on the existence of Lagrangian invariants (quantities constant along fluid-particle or other orbits). A turbulent equipartition corresponds to the spatially uniform distribution of relevant Lagrangian invariants. The existence of such turbulent equilibria is demonstrated in the simple model of two dimensional electrostatically turbulent plasma in an inhomogeneous magnetic field. The turbulence is prescribed, and the turbulent transport is assumed to be much stronger than the classical collisional transport. The simplicity of the model makes it possible to derive the equations describing the relaxation to the TEP state in several limits
Radiation effects on two-dimensional materials
Walker, R.C. II; Robinson, J.A. [Department of Materials Science, Penn State, University Park, PA (United States); Center for Two-Dimensional Layered Materials, Penn State, University Park, PA (United States); Shi, T. [Department of Mechanical and Nuclear Engineering, Penn State, University Park, PA (United States); Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI (United States); Silva, E.C. [GlobalFoundries, Malta, NY (United States); Jovanovic, I. [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI (United States)
2016-12-15
The effects of electromagnetic and particle irradiation on two-dimensional materials (2DMs) are discussed in this review. Radiation creates defects that impact the structure and electronic performance of materials. Determining the impact of these defects is important for developing 2DM-based devices for use in high-radiation environments, such as space or nuclear reactors. As such, most experimental studies have been focused on determining total ionizing dose damage to 2DMs and devices. Total dose experiments using X-rays, gamma rays, electrons, protons, and heavy ions are summarized in this review. We briefly discuss the possibility of investigating single event effects in 2DMs based on initial ion beam irradiation experiments and the development of 2DM-based integrated circuits. Additionally, beneficial uses of irradiation such as ion implantation to dope materials or electron-beam and helium-beam etching to shape materials have begun to be used on 2DMs and are reviewed as well. For non-ionizing radiation, such as low-energy photons, we review the literature on 2DM-based photo-detection from terahertz to UV. The majority of photo-detecting devices operate in the visible and UV range, and for this reason they are the focus of this review. However, we review the progress in developing 2DMs for detecting infrared and terahertz radiation. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Buckled two-dimensional Xene sheets.
Molle, Alessandro; Goldberger, Joshua; Houssa, Michel; Xu, Yong; Zhang, Shou-Cheng; Akinwande, Deji
2017-02-01
Silicene, germanene and stanene are part of a monoelemental class of two-dimensional (2D) crystals termed 2D-Xenes (X = Si, Ge, Sn and so on) which, together with their ligand-functionalized derivatives referred to as Xanes, are comprised of group IVA atoms arranged in a honeycomb lattice - similar to graphene but with varying degrees of buckling. Their electronic structure ranges from trivial insulators, to semiconductors with tunable gaps, to semi-metallic, depending on the substrate, chemical functionalization and strain. More than a dozen different topological insulator states are predicted to emerge, including the quantum spin Hall state at room temperature, which, if realized, would enable new classes of nanoelectronic and spintronic devices, such as the topological field-effect transistor. The electronic structure can be tuned, for example, by changing the group IVA element, the degree of spin-orbit coupling, the functionalization chemistry or the substrate, making the 2D-Xene systems promising multifunctional 2D materials for nanotechnology. This Perspective highlights the current state of the art and future opportunities in the manipulation and stability of these materials, their functions and applications, and novel device concepts.
Thermoelectric transport in two-dimensional giant Rashba systems
Xiao, Cong; Li, Dingping; Ma, Zhongshui; Niu, Qian
Thermoelectric transport in strongly spin-orbit coupled two-dimensional Rashba systems is studied using the analytical solution of the linearized Boltzmann equation. To highlight the effects of inter-band scattering, we assume point-like potential impurities, and obtain the band-and energy-dependent transport relaxation times. Unconventional transport behaviors arise when the Fermi level lies near or below the band crossing point (BCP), such as the non-Drude electrical conducivity below the BCP, the failure of the standard Mott relation linking the Peltier coefficient to the electrical conductivity near the BCP, the enhancement of diffusion thermopower and figure of merit below the BCP, the zero-field Hall coefficient which is not inversely proportional to and not a monotonic function of the carrier density, the enhanced Nernst coefficient below the BCP, and the enhanced current-induced spin-polarization efficiency.
Cooperation in two-dimensional mixed-games
Amaral, Marco A; Silva, Jafferson K L da; Wardil, Lucas
2015-01-01
Evolutionary game theory is a common framework to study the evolution of cooperation, where it is usually assumed that the same game is played in all interactions. Here, we investigate a model where the game that is played by two individuals is uniformly drawn from a sample of two different games. Using the master equation approach we show that the random mixture of two games is equivalent to play the average game when (i) the strategies are statistically independent of the game distribution and (ii) the transition rates are linear functions of the payoffs. We also use Monte-Carlo simulations in a two-dimensional lattice and mean-field techniques to investigate the scenario when the two above conditions do not hold. We find that even outside of such conditions, several quantities characterizing the mixed-games are still the same as the ones obtained in the average game when the two games are not very different. (paper)
Tachyon hair on two-dimensional black holes
Peet, A.; Susskind, L.; Thorlacius, L.
1993-01-01
Static black holes in two-dimensional string theory can carry tachyon hair. Configurations which are nonsingular at the event horizon have a nonvanishing asymptotic energy density. Such solutions can be smoothly extended through the event horizon and have a nonvanishing energy flux emerging from the past singularity. Dynamical processes will not change the amount of tachyon hair on a black hole. In particular, there will be no tachyon hair on a black hole formed in gravitational collapse if the initial geometry is the linear dilaton vacuum. There also exist static solutions with a finite total energy, which have singular event horizons. Simple dynamical arguments suggest that black holes formed in gravitational collapse will not have tachyon hair of this type
On wakefields with two-dimensional planar geometry
Chao, A.W.; Bane, K.L.F.
1996-10-01
In order to reach higher acceleration gradients in linear accelerators, it is advantageous to use a higher accelerating RF frequency, which in turn requires smaller accelerating structures. As the structure size becomes smaller, rectangular structures become increasingly interesting because they are easier to construct than cylindrically symmetric ones. One drawback of small structures, however, is that the wakefields generated by the beam in such structures tend to be strong. Recently, it has been suggested that one way of ameliorating this problem is to use rectangular structures that are very flat and to use flat beams. In the limiting case of a very flat planar geometry, the problem resembles a purely two-dimensional (2-D) problem, the wakefields of which have been studied
An enhanced finite volume method to model 2D linear elastic structures
Suliman, Ridhwaan
2014-04-01
Full Text Available . Suliman) Preprint submitted to Applied Mathematical Modelling July 22, 2013 Keywords: finite volume, finite element, locking, error analysis 1. Introduction Since the 1960s, the finite element method has mainly been used for modelling the mechanics... formulation provides higher accuracy 2 for displacement solutions. It is well known that the linear finite element formulation suffers from sensitivity to element aspect ratio or shear locking when subjected to bend- ing [16]. Fallah [8] and Wheel [6] present...
Lee, Hyeong Y.; Nikbin, Kamran M.; O'Dowd, Noel P.
2005-01-01
A review of through thickness transverse residual stress distribution measurements in a number of components, manufactured from a range of steels, has been carried out. Residual stresses introduced by welding and mechanical deformation have been considered. The geometries consisted of welded T-plate joints, pipe butt joints, tube-on-plate joints, tubular Y-joints and tubular T-joints as well as cold bent tubes and repair welds. In addition, the collected data cover a range of engineering steels including ferritic, austenitic, C-Mn and Cr-Mo steels. The methods used to measure the residual stresses also varied. These included neutron diffraction, X-ray diffraction and deep hole drilling techniques. Measured residual stress data, normalised by their respective yield stress have shown an inverse linear correlation versus the normalised depth of the region containing the residual stress (up to 0.5 of the component thickness). A simplified generic residual stress profile based on a linear fit to the data is proposed for the case of a transverse residual tensile stress field. Whereas the profiles in assessment procedures are case specific the proposed linear profile can be varied to produce a combination of membrane and bending stress distributions to give lower or higher levels of conservatism on stress intensity factors, depending on the amount of case specific data available or the degree of safety required
Lukasievicz, Gustavo V B; Astrath, Nelson G C; Malacarne, Luis C; Herculano, Leandro S; Zanuto, Vitor S; Baesso, Mauro L; Bialkowski, Stephen E
2013-10-01
A theoretical model for a time-resolved photothermal mirror technique using pulsed-laser excitation was developed for low absorption samples. Analytical solutions to the temperature and thermoelastic deformation equations are found for three characteristic pulse profiles and are compared to finite element analysis methods results for finite samples. An analytical expression for the intensity of the center of a continuous probe laser at the detector plane is derived using the Fresnel diffraction theory, which allows modeling of experimental results. Experiments are performed in optical glasses, and the models are fitted to the data. The parameters of the fit are in good agreement with previous literature data for absorption, thermal diffusion, and thermal expansion of the materials tested. The combined modeling and experimental techniques are shown to be useful for quantitative determination of the physical properties of low absorption homogeneous linear elastic material samples.
Pettermann, Heinz E.; DeSimone, Antonio
2017-09-01
A constitutive material law for linear thermo-viscoelasticity in the time domain is presented. The time-dependent relaxation formulation is given for full anisotropy, i.e., both the elastic and the viscous properties are anisotropic. Thereby, each element of the relaxation tensor is described by its own and independent Prony series expansion. Exceeding common viscoelasticity, time-dependent thermal expansion relaxation/creep is treated as inherent material behavior. The pertinent equations are derived and an incremental, implicit time integration scheme is presented. The developments are implemented into an implicit FEM software for orthotropic material symmetry under plane stress assumption. Even if this is a reduced problem, all essential features are present and allow for the entire verification and validation of the approach. Various simulations on isotropic and orthotropic problems are carried out to demonstrate the material behavior under investigation.
Laser-based linear and nonlinear guided elastic waves at surfaces (2D) and wedges (1D).
Hess, Peter; Lomonosov, Alexey M; Mayer, Andreas P
2014-01-01
The characteristic features and applications of linear and nonlinear guided elastic waves propagating along surfaces (2D) and wedges (1D) are discussed. Laser-based excitation, detection, or contact-free analysis of these guided waves with pump-probe methods are reviewed. Determination of material parameters by broadband surface acoustic waves (SAWs) and other applications in nondestructive evaluation (NDE) are considered. The realization of nonlinear SAWs in the form of solitary waves and as shock waves, used for the determination of the fracture strength, is described. The unique properties of dispersion-free wedge waves (WWs) propagating along homogeneous wedges and of dispersive wedge waves observed in the presence of wedge modifications such as tip truncation or coatings are outlined. Theoretical and experimental results on nonlinear wedge waves in isotropic and anisotropic solids are presented. Copyright © 2013 Elsevier B.V. All rights reserved.
BOERTJENS, G. J.; VAN HORSSEN, W. T.
2000-08-01
In this paper an initial-boundary value problem for the vertical displacement of a weakly non-linear elastic beam with an harmonic excitation in the horizontal direction at the ends of the beam is studied. The initial-boundary value problem can be regarded as a simple model describing oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-time-scales perturbation method an approximation of the solution of the initial-boundary value problem is constructed. Interactions between different oscillation modes of the beam are studied. It is shown that for certain external excitations, depending on the phase of an oscillation mode, the amplitude of specific oscillation modes changes.
Two-dimensional multiferroics in monolayer group IV monochalcogenides
Wang, Hua; Qian, Xiaofeng
2017-03-01
Low-dimensional multiferroic materials hold great promises in miniaturized device applications such as nanoscale transducers, actuators, sensors, photovoltaics, and nonvolatile memories. Here, using first-principles theory we predict that two-dimensional (2D) monolayer group IV monochalcogenides including GeS, GeSe, SnS, and SnSe are a class of 2D semiconducting multiferroics with giant strongly-coupled in-plane spontaneous ferroelectric polarization and spontaneous ferroelastic lattice strain that are thermodynamically stable at room temperature and beyond, and can be effectively modulated by elastic strain engineering. Their optical absorption spectra exhibit strong in-plane anisotropy with visible-spectrum excitonic gaps and sizable exciton binding energies, rendering the unique characteristics of low-dimensional semiconductors. More importantly, the predicted low domain wall energy and small migration barrier together with the coupled multiferroic order and anisotropic electronic structures suggest their great potentials for tunable multiferroic functional devices by manipulating external electrical, mechanical, and optical field to control the internal responses, and enable the development of four device concepts including 2D ferroelectric memory, 2D ferroelastic memory, and 2D ferroelastoelectric nonvolatile photonic memory as well as 2D ferroelectric excitonic photovoltaics.
Two-Dimensional Nonlinear Finite Element Analysis of CMC Microstructures
Mital, Subodh K.; Goldberg, Robert K.; Bonacuse, Peter J.
2012-01-01
A research program has been developed to quantify the effects of the microstructure of a woven ceramic matrix composite and its variability on the effective properties and response of the material. In order to characterize and quantify the variations in the microstructure of a five harness satin weave, chemical vapor infiltrated (CVI) SiC/SiC composite material, specimens were serially sectioned and polished to capture images that detailed the fiber tows, matrix, and porosity. Open source quantitative image analysis tools were then used to isolate the constituents, from which two dimensional finite element models were generated which approximated the actual specimen section geometry. A simplified elastic-plastic model, wherein all stress above yield is redistributed to lower stress regions, is used to approximate the progressive damage behavior for each of the composite constituents. Finite element analyses under in-plane tensile loading were performed to examine how the variability in the local microstructure affected the macroscopic stress-strain response of the material as well as the local initiation and progression of damage. The macroscopic stress-strain response appeared to be minimally affected by the variation in local microstructure, but the locations where damage initiated and propagated appeared to be linked to specific aspects of the local microstructure.
On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation
Bory Reyes, Juan; Abreu Blaya, Ricardo; Rodríguez Dagnino, Ramón Martin; Kats, Boris Aleksandrovich
2018-01-01
The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R^2 . Our analysis is based on a suitable operator calculus.
Graphene as a Prototypical Model for Two-Dimensional Continuous Mechanics
Philippe Lambin
2017-08-01
Full Text Available This paper reviews a few problems where continuous-medium theory specialized to two-dimensional media provides a qualitatively correct picture of the mechanical behavior of graphene. A critical analysis of the parameters involved is given. Among other results, a simple mathematical description of a folded graphene sheet is proposed. It is also shown how the graphene–graphene adhesion interaction is related to the cleavage energy of graphite and its C 33 bulk elastic constant.
Two-dimensional vibrational-electronic spectroscopy
Courtney, Trevor L.; Fox, Zachary W.; Slenkamp, Karla M.; Khalil, Munira
2015-10-01
Two-dimensional vibrational-electronic (2D VE) spectroscopy is a femtosecond Fourier transform (FT) third-order nonlinear technique that creates a link between existing 2D FT spectroscopies in the vibrational and electronic regions of the spectrum. 2D VE spectroscopy enables a direct measurement of infrared (IR) and electronic dipole moment cross terms by utilizing mid-IR pump and optical probe fields that are resonant with vibrational and electronic transitions, respectively, in a sample of interest. We detail this newly developed 2D VE spectroscopy experiment and outline the information contained in a 2D VE spectrum. We then use this technique and its single-pump counterpart (1D VE) to probe the vibrational-electronic couplings between high frequency cyanide stretching vibrations (νCN) and either a ligand-to-metal charge transfer transition ([FeIII(CN)6]3- dissolved in formamide) or a metal-to-metal charge transfer (MMCT) transition ([(CN)5FeIICNRuIII(NH3)5]- dissolved in formamide). The 2D VE spectra of both molecules reveal peaks resulting from coupled high- and low-frequency vibrational modes to the charge transfer transition. The time-evolving amplitudes and positions of the peaks in the 2D VE spectra report on coherent and incoherent vibrational energy transfer dynamics among the coupled vibrational modes and the charge transfer transition. The selectivity of 2D VE spectroscopy to vibronic processes is evidenced from the selective coupling of specific νCN modes to the MMCT transition in the mixed valence complex. The lineshapes in 2D VE spectra report on the correlation of the frequency fluctuations between the coupled vibrational and electronic frequencies in the mixed valence complex which has a time scale of 1 ps. The details and results of this study confirm the versatility of 2D VE spectroscopy and its applicability to probe how vibrations modulate charge and energy transfer in a wide range of complex molecular, material, and biological systems.
Two-dimensional silica opens new perspectives
Büchner, Christin; Heyde, Markus
2017-12-01
In recent years, silica films have emerged as a novel class of two-dimensional (2D) materials. Several groups succeeded in epitaxial growth of ultrathin SiO2 layers using different growth methods and various substrates. The structures consist of tetrahedral [SiO4] building blocks in two mirror symmetrical planes, connected via oxygen bridges. This arrangement is called a silica bilayer as it is the thinnest 2D arrangement with the stoichiometry SiO2 known today. With all bonds saturated within the nano-sheet, the interaction with the substrate is based on van der Waals forces. Complex ring networks are observed, including hexagonal honeycomb lattices, point defects and domain boundaries, as well as amorphous domains. The network structures are highly tuneable through variation of the substrate, deposition parameters, cooling procedure, introducing dopants or intercalating small species. The amorphous networks and structural defects were resolved with atomic resolution microscopy and modeled with density functional theory and molecular dynamics. Such data contribute to our understanding of the formation and characteristic motifs of glassy systems. Growth studies and doping with other chemical elements reveal ways to tune ring sizes and defects as well as chemical reactivities. The pristine films have been utilized as molecular sieves and for confining molecules in nanocatalysis. Post growth hydroxylation can be used to tweak the reactivity as well. The electronic properties of silica bilayers are favourable for using silica as insulators in 2D material stacks. Due to the fully saturated atomic structure, the bilayer interacts weakly with the substrate and can be described as quasi-freestanding. Recently, a mm-scale film transfer under structure retention has been demonstrated. The chemical and mechanical stability of silica bilayers is very promising for technological applications in 2D heterostacks. Due to the impact of this bilayer system for glass science
Two-dimensional vibrational-electronic spectroscopy
Courtney, Trevor L.; Fox, Zachary W.; Slenkamp, Karla M.; Khalil, Munira, E-mail: mkhalil@uw.edu [Department of Chemistry, University of Washington, Box 351700, Seattle, Washington 98195 (United States)
2015-10-21
Two-dimensional vibrational-electronic (2D VE) spectroscopy is a femtosecond Fourier transform (FT) third-order nonlinear technique that creates a link between existing 2D FT spectroscopies in the vibrational and electronic regions of the spectrum. 2D VE spectroscopy enables a direct measurement of infrared (IR) and electronic dipole moment cross terms by utilizing mid-IR pump and optical probe fields that are resonant with vibrational and electronic transitions, respectively, in a sample of interest. We detail this newly developed 2D VE spectroscopy experiment and outline the information contained in a 2D VE spectrum. We then use this technique and its single-pump counterpart (1D VE) to probe the vibrational-electronic couplings between high frequency cyanide stretching vibrations (ν{sub CN}) and either a ligand-to-metal charge transfer transition ([Fe{sup III}(CN){sub 6}]{sup 3−} dissolved in formamide) or a metal-to-metal charge transfer (MMCT) transition ([(CN){sub 5}Fe{sup II}CNRu{sup III}(NH{sub 3}){sub 5}]{sup −} dissolved in formamide). The 2D VE spectra of both molecules reveal peaks resulting from coupled high- and low-frequency vibrational modes to the charge transfer transition. The time-evolving amplitudes and positions of the peaks in the 2D VE spectra report on coherent and incoherent vibrational energy transfer dynamics among the coupled vibrational modes and the charge transfer transition. The selectivity of 2D VE spectroscopy to vibronic processes is evidenced from the selective coupling of specific ν{sub CN} modes to the MMCT transition in the mixed valence complex. The lineshapes in 2D VE spectra report on the correlation of the frequency fluctuations between the coupled vibrational and electronic frequencies in the mixed valence complex which has a time scale of 1 ps. The details and results of this study confirm the versatility of 2D VE spectroscopy and its applicability to probe how vibrations modulate charge and energy transfer in a
Kolmogorov flow in two dimensional strongly coupled dusty plasma
Gupta, Akanksha; Ganesh, R., E-mail: ganesh@ipr.res.in; Joy, Ashwin [Institute for Plasma Research, Bhat Gandhinagar, Gujarat 382 428 (India)
2014-07-15
Undriven, incompressible Kolmogorov flow in two dimensional doubly periodic strongly coupled dusty plasma is modelled using generalised hydrodynamics, both in linear and nonlinear regime. A complete stability diagram is obtained for low Reynolds numbers R and for a range of viscoelastic relaxation time τ{sub m} [0 < τ{sub m} < 10]. For the system size considered, using a linear stability analysis, similar to Navier Stokes fluid (τ{sub m} = 0), it is found that for Reynolds number beyond a critical R, say R{sub c}, the Kolmogorov flow becomes unstable. Importantly, it is found that R{sub c} is strongly reduced for increasing values of τ{sub m}. A critical τ{sub m}{sup c} is found above which Kolmogorov flow is unconditionally unstable and becomes independent of Reynolds number. For R < R{sub c}, the neutral stability regime found in Navier Stokes fluid (τ{sub m} = 0) is now found to be a damped regime in viscoelastic fluids, thus changing the fundamental nature of transition of Kolmogorov flow as function of Reynolds number R. A new parallelized nonlinear pseudo spectral code has been developed and is benchmarked against eigen values for Kolmogorov flow obtained from linear analysis. Nonlinear states obtained from the pseudo spectral code exhibit cyclicity and pattern formation in vorticity and viscoelastic oscillations in energy.
Barari, Amin; Ganjavi, B.; Jeloudar, M. Ghanbari
2010-01-01
and fluid mechanics. Design/methodology/approach – Two new but powerful analytical methods, namely, He's VIM and HPM, are introduced to solve some boundary value problems in structural engineering and fluid mechanics. Findings – Analytical solutions often fit under classical perturbation methods. However......, as with other analytical techniques, certain limitations restrict the wide application of perturbation methods, most important of which is the dependence of these methods on the existence of a small parameter in the equation. Disappointingly, the majority of nonlinear problems have no small parameter at all......Purpose – In the last two decades with the rapid development of nonlinear science, there has appeared ever-increasing interest of scientists and engineers in the analytical techniques for nonlinear problems. This paper considers linear and nonlinear systems that are not only regarded as general...
P-S & S-P Elastic Wave Conversions from Linear Arrays of Oriented Microcracks
Jiang, L.; Modiriasari, A.; Bobet, A.; Pyrak-Nolte, L. J.
2017-12-01
Natural and induced processes can produce oriented mechanical discontinuities such as en echelon cracks, fractures and faults. Previous research has shown that compressional to shear (P-S) wave conversions occur at normal incidence to a fracture because of cross-coupling fracture compliances (Nakagawa et al., 2000). Here, experiments and computer simulation are presented to demonstrate the link among cross-coupling stiffness, microcrack orientation and energy partitioning among P, S, and P-S/S-P waves. A FormLabs 2 3D printer was used to fabricate 7 samples (50 mm x 50 mm x 100 mm) with linear arrays of microcracks oriented at 0, 15, 30, 45, 60, 75, and 900 with a print resolution of 0.025 mm. The microcracks were elliptical in cross-sections (2 mm long by 1 mm wide), through the 50 mm thickness of sample, and spaced 3 mm (center-to-center for adjacent cracks). A 25 mm length of each sample contained no microcracks to act as a reference material. Broadband transducers (0.2-1.5 MHz) were used to transmit and receive P and polarized S wave signals that were propagated at normal incidence to the linear array of microcracks. P-wave amplitude increased, while S-wave amplitude remained relatively constant, as the microcrack orientation increased from 0o to 90o. At normal incidence, P-S and S-P wave conversions emerged and increased in amplitude as the crack inclination increased from 00 to 450. From 450 to 900, the amplitude of these converted modes decreased. Between negative and positive crack angles, the P-to-S and S-to-P waves were 1800 phase reversed. The observed energy partitioning matched the computed compliances obtained from numerical simulations with ABAQUS. The cross-coupling compliance for cracks inclined at 450 was found to be the smallest magnitude. 3D printing enabled the study of microstructural effects on macro-scale wave measurements. Information on the orientation of microcracks or even en echelon fractures and faults is contained in P-S conversions
Lie algebra contractions on two-dimensional hyperboloid
Pogosyan, G. S.; Yakhno, A.
2010-01-01
The Inoenue-Wigner contraction from the SO(2, 1) group to the Euclidean E(2) and E(1, 1) group is used to relate the separation of variables in Laplace-Beltrami (Helmholtz) equations for the four corresponding two-dimensional homogeneous spaces: two-dimensional hyperboloids and two-dimensional Euclidean and pseudo-Euclidean spaces. We show how the nine systems of coordinates on the two-dimensional hyperboloids contracted to the four systems of coordinates on E 2 and eight on E 1,1 . The text was submitted by the authors in English.
Dörsek, Philipp; Melenk, Jens M.
2017-01-01
We consider the extension of the p-robust equilibrated error estimator due to Braess, Pillwein and Schöberl to linear elasticity. We derive a formulation where the local mixed auxiliary problems do not require symmetry of the stresses. The resulting error estimator is p-robust, and the reliability estimate is also robust in the incompressible limit if quadratics are included in the approximation space. Extensions to other systems of linear second-order partial differential equations are discu...
I. K. Badalakha
2009-02-01
Full Text Available The article shows the result of solving the problem of stress-strain state of an elastic half-space because of the load action that uniformly distributed over the line, with the use of untraditional linear dependence of deformations on stressed state that is different from the generalized Hooke’s law.
Two-dimensional nonlinear string-type equations and their exact integration
Leznov, A.N.; Saveliev, M.V.
1982-01-01
On the base of group-theoretical formulation for exactly integrable two-dimensional non-linear dynamical systems associated with a local part of an arbitrary graded Lie algebra we study a string-type subclass of the equations. Explicit expressions have been obtained for their general solutions
Brøns, Morten; Hartnack, Johan Nicolai
1998-01-01
Streamline patterns and their bifurcations in two-dimensional incompressible flow are investigated from a topological point of view. The velocity field is expanded at a point in the fluid, and the expansion coefficients are considered as bifurcation parameters. A series of non-linear coordinate c...
Two-dimensional quantum electrodynamics as a model in the constructive quantum field theory
Ito, K.R.
1976-01-01
We investigate two-dimensional quantum electrodynamics((QED) 2 ) type models on the basis of the Hamiltonian formalism of a vector field. The transformation into a sine-Gordon equation is clarified as a generalized mass-shift transformation through canonical linear transformations. (auth.)
Shtromberger, N.L.
1989-01-01
To design a cyclotron magnetic system the legitimacy of two-dimensional approximations application is discussed. In all the calculations the finite difference method is used, and the linearization method with further use of the gradient conjugation method is used to solve the set of finite-difference equations. 3 refs.; 5 figs
Carlos A Bustamante Chaverra
2013-03-01
are employed to build the interpolation function. Unlike the original Kansa’s Method, the LHI is applied locally and the boundary and governing equation diﬀerential operators are used to obtain the interpolation function, giving a symmetric and non-singular collocation matrix. Analytical and Numerical Jacobian matrices are tested for the Newton-Raphson method and the derivatives of the governing equation with respect to the homotopy parameter are obtained analytically. The numerical scheme is veriﬁed by comparing the obtained results to the one-dimensional Burgers’ and two-dimensional Richards’ analytical solutions. The same results are obtained for all the non-linear solvers tested, but better convergence rates are attained with the Newton Raphson method in a double iteration scheme.
A two-dimensional mathematical model of percutaneous drug absorption
Kubota K
2004-06-01
Full Text Available Abstract Background When a drug is applied on the skin surface, the concentration of the drug accumulated in the skin and the amount of the drug eliminated into the blood vessel depend on the value of a parameter, r. The values of r depend on the amount of diffusion and the normalized skin-capillary clearence. It is defined as the ratio of the steady-state drug concentration at the skin-capillary boundary to that at the skin-surface in one-dimensional models. The present paper studies the effect of the parameter values, when the region of contact of the skin with the drug, is a line segment on the skin surface. Methods Though a simple one-dimensional model is often useful to describe percutaneous drug absorption, it may be better represented by multi-dimensional models. A two-dimensional mathematical model is developed for percutaneous absorption of a drug, which may be used when the diffusion of the drug in the direction parallel to the skin surface must be examined, as well as in the direction into the skin, examined in one-dimensional models. This model consists of a linear second-order parabolic equation with appropriate initial conditions and boundary conditions. These boundary conditions are of Dirichlet type, Neumann type or Robin type. A finite-difference method which maintains second-order accuracy in space along the boundary, is developed to solve the parabolic equation. Extrapolation in time is applied to improve the accuracy in time. Solution of the parabolic equation gives the concentration of the drug in the skin at a given time. Results Simulation of the numerical methods described is carried out with various values of the parameter r. The illustrations are given in the form of figures. Conclusion Based on the values of r, conclusions are drawn about (1 the flow rate of the drug, (2 the flux and the cumulative amount of drug eliminated into the receptor cell, (3 the steady-state value of the flux, (4 the time to reach the steady
Amir R. Ali
2017-01-01
Full Text Available This paper presents and verifies the mathematical model of an electric field senor based on the whispering gallery mode (WGM. The sensing element is a dielectric microsphere, where the light is used to tune the optical modes of the microsphere. The light undergoes total internal reflection along the circumference of the sphere; then it experiences optical resonance. The WGM are monitored as sharp dips on the transmission spectrum. These modes are very sensitive to morphology changes of the sphere, such that, for every minute change in the sphere’s morphology, a shift in the transmission spectrum will happen and that is known as WGM shifts. Due to the electrostriction effect, the applied electric field will induce forces acting on the surface of the dielectric sphere. In turn, these forces will deform the sphere causing shifts in its WGM spectrum. The applied electric field can be obtained by calculating these shifts. Navier’s equation for linear elasticity is used to model the deformation of the sphere to find the WGM shift. The finite element numerical studies are performed to verify the introduced model and to study the behavior of the sensor at different values of microspheres’ Young’s modulus and dielectric constant. Furthermore, the sensitivity and resolution of the developed WGM electric filed sensor model will be presented in this paper.
Perruisseau-Carrier, A; Bahlouli, N; Bierry, G; Vernet, P; Facca, S; Liverneaux, P
2017-12-01
Augmented reality could help the identification of nerve structures in brachial plexus surgery. The goal of this study was to determine which law of mechanical behavior was more adapted by comparing the results of Hooke's isotropic linear elastic law to those of Ogden's isotropic hyperelastic law, applied to a biomechanical model of the brachial plexus. A model of finite elements was created using the ABAQUS ® from a 3D model of the brachial plexus acquired by segmentation and meshing of MRI images at 0°, 45° and 135° of shoulder abduction of a healthy subject. The offset between the reconstructed model and the deformed model was evaluated quantitatively by the Hausdorff distance and qualitatively by the identification of 3 anatomical landmarks. In every case the Hausdorff distance was shorter with Ogden's law compared to Hooke's law. On a qualitative aspect, the model deformed by Ogden's law followed the concavity of the reconstructed model whereas the model deformed by Hooke's law remained convex. In conclusion, the results of this study demonstrate that the behavior of Ogden's isotropic hyperelastic mechanical model was more adapted to the modeling of the deformations of the brachial plexus. Copyright © 2017 Elsevier Masson SAS. All rights reserved.
Beginning Introductory Physics with Two-Dimensional Motion
Huggins, Elisha
2009-01-01
During the session on "Introductory College Physics Textbooks" at the 2007 Summer Meeting of the AAPT, there was a brief discussion about whether introductory physics should begin with one-dimensional motion or two-dimensional motion. Here we present the case that by starting with two-dimensional motion, we are able to introduce a considerable…
Two-dimensional black holes and non-commutative spaces
Sadeghi, J.
2008-01-01
We study the effects of non-commutative spaces on two-dimensional black hole. The event horizon of two-dimensional black hole is obtained in non-commutative space up to second order of perturbative calculations. A lower limit for the non-commutativity parameter is also obtained. The observer in that limit in contrast to commutative case see two horizon
Solution of the two-dimensional spectral factorization problem
Lawton, W. M.
1985-01-01
An approximation theorem is proven which solves a classic problem in two-dimensional (2-D) filter theory. The theorem shows that any continuous two-dimensional spectrum can be uniformly approximated by the squared modulus of a recursively stable finite trigonometric polynomial supported on a nonsymmetric half-plane.
Two-dimensional Navier-Stokes turbulence in bounded domains
Clercx, H.J.H.; van Heijst, G.J.F.
In this review we will discuss recent experimental and numerical results of quasi-two-dimensional decaying and forced Navier–Stokes turbulence in bounded domains. We will give a concise overview of developments in two-dimensional turbulence research, with emphasis on the progress made during the
Two-dimensional Navier-Stokes turbulence in bounded domains
Clercx, H.J.H.; Heijst, van G.J.F.
2009-01-01
In this review we will discuss recent experimental and numerical results of quasi-two-dimensional decaying and forced Navier–Stokes turbulence in bounded domains. We will give a concise overview of developments in two-dimensional turbulence research, with emphasis on the progress made during the
Analytical Solution for Two-Dimensional Coupled Thermoelastodynamics in a Cylinder
Morteza Eskandari-Ghadi
2013-12-01
Full Text Available An infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. The two-dimensional coupled thermoelastodynamic PDEs are specified based on equations of motion and energy equation, which are uncoupled using Nowacki potential functions. The Laplace integral transform and Bessel-Fourier series are used to derive the solution for the potential functions, and then the displacements-, stresses- and temperature-potential relationships are used to determine the displacements, stresses and temperature fields. It is shown that the formulation presented here are identically collapsed on the solution existed in the literature for simpler case of axissymetric configuration. A numerical procedure is needed to evaluate the displacements, stresses and temperature at any point and any time. The numerical inversion method proposed by Durbin is applied to evaluate the inverse Laplace transforms of different functions involved in this paper. For numerical inversion, there exist many difficulties such as singular points in the integrand functions, infinite limit of the integral and the time step of integration. With a very precise attention, the desired functions have been numerically evaluated and shown that the boundary conditions have been satisfied very accurately. The numerical evaluations are graphically shown to make engineering sense for the problem involved in this paper for different case of boundary conditions. The results show the wave velocity and the time lack of receiving stress waves. The effect of temperature boundary conditions are shown to be somehow oscillatory, which is used in designing of such an elements.
Kim, Jong Sung; Kim, Yong Woo [Sunchon National University, Suncheon (Korea, Republic of)
2014-10-15
Two acceleration methods, an effective force method (or inertia method) and a large mass method, have been applied for performing time history seismic analysis. The acceleration methods for uncracked structures have been verified via previous studies. However, no study has identified the validity of these acceleration methods for cracked piping. In this study, the validity of the acceleration methods for through-wall cracked piping is assessed via time history implicit dynamic elastic seismic analysis from the viewpoint of linear elastic fracture mechanics. As a result, it is identified that both acceleration methods show the same results for cracked piping if a large mass magnitude and maximum time increment are adequately selected.
Kim, Jong Sung; Kim, Yong Woo
2014-01-01
Two acceleration methods, an effective force method (or inertia method) and a large mass method, have been applied for performing time history seismic analysis. The acceleration methods for uncracked structures have been verified via previous studies. However, no study has identified the validity of these acceleration methods for cracked piping. In this study, the validity of the acceleration methods for through-wall cracked piping is assessed via time history implicit dynamic elastic seismic analysis from the viewpoint of linear elastic fracture mechanics. As a result, it is identified that both acceleration methods show the same results for cracked piping if a large mass magnitude and maximum time increment are adequately selected
Fractional calculus phenomenology in two-dimensional plasma models
Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill
2006-10-01
Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).
Two dimensional spatial distortion correction algorithm for scintillation GAMMA cameras
Chaney, R.; Gray, E.; Jih, F.; King, S.E.; Lim, C.B.
1985-01-01
Spatial distortion in an Anger gamma camera originates fundamentally from the discrete nature of scintillation light sampling with an array of PMT's. Historically digital distortion correction started with the method based on the distortion measurement by using 1-D slit pattern and the subsequent on-line bi-linear approximation with 64 x 64 look-up tables for X and Y. However, the X, Y distortions are inherently two-dimensional in nature, and thus the validity of this 1-D calibration method becomes questionable with the increasing distortion amplitude in association with the effort to get better spatial and energy resolutions. The authors have developed a new accurate 2-D correction algorithm. This method involves the steps of; data collection from 2-D orthogonal hole pattern, 2-D distortion vector measurement, 2-D Lagrangian polynomial interpolation, and transformation to X, Y ADC frame. The impact of numerical precision used in correction and the accuracy of bilinear approximation with varying look-up table size have been carefully examined through computer simulation by using measured single PMT light response function together with Anger positioning logic. Also the accuracy level of different order Lagrangian polynomial interpolations for correction table expansion from hole centroids were investigated. Detailed algorithm and computer simulation are presented along with camera test results
Particle simulation of a two-dimensional electrostatic plasma
Patel, K.
1989-01-01
Computer simulation is a growing field of research and plasma physics is one of the important areas where it is being applied today. This report describes the particle method of simulating a two-dimensional electrostatic plasma. The methods used to discretise the plasma equations and integrate the equations of motion are outlined. The algorithm used in building a simulation program is described. The program is applied to simulating the Two-stream Instability occurring within an infinite plasma. The results of the simulation are presented. The growth rate of the instability as simulated is in excellent agreement with the growth rate as calculated using linear theory. Diagnostic techniques used in interpreting the data generated by the simulation program are discussed. A comparison of the computing environment of the ND and PC from a user's viewpoint is presented. It is observed that the PC is an acceptable computing tool for certain (non-trivial) physics problems, and that more extensive use of its computing power should be made. (author). 5 figs
Coherent and radiative couplings through two-dimensional structured environments
Galve, F.; Zambrini, R.
2018-03-01
We study coherent and radiative interactions induced among two or more quantum units by coupling them to two-dimensional (2D) lattices acting as structured environments. This model can be representative of atoms trapped near photonic crystal slabs, trapped ions in Coulomb crystals, or to surface acoustic waves on piezoelectric materials, cold atoms on state-dependent optical lattices, or even circuit QED architectures, to name a few. We compare coherent and radiative contributions for the isotropic and directional regimes of emission into the lattice, for infinite and finite lattices, highlighting their differences and existing pitfalls, e.g., related to long-time or large-lattice limits. We relate the phenomenon of directionality of emission with linear-shaped isofrequency manifolds in the dispersion relation, showing a simple way to disrupt it. For finite lattices, we study further details such as the scaling of resonant number of lattice modes for the isotropic and directional regimes, and relate this behavior with known van Hove singularities in the infinite lattice limit. Furthermore, we export the understanding of emission dynamics with the decay of entanglement for two quantum, atomic or bosonic, units coupled to the 2D lattice. We analyze in some detail completely subradiant configurations of more than two atoms, which can occur in the finite lattice scenario, in contrast with the infinite lattice case. Finally, we demonstrate that induced coherent interactions for dark states are zero for the finite lattice.
Fluctuations and symmetries in two-dimensional active gels.
Sarkar, N; Basu, A
2011-04-01
Motivated by the unique physical properties of biological active matter, e.g., cytoskeletal dynamics in eukaryotic cells, we set up effective two-dimensional (2d) coarse-grained hydrodynamic equations for the dynamics of thin active gels with polar or nematic symmetries. We use the well-known three-dimensional (3d) descriptions (K. Kruse et al., Eur. Phys. J. E 16, 5 (2005); A. Basu et al., Eur. Phys. J. E 27, 149 (2008)) for thin active-gel samples confined between parallel plates with appropriate boundary conditions to derive the effective 2d constitutive relations between appropriate thermodynamic fluxes and generalised forces for small deviations from equilibrium. We consider three distinct cases, characterised by spatial symmetries and boundary conditions, and show how such considerations dictate the structure of the constitutive relations. We use these to study the linear instabilities, calculate the correlation functions and the diffusion constant of a small tagged particle, and elucidate their dependences on the activity or nonequilibrium drive.
Performance Estimation for Two-Dimensional Brownian Rotary Ratchet Systems
Tutu, Hiroki; Horita, Takehiko; Ouchi, Katsuya
2015-04-01
Within the context of the Brownian ratchet model, a molecular rotary system that can perform unidirectional rotations induced by linearly polarized ac fields and produce positive work under loads was studied. The model is based on the Langevin equation for a particle in a two-dimensional (2D) three-tooth ratchet potential of threefold symmetry. The performance of the system is characterized by the coercive torque, i.e., the strength of the load competing with the torque induced by the ac driving field, and the energy efficiency in force conversion from the driving field to the torque. We propose a master equation for coarse-grained states, which takes into account the boundary motion between states, and develop a kinetic description to estimate the mean angular momentum (MAM) and powers relevant to the energy balance equation. The framework of analysis incorporates several 2D characteristics and is applicable to a wide class of models of smooth 2D ratchet potential. We confirm that the obtained expressions for MAM, power, and efficiency of the model can enable us to predict qualitative behaviors. We also discuss the usefulness of the torque/power relationship for experimental analyses, and propose a characteristic for 2D ratchet systems.
Almost two-dimensional treatment of drift wave turbulence
Albert, J.M.; Similon, P.L.; Sudan, R.N.
1990-01-01
The approximation of two-dimensionality is studied and extended for electrostatic drift wave turbulence in a three-dimensional, magnetized plasma. It is argued on the basis of the direct interaction approximation that in the absence of parallel viscosity, purely 2-D solutions exist for which only modes with k parallel =0 are excited, but that the 2-D spectrum is unstable to perturbations at nonzero k parallel . A 1-D equation for the parallel profile g k perpendicular (k parallel ) of the saturated spectrum at steady state is derived and solved, allowing for parallel viscosity; the spectrum has finite width in k parallel , and hence finite parallel correlation length, as a result of nonlinear coupling. The enhanced energy dissipation rate, a 3-D effect, may be incorporated in the 2-D approximation by a suitable renormalization of the linear dissipation term. An algorithm is presented that reduces the 3-D problem to coupled 1- and 2-D problems. Numerical results from a 2-D spectral direct simulation, thus modified, are compared with the results from the corresponding 3-D (unmodified) simulation for a specific model of drift wave excitation. Damping at high k parallel is included. It is verified that the 1-D solution for g k perpendicular (k parallel ) accurately describes the shape and width of the 3-D spectrum, and that the modified 2-D simulation gives a good estimate of the 3-D energy saturation level and distribution E(k perpendicular )
Zhu, Shuze; Geng, Xiumei; Han, Yang; Benamara, Mourad; Chen, Liao; Li, Jingxiao; Bilgin, Ismail; Zhu, Hongli
2017-10-01
Element sulfur in nature is an insulating solid. While it has been tested that one-dimensional sulfur chain is metallic and conducting, the investigation on two-dimensional sulfur remains elusive. We report that molybdenum disulfide layers are able to serve as the nanotemplate to facilitate the formation of two-dimensional sulfur. Density functional theory calculations suggest that confined in-between layers of molybdenum disulfide, sulfur atoms are able to form two-dimensional triangular arrays that are highly metallic. As a result, these arrays contribute to the high conductivity and metallic phase of the hybrid structures of molybdenum disulfide layers and two-dimensional sulfur arrays. The experimentally measured conductivity of such hybrid structures reaches up to 223 S/m. Multiple experimental results, including X-ray photoelectron spectroscopy (XPS), transition electron microscope (TEM), selected area electron diffraction (SAED), agree with the computational insights. Due to the excellent conductivity, the current density is linearly proportional to the scan rate until 30,000 mV s-1 without the attendance of conductive additives. Using such hybrid structures as electrode, the two-electrode supercapacitor cells yield a power density of 106 Wh kg-1 and energy density 47.5 Wh kg-1 in ionic liquid electrolytes. Our findings offer new insights into using two-dimensional materials and their Van der Waals heterostructures as nanotemplates to pattern foreign atoms for unprecedented material properties.
Optimizing separations in online comprehensive two-dimensional liquid chromatography.
Pirok, Bob W J; Gargano, Andrea F G; Schoenmakers, Peter J
2018-01-01
Online comprehensive two-dimensional liquid chromatography has become an attractive option for the analysis of complex nonvolatile samples found in various fields (e.g. environmental studies, food, life, and polymer sciences). Two-dimensional liquid chromatography complements the highly popular hyphenated systems that combine liquid chromatography with mass spectrometry. Two-dimensional liquid chromatography is also applied to the analysis of samples that are not compatible with mass spectrometry (e.g. high-molecular-weight polymers), providing important information on the distribution of the sample components along chemical dimensions (molecular weight, charge, lipophilicity, stereochemistry, etc.). Also, in comparison with conventional one-dimensional liquid chromatography, two-dimensional liquid chromatography provides a greater separation power (peak capacity). Because of the additional selectivity and higher peak capacity, the combination of two-dimensional liquid chromatography with mass spectrometry allows for simpler mixtures of compounds to be introduced in the ion source at any given time, improving quantitative analysis by reducing matrix effects. In this review, we summarize the rationale and principles of two-dimensional liquid chromatography experiments, describe advantages and disadvantages of combining different selectivities and discuss strategies to improve the quality of two-dimensional liquid chromatography separations. © 2017 The Authors. Journal of Separation Science published by WILEY-VCH Verlag GmbH & Co. KGaA.
Functional inks and printing of two-dimensional materials.
Hu, Guohua; Kang, Joohoon; Ng, Leonard W T; Zhu, Xiaoxi; Howe, Richard C T; Jones, Christopher G; Hersam, Mark C; Hasan, Tawfique
2018-05-08
Graphene and related two-dimensional materials provide an ideal platform for next generation disruptive technologies and applications. Exploiting these solution-processed two-dimensional materials in printing can accelerate this development by allowing additive patterning on both rigid and conformable substrates for flexible device design and large-scale, high-speed, cost-effective manufacturing. In this review, we summarise the current progress on ink formulation of two-dimensional materials and the printable applications enabled by them. We also present our perspectives on their research and technological future prospects.
Third sound in one and two dimensional modulated structures
Komuro, T.; Kawashima, H., Shirahama, K.; Kono, K.
1996-01-01
An experimental technique is developed to study acoustic transmission in one and two dimensional modulated structures by employing third sound of a superfluid helium film. In particular, the Penrose lattice, which is a two dimensional quasiperiodic structure, is studied. In two dimensions, the scattering of third sound is weaker than in one dimension. Nevertheless, the authors find that the transmission spectrum in the Penrose lattice, which is a two dimensional prototype of the quasicrystal, is observable if the helium film thickness is chosen around 5 atomic layers. The transmission spectra in the Penrose lattice are explained in terms of dynamical theory of diffraction
ONE-DIMENSIONAL AND TWO-DIMENSIONAL LEADERSHIP STYLES
Nikola Stefanović
2007-06-01
Full Text Available In order to motivate their group members to perform certain tasks, leaders use different leadership styles. These styles are based on leaders' backgrounds, knowledge, values, experiences, and expectations. The one-dimensional styles, used by many world leaders, are autocratic and democratic styles. These styles lie on the two opposite sides of the leadership spectrum. In order to precisely define the leadership styles on the spectrum between the autocratic leadership style and the democratic leadership style, leadership theory researchers use two dimensional matrices. The two-dimensional matrices define leadership styles on the basis of different parameters. By using these parameters, one can identify two-dimensional styles.
Nahed S. Hussein
2014-01-01
Full Text Available A numerical boundary integral scheme is proposed for the solution to the system of eld equations of plane. The stresses are prescribed on one-half of the circle, while the displacements are given. The considered problem with mixed boundary conditions in the circle is replaced by two problems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way, and the problem at this stage is reduced to the solution to a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution and the unknown boundary values of stresses or displacements on proper parts of the boundary. On the basis of the obtained results, it is inferred that a stress component has a singularity at each of the two separation points, thought to be of logarithmic type. The results are discussed and boundary plots are given. We have also calculated the unknown functions in the bulk directly from the given boundary conditions using the boundary collocation method. The obtained results in the bulk are discussed and three-dimensional plots are given. A tentative form for the singular solution is proposed and the corresponding singular stresses and displacements are plotted in the bulk. The form of the singular tangential stress is seen to be compatible with the boundary values obtained earlier. The efficiency of the used numerical schemes is discussed.
Two-dimensional electronic femtosecond stimulated Raman spectroscopy
Ogilvie J.P.
2013-03-01
Full Text Available We report two-dimensional electronic spectroscopy with a femtosecond stimulated Raman scattering probe. The method reveals correlations between excitation energy and excited state vibrational structure following photoexcitation. We demonstrate the method in rhodamine 6G.
Micromachined two dimensional resistor arrays for determination of gas parameters
van Baar, J.J.J.; Verwey, Willem B.; Dijkstra, Mindert; Dijkstra, Marcel; Wiegerink, Remco J.; Lammerink, Theodorus S.J.; Krijnen, Gijsbertus J.M.; Elwenspoek, Michael Curt
A resistive sensor array is presented for two dimensional temperature distribution measurements in a micromachined flow channel. This allows simultaneous measurement of flow velocity and fluid parameters, like thermal conductivity, diffusion coefficient and viscosity. More general advantages of
Generalized similarity method in unsteady two-dimensional MHD ...
user
International Journal of Engineering, Science and Technology. Vol. 1, No. 1, 2009 ... temperature two-dimensional MHD laminar boundary layer of incompressible fluid. ...... Φ η is Blasius solution for stationary boundary layer on the plate,. ( ). 0.
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Structures of two-dimensional three-body systems
Ruan, W.Y.; Liu, Y.Y.; Bao, C.G.
1996-01-01
Features of the structure of L = 0 states of a two-dimensional three-body model system have been investigated. Three types of permutation symmetry of the spatial part, namely symmetric, antisymmetric, and mixed, have been considered. A comparison has been made between the two-dimensional system and the corresponding three-dimensional one. The effect of symmetry on microscopic structures is emphasized. (author)
Study on two-dimensional induced signal readout of MRPC
Wu Yucheng; Yue Qian; Li Yuanjing; Ye Jin; Cheng Jianping; Wang Yi; Li Jin
2012-01-01
A kind of two-dimensional readout electrode structure for the induced signal readout of MRPC has been studied in both simulation and experiments. Several MRPC prototypes are produced and a series of test experiments have been done to compare with the result of simulation, in order to verify the simulation model. The experiment results are in good agreement with those of simulation. This method will be used to design the two-dimensional signal readout mode of MRPC in the future work.
Controlled Interactions between Two Dimensional Layered Inorganic Nanosheets and Polymers
2016-06-15
AFRL-AFOSR-JP-TR-2016-0071 Controlled Interactions between Two Dimensional Layered Inorganic Nanosheets and Polymers Cheolmin Park YONSEI UNIVERSITY...Interactions between Two Dimensional Layered Inorganic Nanosheets and Polymers 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA2386-14-1-4054 5c. PROGRAM ELEMENT...prospects for a variety of emerging applications in a broad range of fields, such as electronics, energy conversion and storage, catalysis and polymer
A REMARK ON FORMAL MODELS FOR NONLINEARLY ELASTIC MEMBRANE SHELLS
无
2001-01-01
This paper gives all the two-dimensional membrane models obtained from formal asymptotic analysis of the three-dimensional geometrically exact nonlinear model of a thin elastic shell made with a Saint Venant-Kirchhoff material. Therefore, the other models can be quoted as flexural nonlinear ones. The author also gives the formal equations solved by the associated stress tensor and points out that only one of those models leads, by linearization, to the “classical” linear limiting membrane model, whose juetification has already been established by a convergence theorem.
The theory of critical phenomena in two-dimensional systems
Olvera de la C, M.
1981-01-01
An exposition of the theory of critical phenomena in two-dimensional physical systems is presented. The first six chapters deal with the mean field theory of critical phenomena, scale invariance of the thermodynamic functions, Kadanoff's spin block construction, Wilson's renormalization group treatment of critical phenomena in configuration space, and the two-dimensional Ising model on a triangular lattice. The second part of this work is made of four chapters devoted to the application of the ideas expounded in the first part to the discussion of critical phenomena in superfluid films, two-dimensional crystals and the two-dimensional XY model of magnetic systems. Chapters seven to ten are devoted to the following subjects: analysis of long range order in one, two, and three-dimensional physical systems. Topological defects in the XY model, in superfluid films and in two-dimensional crystals. The Thouless-Kosterlitz iterated mean field theory of the dipole gas. The renormalization group treatment of the XY model, superfluid films and two-dimensional crystal. (author)
Two-dimensional multifractal cross-correlation analysis
Xi, Caiping; Zhang, Shuning; Xiong, Gang; Zhao, Huichang; Yang, Yonghong
2017-01-01
Highlights: • We study the mathematical models of 2D-MFXPF, 2D-MFXDFA and 2D-MFXDMA. • Present the definition of the two-dimensional N 2 -partitioned multiplicative cascading process. • Do the comparative analysis of 2D-MC by 2D-MFXPF, 2D-MFXDFA and 2D-MFXDMA. • Provide a reference on the choice and parameter settings of these methods in practice. - Abstract: There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross-correlations. This paper presents two-dimensional multifractal cross-correlation analysis based on the partition function (2D-MFXPF), two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) and two-dimensional multifractal cross-correlation analysis based on the detrended moving average analysis (2D-MFXDMA). We apply these methods to pairs of two-dimensional multiplicative cascades (2D-MC) to do a comparative study. Then, we apply the two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) to real images and unveil intriguing multifractality in the cross correlations of the material structures. At last, we give the main conclusions and provide a valuable reference on how to choose the multifractal algorithms in the potential applications in the field of SAR image classification and detection.
Two-Dimensional Materials for Sensing: Graphene and Beyond
Seba Sara Varghese
2015-09-01
Full Text Available Two-dimensional materials have attracted great scientific attention due to their unusual and fascinating properties for use in electronics, spintronics, photovoltaics, medicine, composites, etc. Graphene, transition metal dichalcogenides such as MoS2, phosphorene, etc., which belong to the family of two-dimensional materials, have shown great promise for gas sensing applications due to their high surface-to-volume ratio, low noise and sensitivity of electronic properties to the changes in the surroundings. Two-dimensional nanostructured semiconducting metal oxide based gas sensors have also been recognized as successful gas detection devices. This review aims to provide the latest advancements in the field of gas sensors based on various two-dimensional materials with the main focus on sensor performance metrics such as sensitivity, specificity, detection limit, response time, and reversibility. Both experimental and theoretical studies on the gas sensing properties of graphene and other two-dimensional materials beyond graphene are also discussed. The article concludes with the current challenges and future prospects for two-dimensional materials in gas sensor applications.
Computer simulation of the martensite transformation in a model two-dimensional body
Chen, S.; Khachaturyan, A.G.; Morris, J.W. Jr.
1979-05-01
An analytical model of a martensitic transformation in an idealized body is constructed and used to carry out a computer simulation of the transformation in a pseudo-two-dimensional crystal. The reaction is assumed to proceed through the sequential transformation of elementary volumes (elementary martensitic particles, EMP) via the Bain strain. The elastic interaction between these volumes is computed and the transformation path chosen so as to minimize the total free energy. The model transformation shows interesting qualitative correspondencies with the known features of martensitic transformations in typical solids
Computer simulation of the martensite transformation in a model two-dimensional body
Chen, S.; Khachaturyan, A.G.; Morris, J.W. Jr.
1979-06-01
An analytical model of a martensitic transformation in an idealized body is constructed and used to carry out a computer simulation of the transformation in a pseudo-two-dimensional crystal. The reaction is assumed to proceed through the sequential transformation of elementary volumes (elementary martensitic particles, EMP) via the Bain strain. The elastic interaction between these volumes is computed and the transformation path chosen so as to minimize the total free energy. The model transformation shows interesting qualitative correspondencies with the known features of martensitic transformations in typical solids
State-space representation of instationary two-dimensional airfoil aerodynamics
Meyer, Marcus; Matthies, Hermann G. [Institute of Scientific Computing, Technical University Braunschweig, Hans-Sommer-Str. 65, Braunschweig 38106 (Germany)
2004-03-01
In the aero-elastic analysis of wind turbines the need to include a model of the local, two-dimensional instationary aerodynamic loads, commonly referred to as dynamic stall model, has become obvious in the last years. In this contribution an alternative choice for such a model is described, based on the DLR model. Its derivation is governed by the flow physics, thus enabling interpolation between different profile geometries. An advantage of the proposed model is its state-space form, i.e. a system of differential equations, which facilitates the important tasks of aeroelastic stability and sensitivity investigations. The model is validated with numerical calculations.
Náprstek, Jiří; Pospíšil, Stanislav
2012-01-01
Roč. 111, č. 1 (2012), s. 1-13 ISSN 0167-6105 R&D Projects: GA ČR(CZ) GA103/09/0094; GA AV ČR(CZ) IAA200710902 Institutional support: RVO:68378297 Keywords : aero-elastic system * self-excited vibration * instability * aero-elastic derivatives Subject RIV: JN - Civil Engineering Impact factor: 1.342, year: 2012
Hou, Fang
With the extensive application of fiber-reinforced composite laminates in industry, research on the fracture mechanisms of this type of materials have drawn more and more attentions. A variety of fracture theories and models have been developed. Among them, the linear elastic fracture mechanics (LEFM) and cohesive-zone model (CZM) are two widely-accepted fracture models, which have already shown applicability in the fracture analysis of fiber-reinforced composite laminates. However, there remain challenges which prevent further applications of the two fracture models, such as the experimental measurement of fracture resistance. This dissertation primarily focused on the study of the applicability of LEFM and CZM for the fracture analysis of translaminar fracture in fibre-reinforced composite laminates. The research for each fracture model consisted of two sections: the analytical characterization of crack-tip fields and the experimental measurement of fracture resistance parameters. In the study of LEFM, an experimental investigation based on full-field crack-tip displacement measurements was carried out as a way to characterize the subcritical and steady-state crack advances in translaminar fracture of fiber-reinforced composite laminates. Here, the fiber-reinforced composite laminates were approximated as anisotropic solids. The experimental investigation relied on the LEFM theory with a modification with respect to the material anisotropy. Firstly, the full-field crack-tip displacement fields were measured by Digital Image Correlation (DIC). Then two methods, separately based on the stress intensity approach and the energy approach, were developed to measure the crack-tip field parameters from crack-tip displacement fields. The studied crack-tip field parameters included the stress intensity factor, energy release rate and effective crack length. Moreover, the crack-growth resistance curves (R-curves) were constructed with the measured crack-tip field parameters
A geometrical approach to two-dimensional Conformal Field Theory
Dijkgraaf, Robertus Henricus
1989-09-01
manifold obtained as the quotient of a smooth manifold by a discrete group. In Chapter 6 our considerations will be of a somewhat complementary nature. We will investigate models with central charge c = 1 by deformation techniques. The central charge is a fundamental parameter in any conformal invariant model, and the value c = 1 is of considerable interest, since it forms in many ways a threshold value. For c 1 is still very much terra incognita. Our results give a partial classification for the intermediate case of c = 1 models. The formulation of these c = 1 CFT's on surfaces of arbitrary topology is central in Chapter 7. Here we will provide many explicit results that provide illustrations for our more abstract discussions of higher genus quantities in Chapters 3 and 1. Unfortunately, our calculations will become at this point rather technical, since we have to make extensive use of the mathematics of Riemann surfaces and their coverings. Finally, in Chapter 8 we leave the two-dimensional point of view that we have been so loyal to up to then , and ascend to threedimensions where we meet topological gauge theories. These so-called Chern-Simons theories encode in a very economic way much of the structure of two-dimensional (rational) conformal field theories, and this direction is generally seen to be very promising. We will show in particular how many of our results of Chapter 5 have a natural interpretation in three dimensions.
Application of CRAFT in two-dimensional NMR data processing.
Krishnamurthy, Krish; Sefler, Andrea M; Russell, David J
2017-03-01
Two-dimensional (2D) data are typically truncated in both dimensions, but invariably and severely so in the indirect dimension. These truncated FIDs and/or interferograms are extensively zero filled, and Fourier transformation of such zero-filled data is always preceded by a rapidly decaying apodization function. Hence, the frequency line width in the spectrum (at least parallel to the evolution dimension) is almost always dominated by the apodization function. Such apodization-driven line broadening in the indirect (t 1 ) dimension leads to the lack of clear resolution of cross peaks in the 2D spectrum. Time-domain analysis (i.e. extraction of frequency, amplitudes, line width, and phase parameters directly from the FID, in this case via Bayesian modeling into a tabular format) of NMR data is another approach for spectral resonance characterization and quantification. The recently published complete reduction to amplitude frequency table (CRAFT) technique converts the raw FID data (i.e. time-domain data) into a table of frequencies, amplitudes, decay rate constants, and phases. CRAFT analyses of time-domain data require minimal or no apodization prior to extraction of the four parameters. We used the CRAFT processing approach for the decimation of the interferograms and compared the results from a variety of 2D spectra against conventional processing with and without linear prediction. The results show that use of the CRAFT technique to decimate the t 1 interferograms yields much narrower spectral line width of the resonances, circumventing the loss of resolution due to apodization. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Family of two-dimensional Born-Infeld equations and a system of conservation laws
Koiv, M.; Rosenhaus, V.
1979-01-01
Lower-order conserved quantities, the ''currents'', for two-dimensional Lorentz-invariant Born-Infeld equation are considered. The currents are divided into pairs, which contain a class (basic currents) leading to the family equations. The basic currents determine the transformations between the solutions of the Born-Infeld eqution family. The equations belonging to the family are fully hodograph-invariant, partly hodograph-invariant, and effectively linear, i.e. non-linear equations with linear image of hodograph transformation
Xu Quan; Tian Qiang
2013-01-01
Using numerical method, we investigate whether periodic, quasiperiodic, and chaotic breathers are supported by the two-dimensional discrete Fermi—Pasta—Ulam (FPU) lattice with linear dispersion term. The spatial profile and time evolution of the two-dimensional discrete β-FPU lattice are segregated by the method of separation of variables, and the numerical simulations suggest that the discrete breathers (DBs) are supported by the system. By introducing a periodic interaction into the linear interaction between the atoms, we achieve the coupling of two incommensurate frequencies for a single DB, and the numerical simulations suggest that the quasiperiodic and chaotic breathers are supported by the system, too. (condensed matter: structural, mechanical, and thermal properties)
Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction
Sid, S.; Terrapon, V. E.; Dubief, Y.
2018-02-01
The goal of the present study is threefold: (i) to demonstrate the two-dimensional nature of the elasto-inertial instability in elasto-inertial turbulence (EIT), (ii) to identify the role of the bidimensional instability in three-dimensional EIT flows, and (iii) to establish the role of the small elastic scales in the mechanism of self-sustained EIT. Direct numerical simulations of viscoelastic fluid flows are performed in both two- and three-dimensional straight periodic channels using the Peterlin finitely extensible nonlinear elastic model (FENE-P). The Reynolds number is set to Reτ=85 , which is subcritical for two-dimensional flows but beyond the transition for three-dimensional ones. The polymer properties selected correspond to those of typical dilute polymer solutions, and two moderate Weissenberg numbers, Wiτ=40 ,100 , are considered. The simulation results show that sustained turbulence can be observed in two-dimensional subcritical flows, confirming the existence of a bidimensional elasto-inertial instability. The same type of instability is also observed in three-dimensional simulations where both Newtonian and elasto-inertial turbulent structures coexist. Depending on the Wi number, one type of structure can dominate and drive the flow. For large Wi values, the elasto-inertial instability tends to prevail over the Newtonian turbulence. This statement is supported by (i) the absence of typical Newtonian near-wall vortices and (ii) strong similarities between two- and three-dimensional flows when considering larger Wi numbers. The role of small elastic scales is investigated by introducing global artificial diffusion (GAD) in the hyperbolic transport equation for polymers. The aim is to measure how the flow reacts when the smallest elastic scales are progressively filtered out. The study results show that the introduction of large polymer diffusion in the system strongly damps a significant part of the elastic scales that are necessary to feed
Kinetic Theory of a Confined Quasi-Two-Dimensional Gas of Hard Spheres
J. Javier Brey
2017-02-01
Full Text Available The dynamics of a system of hard spheres enclosed between two parallel plates separated a distance smaller than two particle diameters is described at the level of kinetic theory. The interest focuses on the behavior of the quasi-two-dimensional fluid seen when looking at the system from above or below. In the first part, a collisional model for the effective two-dimensional dynamics is analyzed. Although it is able to describe quite well the homogeneous evolution observed in the experiments, it is shown that it fails to predict the existence of non-equilibrium phase transitions, and in particular, the bimodal regime exhibited by the real system. A critical revision analysis of the model is presented , and as a starting point to get a more accurate description, the Boltzmann equation for the quasi-two-dimensional gas has been derived. In the elastic case, the solutions of the equation verify an H-theorem implying a monotonic tendency to a non-uniform steady state. As an example of application of the kinetic equation, here the evolution equations for the vertical and horizontal temperatures of the system are derived in the homogeneous approximation, and the results compared with molecular dynamics simulation results.
Calculation of two-dimensional thermal transients by the finite element method
Fontoura Rodrigues, J.L.A. da; Barcellos, C.S. de
1981-01-01
The linear heat conduction through anisotropic and/or heterogeneous matter, in either two-dimensional fields with any kind of geometry or three-dimensional fields with axial symmetry is analysed. It only accepts time-independent boundary conditions and it is possible to have internal heat generation. The solution is obtained by modal analysis employing the finite element method under Galerkin formulation. (Author) [pt
Moment-based method for computing the two-dimensional discrete Hartley transform
Dong, Zhifang; Wu, Jiasong; Shu, Huazhong
2009-10-01
In this paper, we present a fast algorithm for computing the two-dimensional (2-D) discrete Hartley transform (DHT). By using kernel transform and Taylor expansion, the 2-D DHT is approximated by a linear sum of 2-D geometric moments. This enables us to use the fast algorithms developed for computing the 2-D moments to efficiently calculate the 2-D DHT. The proposed method achieves a simple computational structure and is suitable to deal with any sequence lengths.
Interplay between topology and disorder in a two-dimensional semi-Dirac material
Sriluckshmy, P. V.; Saha, Kush; Moessner, Roderich
2017-01-01
We investigate the role of disorder in a two-dimensional semi-Dirac material characterized by a linear dispersion in one, and a parabolic dispersion in the orthogonal, direction. Using the self-consistent Born approximation, we show that disorder can drive a topological Lifshitz transition from an insulator to a semi-metal, as it generates a momentum independent off-diagonal contribution to the self-energy. Breaking time-reversal symmetry enriches the topological phase diagram with three dist...
Consistent calculation of the stopping power for slow ions in two-dimensional electron gases
Wang, You-Nian; Ma, Teng-Gai
1997-01-01
Within the framework of quantum scattering theory, we present a consistent calculation of the stopping power for slow protons and antiprotons moving in two-dimensional electron gases. The Friedel sum rule is used to determine the screening constant in the scattering potential. For the stopping power our results are compared with that of the random-phase approximation dielectric theory and that predicted by the linear Thomas-Fermi potential. copyright 1997 The American Physical Society
Traditional Semiconductors in the Two-Dimensional Limit.
Lucking, Michael C; Xie, Weiyu; Choe, Duk-Hyun; West, Damien; Lu, Toh-Ming; Zhang, S B
2018-02-23
Interest in two-dimensional materials has exploded in recent years. Not only are they studied due to their novel electronic properties, such as the emergent Dirac fermion in graphene, but also as a new paradigm in which stacking layers of distinct two-dimensional materials may enable different functionality or devices. Here, through first-principles theory, we reveal a large new class of two-dimensional materials which are derived from traditional III-V, II-VI, and I-VII semiconductors. It is found that in the ultrathin limit the great majority of traditional binary semiconductors studied (a series of 28 semiconductors) are not only kinetically stable in a two-dimensional double layer honeycomb structure, but more energetically stable than the truncated wurtzite or zinc-blende structures associated with three dimensional bulk. These findings both greatly increase the landscape of two-dimensional materials and also demonstrate that in the double layer honeycomb form, even ordinary semiconductors, such as GaAs, can exhibit exotic topological properties.
Two-dimensional analytic weighting functions for limb scattering
Zawada, D. J.; Bourassa, A. E.; Degenstein, D. A.
2017-10-01
Through the inversion of limb scatter measurements it is possible to obtain vertical profiles of trace species in the atmosphere. Many of these inversion methods require what is often referred to as weighting functions, or derivatives of the radiance with respect to concentrations of trace species in the atmosphere. Several radiative transfer models have implemented analytic methods to calculate weighting functions, alleviating the computational burden of traditional numerical perturbation methods. Here we describe the implementation of analytic two-dimensional weighting functions, where derivatives are calculated relative to atmospheric constituents in a two-dimensional grid of altitude and angle along the line of sight direction, in the SASKTRAN-HR radiative transfer model. Two-dimensional weighting functions are required for two-dimensional inversions of limb scatter measurements. Examples are presented where the analytic two-dimensional weighting functions are calculated with an underlying one-dimensional atmosphere. It is shown that the analytic weighting functions are more accurate than ones calculated with a single scatter approximation, and are orders of magnitude faster than a typical perturbation method. Evidence is presented that weighting functions for stratospheric aerosols calculated under a single scatter approximation may not be suitable for use in retrieval algorithms under solar backscatter conditions.
Contoyannis, Paul; Hurley, Jeremiah; Grootendorst, Paul; Jeon, Sung-Hee; Tamblyn, Robyn
2005-09-01
The price elasticity of demand for prescription drugs is a crucial parameter of interest in designing pharmaceutical benefit plans. Estimating the elasticity using micro-data, however, is challenging because insurance coverage that includes deductibles, co-insurance provisions and maximum expenditure limits create a non-linear price schedule, making price endogenous (a function of drug consumption). In this paper we exploit an exogenous change in cost-sharing within the Quebec (Canada) public Pharmacare program to estimate the price elasticity of expenditure for drugs using IV methods. This approach corrects for the endogeneity of price and incorporates the concept of a 'rational' consumer who factors into consumption decisions the price they expect to face at the margin given their expected needs. The IV method is adapted from an approach developed in the public finance literature used to estimate income responses to changes in tax schedules. The instrument is based on the price an individual would face under the new cost-sharing policy if their consumption remained at the pre-policy level. Our preferred specification leads to expenditure elasticities that are in the low range of previous estimates (between -0.12 and -0.16). Naïve OLS estimates are between 1 and 4 times these magnitudes. (c) 2005 John Wiley & Sons, Ltd.
Shen, Aijin; Wei, Jie; Yan, Jingyu; Jin, Gaowa; Ding, Junjie; Yang, Bingcheng; Guo, Zhimou; Zhang, Feifang; Liang, Xinmiao
2017-03-01
An orthogonal two-dimensional solid-phase extraction strategy was established for the selective enrichment of three aminoglycosides including spectinomycin, streptomycin, and dihydrostreptomycin in milk. A reversed-phase liquid chromatography material (C 18 ) and a weak cation-exchange material (TGA) were integrated in a single solid-phase extraction cartridge. The feasibility of two-dimensional clean-up procedure that experienced two-step adsorption, two-step rinsing, and two-step elution was systematically investigated. Based on the orthogonality of reversed-phase and weak cation-exchange procedures, the two-dimensional solid-phase extraction strategy could minimize the interference from the hydrophobic matrix existing in traditional reversed-phase solid-phase extraction. In addition, high ionic strength in the extracts could be effectively removed before the second dimension of weak cation-exchange solid-phase extraction. Combined with liquid chromatography and tandem mass spectrometry, the optimized procedure was validated according to the European Union Commission directive 2002/657/EC. A good performance was achieved in terms of linearity, recovery, precision, decision limit, and detection capability in milk. Finally, the optimized two-dimensional clean-up procedure incorporated with liquid chromatography and tandem mass spectrometry was successfully applied to the rapid monitoring of aminoglycoside residues in milk. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Generation of acoustic phonons from quasi-two-dimensional hole gas
Singh, J.; Oh, I.K.
2002-01-01
Full text: Generation of phonons from two dimensional electron and hole gases in quantum wells has attracted much attraction recently. The mechanism of phonon emission plays an important role in the phonon spectroscopy which enables us to study the angular and polarization dependence of phonon emission. The acoustic phonon emission from a quasi-two-dimensional hole gas (2DHG) in quantum wells is influenced by the anisotropic factors in the valence band structure, screening, elastic property, etc. The anisotropy in the valence band structure gives rise to anisotropic effective mass and deformation potential and that in the elastic constants leads to anisotropic sound velocity. Piezoelectric coupling in non-centrosymmetric materials such as GaAs is also anisotropic. In this paper, considering the anisotropy in the effective mass, deformation potential, piezoelectric coupling and screening effect, we present a theory to study the angular and polarization dependence of acoustic phonon emission from a quasi-2DHG in quantum wells. The theory is finally applied to calculate the rate of acoustic phonon emission in GaAs quantum wells
Ueshima, N; Yoshiya, M; Yasuda, H; Fukuda, T; Kakeshita, T
2015-01-01
Through three-dimensional (3D) simulations of microstructure evolution by phase-field modeling (PFM), microstructures have been quantified during their time evolution by an image processing technique with particular attention to the shape of variants in the course of variant selection. It is found that the emerging variants exhibit planar shapes rather than 3D shapes due to the elastic field around the variants arising upon disorder-to-order transition to the L1 0 phase. The two-dimensionality is more pronounced as variant selection proceeds. Although three equivalent variants compete for dominance under an external field, one of the three variants vanishes before final competition occurs between the remaining variants, which can be explained by the elastic strain energy. These numerical analyses provide better understanding of the microstructure evolution in a more quantitative manner, including the small influence of the third variant, and the results obtained confirm that the understanding of variant selection obtained from two-dimensional (2D) simulations by PFM is valid. (paper)
Dynamical class of a two-dimensional plasmonic Dirac system.
Silva, Érica de Mello
2015-10-01
A current goal in plasmonic science and technology is to figure out how to manage the relaxational dynamics of surface plasmons in graphene since its damping constitutes a hinder for the realization of graphene-based plasmonic devices. In this sense we believe it might be of interest to enlarge the knowledge on the dynamical class of two-dimensional plasmonic Dirac systems. According to the recurrence relations method, different systems are said to be dynamically equivalent if they have identical relaxation functions at all times, and such commonality may lead to deep connections between seemingly unrelated physical systems. We employ the recurrence relations approach to obtain relaxation and memory functions of density fluctuations and show that a two-dimensional plasmonic Dirac system at long wavelength and zero temperature belongs to the same dynamical class of standard two-dimensional electron gas and classical harmonic oscillator chain with an impurity mass.
Hamiltonian formalism of two-dimensional Vlasov kinetic equation.
Pavlov, Maxim V
2014-12-08
In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.
Control Operator for the Two-Dimensional Energized Wave Equation
Sunday Augustus REJU
2006-07-01
Full Text Available This paper studies the analytical model for the construction of the two-dimensional Energized wave equation. The control operator is given in term of space and time t independent variables. The integral quadratic objective cost functional is subject to the constraint of two-dimensional Energized diffusion, Heat and a source. The operator that shall be obtained extends the Conjugate Gradient method (ECGM as developed by Hestenes et al (1952, [1]. The new operator enables the computation of the penalty cost, optimal controls and state trajectories of the two-dimensional energized wave equation when apply to the Conjugate Gradient methods in (Waziri & Reju, LEJPT & LJS, Issues 9, 2006, [2-4] to appear in this series.
Velocity and Dispersion for a Two-Dimensional Random Walk
Li Jinghui
2009-01-01
In the paper, we consider the transport of a two-dimensional random walk. The velocity and the dispersion of this two-dimensional random walk are derived. It mainly show that: (i) by controlling the values of the transition rates, the direction of the random walk can be reversed; (ii) for some suitably selected transition rates, our two-dimensional random walk can be efficient in comparison with the one-dimensional random walk. Our work is motivated in part by the challenge to explain the unidirectional transport of motor proteins. When the motor proteins move at the turn points of their tracks (i.e., the cytoskeleton filaments and the DNA molecular tubes), some of our results in this paper can be used to deal with the problem. (general)
Shokouhi, Parisa; Rivière, Jacques; Lake, Colton R; Le Bas, Pierre-Yves; Ulrich, T J
2017-11-01
The use of nonlinear acoustic techniques in solids consists in measuring wave distortion arising from compliant features such as cracks, soft intergrain bonds and dislocations. As such, they provide very powerful nondestructive tools to monitor the onset of damage within materials. In particular, a recent technique called dynamic acousto-elasticity testing (DAET) gives unprecedented details on the nonlinear elastic response of materials (classical and non-classical nonlinear features including hysteresis, transient elastic softening and slow relaxation). Here, we provide a comprehensive set of linear and nonlinear acoustic responses on two prismatic concrete specimens; one intact and one pre-compressed to about 70% of its ultimate strength. The two linear techniques used are Ultrasonic Pulse Velocity (UPV) and Resonance Ultrasound Spectroscopy (RUS), while the nonlinear ones include DAET (fast and slow dynamics) as well as Nonlinear Resonance Ultrasound Spectroscopy (NRUS). In addition, the DAET results correspond to a configuration where the (incoherent) coda portion of the ultrasonic record is used to probe the samples, as opposed to a (coherent) first arrival wave in standard DAET tests. We find that the two visually identical specimens are indistinguishable based on parameters measured by linear techniques (UPV and RUS). On the contrary, the extracted nonlinear parameters from NRUS and DAET are consistent and orders of magnitude greater for the damaged specimen than those for the intact one. This compiled set of linear and nonlinear ultrasonic testing data including the most advanced technique (DAET) provides a benchmark comparison for their use in the field of material characterization. Copyright © 2017 Elsevier B.V. All rights reserved.
Two-dimensional nonlinear equations of supersymmetric gauge theories
Savel'ev, M.V.
1985-01-01
Supersymmetric generalization of two-dimensional nonlinear dynamical equations of gauge theories is presented. The nontrivial dynamics of a physical system in the supersymmetry and supergravity theories for (2+2)-dimensions is described by the integrable embeddings of Vsub(2/2) superspace into the flat enveloping superspace Rsub(N/M), supplied with the structure of a Lie superalgebra. An equation is derived which describes a supersymmetric generalization of the two-dimensional Toda lattice. It contains both super-Liouville and Sinh-Gordon equations
Spin dynamics in a two-dimensional quantum gas
Pedersen, Poul Lindholm; Gajdacz, Miroslav; Deuretzbacher, Frank
2014-01-01
We have investigated spin dynamics in a two-dimensional quantum gas. Through spin-changing collisions, two clouds with opposite spin orientations are spontaneously created in a Bose-Einstein condensate. After ballistic expansion, both clouds acquire ring-shaped density distributions with superimp......We have investigated spin dynamics in a two-dimensional quantum gas. Through spin-changing collisions, two clouds with opposite spin orientations are spontaneously created in a Bose-Einstein condensate. After ballistic expansion, both clouds acquire ring-shaped density distributions...
Two dimensional nonlinear spectral estimation techniques for breast cancer localization
Stathaki, P.T.; Constantinides, A.G.
1994-01-01
In this paper the problem of image texture analysis in the presence of noise is examined from a higher-order statistical perspective. The approach taken involves the use of two dimensional second order Volterra filters where the filter weights are derived from third order cumulants of the two dimensional signal. The specific application contained in this contribution is in mammography, an area in which it is difficult to discern the appropriate features. The paper describes the fundamental issues of the various components of the approach. The results of the entire texture modelling, classification and segmentation scheme contained in this paper are very encouraging
Densis. Densimetric representation of two-dimensional matrices
Los Arcos Merino, J.M.
1978-01-01
Densis is a Fortran V program which allows off-line control of a Calcomp digital plotter, to represent a two-dimensional matrix of numerical elements in the form of a variable shading intensity map in two colours. Each matrix element is associated to a square of a grid which is traced over by lines whose number is a function of the element value according to a selected scale. Program features, subroutine structure and running instructions, are described. Some typical results, for gamma-gamma coincidence experimental data and a sampled two-dimensional function, are indicated. (author)
Two-dimensional QCD in the Coulomb gauge
Kalashnikova, Yu.S.; Nefed'ev, A.V.
2002-01-01
Various aspects of the 't Hooft model for two-dimensional QCD in the limit of infinite number of colours in the Coulomb gauge are discussed. The properties of mesonic excitations are studied, with special emphasis on the pion. Attention is paid to the dual role of the pion. which, while a genuine qq-bar state, is a Goldstone boson of two-dimensional QCD as well. In particular, the validity of the soft-pion theorems is demonstrated. It is shown that the Coulomb gauge is the most suitable choice for the study of hadronic observables involving pions [ru
Quantum Communication Through a Two-Dimensional Spin Network
Wang Zhaoming; Gu Yongjian
2012-01-01
We investigate the state or entanglement transfer through a two-dimensional spin network. We show that for state transfer, better fidelity can be gained along the diagonal direction but for entanglement transfer, when the initial entanglement is created along the boundary, the concurrence is more inclined to propagate along the boundary. This behavior is produced by quantum mechanical interference and the communication quality depends on the precise size of the network. For some number of sites, the fidelity in a two-dimensional channel is higher than one-dimensional case. This is an important result for realizing quantum communication through high dimension spin chain networks.
Critical Behaviour of a Two-Dimensional Random Antiferromagnet
Als-Nielsen, Jens Aage; Birgeneau, R. J.; Guggenheim, H. J.
1976-01-01
A neutron scattering study of the order parameter, correlation length and staggered susceptibility of the two-dimensional random antiferromagnet Rb2Mn0.5Ni0.5F4 is reported. The system is found to exhibit a well-defined phase transition with critical exponents identical to those of the isomorphou...... pure materials K2NiF4 and K2MnF4. Thus, in these systems, which have the asymptotic critical behaviour of the two-dimensional Ising model, randomness has no measurable effect on the phase-transition behaviour....
Two dimensional nonlinear spectral estimation techniques for breast cancer localization
Stathaki, P T; Constantinides, A G [Signal Processing Section, Department of Electrical and Electronic Engineering, Imperial College, Exhibition Road, London SW7 2BT, UK (United Kingdom)
1994-12-31
In this paper the problem of image texture analysis in the presence of noise is examined from a higher-order statistical perspective. The approach taken involves the use of two dimensional second order Volterra filters where the filter weights are derived from third order cumulants of the two dimensional signal. The specific application contained in this contribution is in mammography, an area in which it is difficult to discern the appropriate features. The paper describes the fundamental issues of the various components of the approach. The results of the entire texture modelling, classification and segmentation scheme contained in this paper are very encouraging. 7 refs, 2 figs.
Finite element solution of two dimensional time dependent heat equation
Maaz
1999-01-01
A Microsoft Windows based computer code, named FHEAT, has been developed for solving two dimensional heat problems in Cartesian and Cylindrical geometries. The programming language is Microsoft Visual Basic 3.0. The code makes use of Finite element formulation for spatial domain and Finite difference formulation for time domain. Presently the code is capable of solving two dimensional steady state and transient problems in xy- and rz-geometries. The code is capable excepting both triangular and rectangular elements. Validation and benchmarking was done against hand calculations and published results. (author)
Chaotic dynamics in two-dimensional noninvertible maps
Mira, Christian; Cathala, Jean-Claude; Gardini, Laura
1996-01-01
This book is essentially devoted to complex properties (Phase plane structure and bifurcations) of two-dimensional noninvertible maps, i.e. maps having either a non-unique inverse, or no real inverse, according to the plane point. They constitute models of sets of discrete dynamical systems encountered in Engineering (Control, Signal Processing, Electronics), Physics, Economics, Life Sciences. Compared to the studies made in the one-dimensional case, the two-dimensional situation remained a long time in an underdeveloped state. It is only since these last years that the interest for this resea
Chiral anomaly, fermionic determinant and two dimensional models
Rego Monteiro, M.A. do.
1985-01-01
The chiral anomaly in random pair dimension is analysed. This anomaly is perturbatively calculated by dimensional regularization method. A new method for non-perturbative Jacobian calculation of a general chiral transformation, 1.e., finite and non-Abelian, is developed. This method is used for non-perturbative chiral anomaly calculation, as an alternative to bosonization of two-dimensional theories for massless fermions and to study the phenomenum of fermion number fractionalization. The fermionic determinant from two-dimensional quantum chromodynamics is also studied, and calculated, exactly, as in decoupling gauge as with out reference to a particular gauge. (M.C.K.) [pt
Growth and electronic properties of two-dimensional systems on (110) oriented GaAs
Fischer, F.
2005-07-01
As the only non-polar plane the (110) surface has a unique role in GaAs. Together with Silicon as a dopant it is an important substrate orientation for the growth of n-type or p-type heterostructures. As a consequence, this thesis will concentrate on growth and research on that surface. In the course of this work we were able to realize two-dimensional electron systems with the highest mobilities reported so far on this orientation. Therefore, we review the necessary growth conditions and the accompanying molecular process. The two-dimensional electron systems allowed the study of a new, intriguing transport anisotropy not explained by current theory. Moreover, we were the first growing a two-dimensional hole gas on (110) GaAs with Si as dopant. For this purpose we invented a new growth modulation technique necessary to retrieve high mobility systems. In addition, we discovered and studied the metal-insulator transition in thin bulk p-type layers on (110) GaAs. Besides we investigated the activation process related to the conduction in the valence band and a parallelly conducting hopping band. The new two-dimensional hole gases revealed interesting physics. We studied the zero B-field spin splitting in these systems and compared it with the known theory. Furthermore, we investigated the anisotropy of the mobility. As opposed to the expectations we observed a strong persistent photoconductivity in our samples. Landau levels for two dimensional hole systems are non-linear and can show anticrossings. For the first time we were able to resolve anticrossings in a transport experiment and study the corresponding activation process. Finally, we compared these striking results with theoretical calculations. (orig.)
The background-quantum split symmetry in two-dimensional σ-models
Blasi, A.; Delduc, F.; Sorella, S.P.
1989-01-01
A generic, non-linear, background-quantum split is translated into a BRS symmetry. The renormalization of the resulting Slavnov-Taylor identity is analyzed in the class of two-dimensional σ-models with Wess-Zumino term which suggests the adoption of a regularization independent method. We discuss the cohomology of the linearized nilpotent operator derived from the Slavnov-Taylor identity. In particular, the cohomology class with zero Faddeev-Popov charge ensures the stability of the action, while the fact that the cohomology class with one unit of Faddeev-Popov charge is empty ensures the absence of anomalies. (orig.)
Level crossings in complex two-dimensional potentials
Two-dimensional P T -symmetric quantum-mechanical systems with the complex cubic potential 12 = 2 + 2 + 2 and the complex Hénon–Heiles potential HH = 2 + 2 + (2 − 3/3) are investigated. Using numerical and perturbative methods, energy spectra are obtained to high levels. Although both ...
Zero sound in a two-dimensional dipolar Fermi gas
Lu, Z.K.; Matveenko, S.I.; Shlyapnikov, G.V.
2013-01-01
We study zero sound in a weakly interacting two-dimensional (2D) gas of single-component fermionic dipoles (polar molecules or atoms with a large magnetic moment) tilted with respect to the plane of their translational motion. It is shown that the propagation of zero sound is provided by both
Interior design of a two-dimensional semiclassical black hole
Levanony, Dana; Ori, Amos
2009-10-01
We look into the inner structure of a two-dimensional dilatonic evaporating black hole. We establish and employ the homogenous approximation for the black-hole interior. Two kinds of spacelike singularities are found inside the black hole, and their structure is investigated. We also study the evolution of spacetime from the horizon to the singularity.
On final states of two-dimensional decaying turbulence
Yin, Z.
2004-01-01
Numerical and analytical studies of final states of two-dimensional (2D) decaying turbulence are carried out. The first part of this work is trying to give a definition for final states of 2D decaying turbulence. The functional relation of ¿-¿, which is frequently adopted as the characterization of
Vibrations of thin piezoelectric shallow shells: Two-dimensional ...
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
In this paper we consider the eigenvalue problem for piezoelectric shallow shells and we show that, as the thickness of the shell goes to zero, the eigensolutions of the three-dimensional piezoelectric shells converge to the eigensolutions of a two- dimensional eigenvalue problem. Keywords. Vibrations; piezoelectricity ...
Inter-layer Cooper pairing of two-dimensional electrons
Inoue, Masahiro; Takemori, Tadashi; Yoshizaki, Ryozo; Sakudo, Tunetaro; Ohtaka, Kazuo
1987-01-01
The authors point out the possibility that the high transition temperatures of the recently discovered oxide superconductors are dominantly caused by the inter-layer Cooper pairing of two-dimensional electrons that are coupled through the exchange of three-dimensional phonons. (author)
Two-dimensional generalized harmonic oscillators and their Darboux partners
Schulze-Halberg, Axel
2011-01-01
We construct two-dimensional Darboux partners of the shifted harmonic oscillator potential and of an isotonic oscillator potential belonging to the Smorodinsky–Winternitz class of superintegrable systems. The transformed solutions, their potentials and the corresponding discrete energy spectra are computed in explicit form. (paper)
First principles calculation of two dimensional antimony and antimony arsenide
Pillai, Sharad Babu, E-mail: sbpillai001@gmail.com; Narayan, Som; Jha, Prafulla K. [Department. of Physics, Faculty of Science, The M. S. University of Baroda, Vadodara-390002 (India); Dabhi, Shweta D. [Department of Physics, Maharaja Krishnakumarsinhji Bhavnagar University, Bhavnagar-364001 (India)
2016-05-23
This work focuses on the strain dependence of the electronic properties of two dimensional antimony (Sb) material and its alloy with As (SbAs) using density functional theory based first principles calculations. Both systems show indirect bandgap semiconducting character which can be transformed into a direct bandgap material with the application of relatively small strain.
Two-dimensional models in statistical mechanics and field theory
Koberle, R.
1980-01-01
Several features of two-dimensional models in statistical mechanics and Field theory, such as, lattice quantum chromodynamics, Z(N), Gross-Neveu and CP N-1 are discussed. The problems of confinement and dynamical mass generation are also analyzed. (L.C.) [pt
Theory of the one- and two-dimensional electron gas
Emery, V.J.
1987-01-01
Two topics are discussed: (1) the competition between 2k/sub F/ and 4k/sub F/ charge state waves in a one-dimensional electron gas and (2) a two-dimensional model of high T/sub c/ superconductivity in the oxides
Two-dimensional turbulent flows on a bounded domain
Kramer, W.
2006-01-01
Large-scale flows in the oceans and the atmosphere reveal strong similarities with purely two-dimensional flows. One of the most typical features is the cascade of energy from smaller flow scales towards larger scales. This is opposed to three-dimensional turbulence where larger flow structures
Quantitative optical mapping of two-dimensional materials
Jessen, Bjarke S.; Whelan, Patrick R.; Mackenzie, David M. A.
2018-01-01
The pace of two-dimensional materials (2DM) research has been greatly accelerated by the ability to identify exfoliated thicknesses down to a monolayer from their optical contrast. Since this process requires time-consuming and error-prone manual assignment to avoid false-positives from image...
Temperature maxima in stable two-dimensional shock waves
Kum, O.; Hoover, W.G.; Hoover, C.G.
1997-01-01
We use molecular dynamics to study the structure of moderately strong shock waves in dense two-dimensional fluids, using Lucy pair potential. The stationary profiles show relatively broad temperature maxima, for both the longitudinal and the average kinetic temperatures, just as does Mott-Smith model for strong shock waves in dilute three-dimensional gases. copyright 1997 The American Physical Society
Two-dimensional molecular line transfer for a cometary coma
Szutowicz, S.
2017-09-01
In the proposed axisymmetric model of the cometary coma the gas density profile is described by an angular density function. Three methods for treating two-dimensional radiative transfer are compared: the Large Velocity Gradient (LVG) (the Sobolev method), Accelerated Lambda Iteration (ALI) and accelerated Monte Carlo (MC).
Sub-Nanometer Channels Embedded in Two-Dimensional Materials
Han, Yimo; Li, Ming-yang; Jung, Gang-Seob; Marsalis, Mark A.; Qin, Zhao; Buehler, Markus J.; Li, Lain-Jong; Muller, David A.
2017-01-01
Two-dimensional (2D) materials are among the most promising candidates for next-generation electronics due to their atomic thinness, allowing for flexible transparent electronics and ultimate length scaling1. Thus far, atomically-thin p-n junctions2
Complex dynamical invariants for two-dimensional complex potentials
Abstract. Complex dynamical invariants are searched out for two-dimensional complex poten- tials using rationalization method within the framework of an extended complex phase space characterized by x = x1 + ip3, y = x2 + ip4, px = p1 + ix3, py = p2 + ix4. It is found that the cubic oscillator and shifted harmonic oscillator ...
Coherent Electron Focussing in a Two-Dimensional Electron Gas.
Houten, H. van; Wees, B.J. van; Mooij, J.E.; Beenakker, C.W.J.; Williamson, J.G.; Foxon, C.T.
1988-01-01
The first experimental realization of ballistic point contacts in a two-dimensional electron gas for the study of transverse electron focussing by a magnetic field is reported. Multiple peaks associated with skipping orbits of electrons reflected specularly by the channel boundary are observed. At
Two-dimensional ion effects in relativistic diodes
Poukey, J.W.
1975-01-01
In relativistic diodes, ions are emitted from the anode plasma. The effects and properties of these ions are studied via a two-dimensional particle simulation code. The space charge of these ions enhances the electron emission, and this additional current (including that of the ions, themselves) aids in obtaining superpinched electron beams for use in pellet fusion studies. (U.S.)
Bounds on the capacity of constrained two-dimensional codes
Forchhammer, Søren; Justesen, Jørn
2000-01-01
Bounds on the capacity of constrained two-dimensional (2-D) codes are presented. The bounds of Calkin and Wilf apply to first-order symmetric constraints. The bounds are generalized in a weaker form to higher order and nonsymmetric constraints. Results are given for constraints specified by run-l...
Interior design of a two-dimensional semiclassical black hole
Levanony, Dana; Ori, Amos
2009-01-01
We look into the inner structure of a two-dimensional dilatonic evaporating black hole. We establish and employ the homogenous approximation for the black-hole interior. Two kinds of spacelike singularities are found inside the black hole, and their structure is investigated. We also study the evolution of spacetime from the horizon to the singularity.
Two-dimensional profiling of Xanthomonas campestris pv. viticola ...
However, the analysis of the 2D-PAGE gel images revealed a larger number of spots in the lysis method when compared to the others. Taking ... Keywords: Bacterial canker, Vitis vinifera, proteomics, sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE), two-dimensional gel electrophoresis (2D-PAGE).
Image Making in Two Dimensional Art; Experiences with Straw and ...
Image making in art is professionally referred to as bust in Sculpture andPortraiture in Painting. ... havebeen used to achieve these forms of art; like clay cement, marble, stone,different metals and, fibre glass in the three dimensional form; We also have Pencil, Charcoal Pastel and, Acrylic oil-paint in two dimensional form.
Image Making in Two Dimensional Art; Experiences with Straw and ...
Image making in art is professionally referred to as bust in Sculpture andPortraiture in Painting. It is an art form executed in three dimensional (3D)and two dimensional (2D) formats respectively. Uncountable materials havebeen used to achieve these forms of art; like clay cement, marble, stone,different metals and, fibre ...
Mass relations for two-dimensional classical configurations
Tataru-Mihai, P.
1980-01-01
Using the two-dimensional sigma-nonlinear models as a framework mass relations for classical configurations of instanton/soliton type are derived. Our results suggest an interesting differential-geometric interpretation of the mass of a classical configuration in terms of the topological characteristics of an associated manifold. (orig.)
Seismically constrained two-dimensional crustal thermal structure of ...
The temperature field within the crust is closely related to tectonic history as well as many other geological processes inside the earth. Therefore, knowledge of the crustal thermal structure of a region is of great importance for its tectonophysical studies. This work deals with the two-dimensional thermal modelling to ...
Waiting Time Dynamics in Two-Dimensional Infrared Spectroscopy
Jansen, Thomas L. C.; Knoester, Jasper
We review recent work on the waiting time dynamics of coherent two-dimensional infrared (2DIR) spectroscopy. This dynamics can reveal chemical and physical processes that take place on the femto- and picosecond time scale, which is faster than the time scale that may be probed by, for example,
Two-dimensional NMR studies of allyl palladium complexes of ...
Administrator
h3-Allyl complexes are intermediates in organic synthetic reactions such as allylic alkylation and amination. There is growing interest in understanding the structures of chiral h3-allyl intermediates as this would help to unravel the mechanism of enantioselective C–C bond forming reactions. Two-dimensional NMR study is a.
Two-dimensional effects in nonlinear Kronig-Penney models
Gaididei, Yuri Borisovich; Christiansen, Peter Leth; Rasmussen, Kim
1997-01-01
An analysis of two-dimensional (2D) effects in the nonlinear Kronig-Penney model is presented. We establish an effective one-dimensional description of the 2D effects, resulting in a set of pseudodifferential equations. The stationary states of the 2D system and their stability is studied...
Two-dimensional position sensitive Si(Li) detector
Walton, J.T.; Hubbard, G.S.; Haller, E.E.; Sommer, H.A.
1978-11-01
Circular, large-area two-dimensional Si(Li) position sensitive detectors have been fabricated. The detectors employ a thin lithium-diffused n + resisitive layer for one contact and a boron implanted p + resistive layer for the second contact. A position resolution of the order of 100 μm is indicated
A TWO-DIMENSIONAL POSITION SENSITIVE SI(LI) DETECTOR
Walton, Jack T.; Hubbard, G. Scott; Haller, Eugene E.; Sommer, Heinrich A.
1978-11-01
Circular, large-area two-dimensional Si(Li) position sensitive detectors have been fabricated. The detectors employ a thin lithium-diffused n{sup +} resistive layer for one contact and a boron implanted p{sup +} resistive layer for the second contact. A position resolution of the order of 100 {micro}m is indicated.
Solar Internal Rotation and Dynamo Waves: A Two Dimensional ...
tribpo
Solar Internal Rotation and Dynamo Waves: A Two Dimensional. Asymptotic Solution in the Convection Zone ... We calculate here a spatial 2 D structure of the mean magnetic field, adopting real profiles of the solar internal ... of the asymptotic solution in low (middle) and high (right panel) latitudes. field is shifted towards the ...
Linkage analysis by two-dimensional DNA typing
te Meerman, G J; Mullaart, E; Meulen ,van der Martin; den Daas, J H; Morolli, B; Uitterlinden, A G; Vijg, J
1993-01-01
In two-dimensional (2-D) DNA typing, genomic DNA fragments are separated, first according to size by electrophoresis in a neutral polyacrylamide gel and second according to sequence by denaturing gradient gel electrophoresis, followed by hybridization analysis using micro- and minisatellite core
Proximity Induced Superconducting Properties in One and Two Dimensional Semiconductors
Kjærgaard, Morten
This report is concerned with the properties of one and two dimensional semiconducting materials when brought into contact with a superconductor. Experimentally we study the 2D electron gas in an InGaAs/InAs heterostructure with aluminum grown in situ on the surface, and theoretically we show tha...
Two-Dimensional Charge Transport in Disordered Organic Semiconductors
Brondijk, J. J.; Roelofs, W. S. C.; Mathijssen, S. G. J.; Shehu, A.; Cramer, T.; Biscarini, F.; Blom, P. W. M.; de Leeuw, D. M.
2012-01-01
We analyze the effect of carrier confinement on the charge-transport properties of organic field-effect transistors. Confinement is achieved experimentally by the use of semiconductors of which the active layer is only one molecule thick. The two-dimensional confinement of charge carriers provides
Noninteracting beams of ballistic two-dimensional electrons
Spector, J.; Stormer, H.L.; Baldwin, K.W.; Pfeiffer, L.N.; West, K.W.
1991-01-01
We demonstrate that two beams of two-dimensional ballistic electrons in a GaAs-AlGaAs heterostructure can penetrate each other with negligible mutual interaction analogous to the penetration of two optical beams. This allows electrical signal channels to intersect in the same plane with negligible crosstalk between the channels
Graphene: a promising two-dimensional support for heterogeneous catalysts
Xiaobin eFan
2015-01-01
Full Text Available Graphene has many advantages that make it an attractive two-dimensional (2D support for heterogeneous catalysts. It not only allows the high loading of targeted catalytic species, but also facilitates the mass transfer during the reaction processes. These advantages, along with its unique physical and chemical properties, endow graphene great potential as catalyst support in heterogeneous catalysis.
Two-dimensional interpolation with experimental data smoothing
Trejbal, Z.
1989-01-01
A method of two-dimensional interpolation with smoothing of time statistically deflected points is developed for processing of magnetic field measurements at the U-120M field measurements at the U-120M cyclotron. Mathematical statement of initial requirements and the final result of relevant algebraic transformations are given. 3 refs
Tunneling between parallel two-dimensional electron liquids
Jungwirth, Tomáš; MacDonald, A. H.
361/362, - (1996), s. 167-170 ISSN 0039-6028. [International Conference on the Electronic Properties of Two Dimensional Systems /11./. Nottingham, 07.08.1995-11.08.1995] R&D Projects: GA ČR GA202/94/1278 Grant - others:INT(XX) 9106888 Impact factor: 2.783, year: 1996
Influence of index contrast in two dimensional photonic crystal lasers
Jørgensen, Mette Marie; Petersen, Sidsel Rübner; Christiansen, Mads Brøkner
2010-01-01
The influence of index contrast variations for obtaining single-mode operation and low threshold in dye doped polymer two dimensional photonic crystal (PhC) lasers is investigated. We consider lasers made from Pyrromethene 597 doped Ormocore imprinted with a rectangular lattice PhC having a cavity...
Two-Dimensional Tellurene as Excellent Thermoelectric Material
Sharma, Sitansh; Singh, Nirpendra; Schwingenschlö gl, Udo
2018-01-01
We study the thermoelectric properties of two-dimensional tellurene by first-principles calculations and semiclassical Boltzmann transport theory. The HSE06 hybrid functional results in a moderate direct band gap of 1.48 eV at the Γ point. A high
Analysis of Two-Dimensional Electrophoresis Gel Images
Pedersen, Lars
2002-01-01
This thesis describes and proposes solutions to some of the currently most important problems in pattern recognition and image analysis of two-dimensional gel electrophoresis (2DGE) images. 2DGE is the leading technique to separate individual proteins in biological samples with many biological...
Patched Green's function techniques for two-dimensional systems
Settnes, Mikkel; Power, Stephen; Lin, Jun
2015-01-01
We present a numerically efficient technique to evaluate the Green's function for extended two-dimensional systems without relying on periodic boundary conditions. Different regions of interest, or “patches,” are connected using self-energy terms which encode the information of the extended parts...
Transient two-dimensional flow in porous media
Sharpe, L. Jr.
1979-01-01
The transient flow of an isothermal ideal gas from the cavity formed by an underground nuclear explosion is investigated. A two-dimensional finite element method is used in analyzing the gas flow. Numerical results of the pressure distribution are obtained for both the stemming column and the surrounding porous media
Two-dimensional QCD as a model for strong interaction
Ellis, J.
1977-01-01
After an introduction to the formalism of two-dimensional QCD, its applications to various strong interaction processes are reviewed. Among the topics discussed are spectroscopy, deep inelastic cross-sections, ''hard'' processes involving hadrons, ''Regge'' behaviour, the existence of the Pomeron, and inclusive hadron cross-sections. Attempts are made to abstracts features useful for four-dimensional QCD phenomenology. (author)
Two-dimensional gel electrophoresis analysis of different parts of ...
Two-dimensional gel electrophoresis analysis of different parts of Panax quinquefolius L. root. ... From these results it was concluded that proteomic analysis method was an effective way to identify the different parts of quinquefolius L. root. These findings may contribute to further understanding of the physiological ...
Two-dimensional optimization of free-electron-laser designs
Prosnitz, D.; Haas, R.A.
1982-05-04
Off-axis, two-dimensional designs for free electron lasers are described that maintain correspondence of a light beam with a synchronous electron at an optimal transverse radius r > 0 to achieve increased beam trapping efficiency and enhanced laser beam wavefront control so as to decrease optical beam diffraction and other deleterious effects.
Kubo conductivity of a strongly magnetized two-dimensional plasma.
Montgomery, D.; Tappert, F.
1971-01-01
The Kubo formula is used to evaluate the bulk electrical conductivity of a two-dimensional guiding-center plasma in a strong dc magnetic field. The particles interact only electrostatically. An ?anomalous' electrical conductivity is derived for this system, which parallels a recent result of Taylor and McNamara for the coefficient of spatial diffusion.
Bayesian approach for peak detection in two-dimensional chromatography
Vivó-Truyols, G.
2012-01-01
A new method for peak detection in two-dimensional chromatography is presented. In a first step, the method starts with a conventional one-dimensional peak detection algorithm to detect modulated peaks. In a second step, a sophisticated algorithm is constructed to decide which of the individual
Equilibrium spherically curved two-dimensional Lennard-Jones systems
Voogd, J.M.; Sloot, P.M.A.; van Dantzig, R.
2005-01-01
To learn about basic aspects of nano-scale spherical molecular shells during their formation, spherically curved two-dimensional N-particle Lennard-Jones systems are simulated, studying curvature evolution paths at zero-temperature. For many N-values (N < 800) equilibrium configu- rations are traced
Giant 1/f noise in two-dimensional polycrystalline media
Snarskii, A.; Bezsudnov, I.
2008-01-01
The behaviour of excess (1/f noise) in two-dimensional polycrystalline media is investigated. On the base of current trap model, it is shown that there exists a certain anisotropy value of conductivity tensor for polycrystalline media when the amplitude of 1/f noise becomes giant
Two-dimensional servo control of surface motor; Surface motor no nijigen servo control
Ebihara, D; Takahashi, T; Watada, M [Musashi Institute of Technology, Tokyo (Japan)
1995-08-20
Two dimensional (2D) drive system is needed in many aspects of factory automation (FA) and office automation (OA) machines, such as pen drivers in X-Y plotters, X-Y stage for machining, 2D moving robots, etc. Conventional 2D drive systems are consisted from two sets of rotational motor drive and several types of rotary-to-linear transform mechanisms. Linear motors, in these days, have become to be effective as the requirement for high speed increases. We have been studying about Surface Motor which enables 2D drive on a surface by single mover, and the characteristics are measured. Main difficulty of the actuator is that it is short of thrust forces. Also the feasibility is limited because of its vocational uncertainty caused by the open loop control. Our interest is to introduce the closed loop digital control, to obtain required thrust force at any point on the stator. Since open loop control is used, that is, stability point where the thrust force is zero is moved one after another, generated thrust force within the range of synchronization is small. We have been studying about the peculiar expression of exciting currents to generate required direction at all the stator. On the basis of results, two dimensional position feedback system is assembled, which detect the two dimensional location of the mover by optical sensors and direct current instructions are generated for all the four phases of the mover. 14 refs., 11 figs., 1 tab.
Lucchetti, Liana; Fraccia, Tommaso P.; Ciciulla, Fabrizio; Bellini, Tommaso
2017-01-01
Throughout the whole history of liquid crystals science, the balancing of intrinsic elasticity with coupling to external forces has been the key strategy for most application and investigation. While the coupling of the optical field to the nematic director is at the base of a wealth of thoroughly described optical effects, a significant variety of geometries and materials have not been considered yet. Here we show that by adopting a simple cell geometry and measuring the optically induced bi...
Mitsak, Anna G; Dunn, Andrew M; Hollister, Scott J
2012-07-01
Scaffold tissue engineering strategies for repairing and replacing soft tissue aim to improve reconstructive and corrective surgical techniques whose limitations include suboptimal mechanical properties, fibrous capsule formation and volume loss due to graft resorption. An effective tissue engineering strategy requires a scaffolding material with low elastic modulus that behaves similarly to soft tissue, which has been characterized as a nonlinear elastic material. The material must also have the ability to be manufactured into specifically designed architectures. Poly(glycerol sebacate) (PGS) is a thermoset elastomer that meets these criteria. We hypothesize that the mechanical properties of PGS can be modulated through curing condition and architecture to produce materials with a range of stiffnesses. To evaluate this hypothesis, we manufactured PGS constructs cured under various conditions and having one of two architectures (solid or porous). Specimens were then tensile tested according to ASTM standards and the data were modeled using a nonlinear elastic Neo-Hookean model. Architecture and testing conditions, including elongation rate and wet versus dry conditions, affected the mechanical properties. Increasing curing time and temperature led to increased tangent modulus and decreased maximum strain for solid constructs. Porous constructs had lower nonlinear elastic properties, as did constructs of both architectures tested under simulated physiological conditions (wetted at 37 °C). Both solid and porous PGS specimens could be modeled well with the Neo-Hookean model. Future studies include comparing PGS properties to other biological tissue types and designing and characterizing PGS scaffolds for regenerating these tissues. Copyright © 2012 Elsevier Ltd. All rights reserved.
Lucchetti, Liana; Fraccia, Tommaso P; Ciciulla, Fabrizio; Bellini, Tommaso
2017-07-10
Throughout the whole history of liquid crystals science, the balancing of intrinsic elasticity with coupling to external forces has been the key strategy for most application and investigation. While the coupling of the optical field to the nematic director is at the base of a wealth of thoroughly described optical effects, a significant variety of geometries and materials have not been considered yet. Here we show that by adopting a simple cell geometry and measuring the optically induced birefringence, we can readily extract the twist elastic coefficient K 22 of thermotropic and lyotropic chiral nematics (N*). The value of K 22 we obtain for chiral doped 5CB thermotropic N* well matches those reported in the literature. With this same strategy, we could determine for the first time K 22 of the N* phase of concentrated aqueous solutions of DNA oligomers, bypassing the limitations that so far prevented measuring the elastic constants of this class of liquid crystalline materials. The present study also enlightens the significant nonlinear optical response of DNA liquid crystals.
Numerical simulation of potato slices drying using a two-dimensional finite element model
Beigi Mohsen
2017-01-01
Full Text Available An experimental and numerical study was conducted to investigate the process of potato slices drying. For simulating the moisture transfer in the samples and predict the dehydration curves, a two-dimensional finite element model was developed and programmed in Compaq Visual Fortran, version 6.5. The model solved the Fick’s second law for slab in a shrinkage system to calculate the unsteady two-dimensional moisture transmission in rectangular coordinates (x,y. Moisture diffusivity and moisture transfer coefficient were determined by minimizing the sum squares of residuals between experimental and numerical predicted data. Shrinkage kinetics of the potato slices during dehydration was determined experimentally and found to be a linear function of removed moisture. The determined parameters were used in the mathematical model. The predicted moisture content values were compared to the experimental data and the validation results demonstrated that the dynamic drying curves were predicted by the methodology very well.
Rheological properties of the soft-disk model of two-dimensional foams
Langlois, Vincent; Hutzler, Stefan; Weaire, Denis
2008-01-01
The soft-disk model previously developed and applied by Durian [D. J. Durian, Phys. Rev. Lett. 75, 4780 (1995)] is brought to bear on problems of foam rheology of longstanding and current interest, using two-dimensional systems. The questions at issue include the origin of the Herschel-Bulkley re......The soft-disk model previously developed and applied by Durian [D. J. Durian, Phys. Rev. Lett. 75, 4780 (1995)] is brought to bear on problems of foam rheology of longstanding and current interest, using two-dimensional systems. The questions at issue include the origin of the Herschel......-Bulkley relation, normal stress effects (dilatancy), and localization in the presence of wall drag. We show that even a model that incorporates only linear viscous effects at the local level gives rise to nonlinear (power-law) dependence of the limit stress on strain rate. With wall drag, shear localization...
Time-dependent perturbations in two-dimensional string black holes
Diamandis, G A; Maintas, X N; Mavromatos, Nikolaos E
1992-01-01
We discuss time-dependent perturbations (induced by matter fields) of a black-hole background in tree-level two-dimensional string theory. We analyse the linearized case and show the possibility of having black-hole solutions with time-dependent horizons. The latter exist only in the presence of time-dependent `tachyon' matter fields, which constitute the only propagating degrees of freedom in two-dimensional string theory. For real tachyon field configurations it is not possible to obtain solutions with horizons shrinking to a point. On the other hand, such a possibility seems to be realized in the case of string black-hole models formulated on higher world-sheet genera. We connect this latter result with black hole evaporation/decay at a quantum level.}
Chen, G.S.
1997-01-01
We apply and compare the preconditioned generalized conjugate gradient methods to solve the linear system equation that arises in the two-dimensional neutron and photon transport equation in this paper. Several subroutines are developed on the basis of preconditioned generalized conjugate gradient methods for time-independent, two-dimensional neutron and photon transport equation in the transport theory. These generalized conjugate gradient methods are used. TFQMR (transpose free quasi-minimal residual algorithm), CGS (conjuage gradient square algorithm), Bi-CGSTAB (bi-conjugate gradient stabilized algorithm) and QMRCGSTAB (quasi-minimal residual variant of bi-conjugate gradient stabilized algorithm). These sub-routines are connected to computer program DORT. Several problems are tested on a personal computer with Intel Pentium CPU. (author)
Optical conductivity of three and two dimensional topological nodal-line semimetals
Barati, Shahin; Abedinpour, Saeed H.
2017-10-01
The peculiar shape of the Fermi surface of topological nodal-line semimetals at low carrier concentrations results in their unusual optical and transport properties. We analytically investigate the linear optical responses of three- and two-dimensional nodal-line semimetals using the Kubo formula. The optical conductivity of a three-dimensional nodal-line semimetal is anisotropic. Along the axial direction (i.e., the direction perpendicular to the nodal-ring plane), the Drude weight has a linear dependence on the chemical potential at both low and high carrier dopings. For the radial direction (i.e., the direction parallel to the nodal-ring plane), this dependence changes from linear into quadratic in the transition from low into high carrier concentration. The interband contribution into optical conductivity is also anisotropic. In particular, at large frequencies, it saturates to a constant value for the axial direction and linearly increases with frequency along the radial direction. In two-dimensional nodal-line semimetals, no interband optical transition could be induced and the only contribution to the optical conductivity arises from the intraband excitations. The corresponding Drude weight is independent of the carrier density at low carrier concentrations and linearly increases with chemical potential at high carrier doping.
Interface Effects Enabling New Applications of Two-Dimensional Materials
Sattar, Shahid
2018-05-01
Interface effects in two-dimensional (2D) materials play a critical role for the electronic properties and device characteristics. Here we use first-principles calculations to investigate interface effects in 2D materials enabling new applications. We first show that graphene in contact with monolayer and bilayer PtSe2 experiences weak van der Waals interaction. Analysis of the work functions and band bending at the interface reveals that graphene forms an n-type Schottky contact with monolayer PtSe2 and a p-type Schottky contact with bilayer PtSe2, whereas a small biaxial tensile strain makes the contact Ohmic in the latter case as required for transistor operation. For silicene, which is a 2D Dirac relative of graphene, structural buckling complicates the experimental synthesis and strong interaction with the substrate perturbs the characteristic linear dispersion. To remove this obstacle, we propose solid argon as a possible substrate for realizing quasi-freestanding silicene and argue that a weak van der Waals interaction and small binding energy indicate the possibility to separate silicene from the substrate. For the silicene-PtSe2 interface, we demonstrate much stronger interlayer interaction than previously reported for silicene on other semiconducting substrates. Due to the inversion symmetry breaking and proximity to PtSe2, a band gap opening and spin splittings in the valence and conduction bands of silicene are observed. It is also shown that the strong interlayer interaction can be effectively reduced by intercalating NH3 molecules between silicene and PtSe2, and a small NH3 discussion barrier makes intercalation a viable experimental approach. Silicene/germanene are categorized as key materials for the field of valleytronics due to stronger spin-orbit coupling as compared to graphene. However, no viable route exists so far to experimental realization. We propose F-doped WS2 as substrate that avoids detrimental effects and at the same time induces the
Sanchez, Richard.
1980-11-01
This work is divided into two parts: the first part deals with the solution of complex two-dimensional transport problems, the second one (note CEA-N-2166) treats the critically mixed methods of resolution. A set of approximate solutions for the isotropic two-dimensional neutron transport problem has been developed using the interface current formalism. The method has been applied to regular lattices of rectangular cells containing a fuel pin, cladding, and water, or homogenized structural material. The cells are divided into zones that are homogeneous. A zone-wise flux expansion is used to formulate a direct collision probability problem within a cell. The coupling of the cells is effected by making extra assumptions on the currents entering and leaving the interfaces. Two codes have been written: CALLIOPE uses a cylindrical cell model and one or three terms for the flux expansion, and NAUSICAA uses a two-dimensional flux representation and does a truly two-dimensional calculation inside each cell. In both codes, one or three terms can be used to make a space-independent expansion of the angular fluxes entering and leaving each side of the cell. The accuracies and computing times achieved with the different approximations are illustrated by numerical studies on two benchmark problems and by calculations performed in the APOLLO multigroup code [fr
Topology optimization for elastic base under rectangular plate subjected to moving load
Jilavyan Samvel H.
2015-09-01
Full Text Available Distribution optimization of elastic material under elastic isotropic rectangular thin plate subjected to concentrated moving load is investigated in the present paper. The aim of optimization is to damp its vibrations in finite (fixed time. Accepting Kirchhoff hypothesis with respect to the plate and Winkler hypothesis with respect to the base, the mathematical model of the problem is constructed as two-dimensional bilinear equation, i.e. linear in state and control function. The maximal quantity of the base material is taken as optimality criterion to be minimized. The Fourier distributional transform and the Bubnov-Galerkin procedures are used to reduce the problem to integral equality type constraints. The explicit solution in terms of two- dimensional Heaviside‘s function is obtained, describing piecewise-continuous distribution of the material. The determination of the switching points is reduced to a problem of nonlinear programming. Data from numerical analysis are presented.
De Beer, Morris
2008-07-01
Full Text Available - wave and ρ the material density. The elastic moduli P-wave modulus, M, is defined so that M = K + 4µ / 3 and M can then be determined by Equation 11, with a known speed Vp P MV 2 ρ = (11) It should however also... gas (such as air within compacted road materials), the adiabatic bulk modulus KS is approximately given by pKS κ= (4) Where: κ is the adiabatic index, (sometimes calledγ ); p is the pressure. In a fluid (such as moisture...
Two dimensional analytical model for a reconfigurable field effect transistor
Ranjith, R.; Jayachandran, Remya; Suja, K. J.; Komaragiri, Rama S.
2018-02-01
This paper presents two-dimensional potential and current models for a reconfigurable field effect transistor (RFET). Two potential models which describe subthreshold and above-threshold channel potentials are developed by solving two-dimensional (2D) Poisson's equation. In the first potential model, 2D Poisson's equation is solved by considering constant/zero charge density in the channel region of the device to get the subthreshold potential characteristics. In the second model, accumulation charge density is considered to get above-threshold potential characteristics of the device. The proposed models are applicable for the device having lightly doped or intrinsic channel. While obtaining the mathematical model, whole body area is divided into two regions: gated region and un-gated region. The analytical models are compared with technology computer-aided design (TCAD) simulation results and are in complete agreement for different lengths of the gated regions as well as at various supply voltage levels.
Boron nitride as two dimensional dielectric: Reliability and dielectric breakdown
Ji, Yanfeng; Pan, Chengbin; Hui, Fei; Shi, Yuanyuan; Lanza, Mario, E-mail: mlanza@suda.edu.cn [Institute of Functional Nano and Soft Materials, Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, 199 Ren-Ai Road, Suzhou 215123 (China); Zhang, Meiyun; Long, Shibing [Key Laboratory of Microelectronics Devices & Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029 (China); Lian, Xiaojuan; Miao, Feng [National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093 (China); Larcher, Luca [DISMI, Università di Modena e Reggio Emilia, 42122 Reggio Emilia (Italy); Wu, Ernest [IBM Research Division, Essex Junction, Vermont 05452 (United States)
2016-01-04
Boron Nitride (BN) is a two dimensional insulator with excellent chemical, thermal, mechanical, and optical properties, which make it especially attractive for logic device applications. Nevertheless, its insulating properties and reliability as a dielectric material have never been analyzed in-depth. Here, we present the first thorough characterization of BN as dielectric film using nanoscale and device level experiments complementing with theoretical study. Our results reveal that BN is extremely stable against voltage stress, and it does not show the reliability problems related to conventional dielectrics like HfO{sub 2}, such as charge trapping and detrapping, stress induced leakage current, and untimely dielectric breakdown. Moreover, we observe a unique layer-by-layer dielectric breakdown, both at the nanoscale and device level. These findings may be of interest for many materials scientists and could open a new pathway towards two dimensional logic device applications.
Quasi-two-dimensional thermoelectricity in SnSe
Tayari, V.; Senkovskiy, B. V.; Rybkovskiy, D.; Ehlen, N.; Fedorov, A.; Chen, C.-Y.; Avila, J.; Asensio, M.; Perucchi, A.; di Pietro, P.; Yashina, L.; Fakih, I.; Hemsworth, N.; Petrescu, M.; Gervais, G.; Grüneis, A.; Szkopek, T.
2018-01-01
Stannous selenide is a layered semiconductor that is a polar analog of black phosphorus and of great interest as a thermoelectric material. Unusually, hole doped SnSe supports a large Seebeck coefficient at high conductivity, which has not been explained to date. Angle-resolved photoemission spectroscopy, optical reflection spectroscopy, and magnetotransport measurements reveal a multiple-valley valence-band structure and a quasi-two-dimensional dispersion, realizing a Hicks-Dresselhaus thermoelectric contributing to the high Seebeck coefficient at high carrier density. We further demonstrate that the hole accumulation layer in exfoliated SnSe transistors exhibits a field effect mobility of up to 250 cm2/V s at T =1.3 K . SnSe is thus found to be a high-quality quasi-two-dimensional semiconductor ideal for thermoelectric applications.
Folding two dimensional crystals by swift heavy ion irradiation
Ochedowski, Oliver; Bukowska, Hanna [Fakultät für Physik and CENIDE, Universität Duisburg-Essen, D-47048 Duisburg (Germany); Freire Soler, Victor M. [Fakultät für Physik and CENIDE, Universität Duisburg-Essen, D-47048 Duisburg (Germany); Departament de Fisica Aplicada i Optica, Universitat de Barcelona, E08028 Barcelona (Spain); Brökers, Lara [Fakultät für Physik and CENIDE, Universität Duisburg-Essen, D-47048 Duisburg (Germany); Ban-d' Etat, Brigitte; Lebius, Henning [CIMAP (CEA-CNRS-ENSICAEN-UCBN), 14070 Caen Cedex 5 (France); Schleberger, Marika, E-mail: marika.schleberger@uni-due.de [Fakultät für Physik and CENIDE, Universität Duisburg-Essen, D-47048 Duisburg (Germany)
2014-12-01
Ion irradiation of graphene, the showcase model of two dimensional crystals, has been successfully applied to induce various modifications in the graphene crystal. One of these modifications is the formation of origami like foldings in graphene which are created by swift heavy ion irradiation under glancing incidence angle. These foldings can be applied to locally alter the physical properties of graphene like mechanical strength or chemical reactivity. In this work we show that the formation of foldings in two dimensional crystals is not restricted to graphene but can be applied for other materials like MoS{sub 2} and hexagonal BN as well. Further we show that chemical vapour deposited graphene forms foldings after swift heavy ion irradiation while chemical vapour deposited MoS{sub 2} does not.
Folding two dimensional crystals by swift heavy ion irradiation
Ochedowski, Oliver; Bukowska, Hanna; Freire Soler, Victor M.; Brökers, Lara; Ban-d'Etat, Brigitte; Lebius, Henning; Schleberger, Marika
2014-01-01
Ion irradiation of graphene, the showcase model of two dimensional crystals, has been successfully applied to induce various modifications in the graphene crystal. One of these modifications is the formation of origami like foldings in graphene which are created by swift heavy ion irradiation under glancing incidence angle. These foldings can be applied to locally alter the physical properties of graphene like mechanical strength or chemical reactivity. In this work we show that the formation of foldings in two dimensional crystals is not restricted to graphene but can be applied for other materials like MoS 2 and hexagonal BN as well. Further we show that chemical vapour deposited graphene forms foldings after swift heavy ion irradiation while chemical vapour deposited MoS 2 does not
Two-dimensional time dependent Riemann solvers for neutron transport
Brunner, Thomas A.; Holloway, James Paul
2005-01-01
A two-dimensional Riemann solver is developed for the spherical harmonics approximation to the time dependent neutron transport equation. The eigenstructure of the resulting equations is explored, giving insight into both the spherical harmonics approximation and the Riemann solver. The classic Roe-type Riemann solver used here was developed for one-dimensional problems, but can be used in multidimensional problems by treating each face of a two-dimensional computation cell in a locally one-dimensional way. Several test problems are used to explore the capabilities of both the Riemann solver and the spherical harmonics approximation. The numerical solution for a simple line source problem is compared to the analytic solution to both the P 1 equation and the full transport solution. A lattice problem is used to test the method on a more challenging problem
Dynamics of vortex interactions in two-dimensional flows
Juul Rasmussen, J.; Nielsen, A.H.; Naulin, V.
2002-01-01
The dynamics and interaction of like-signed vortex structures in two dimensional flows are investigated by means of direct numerical solutions of the two-dimensional Navier-Stokes equations. Two vortices with distributed vorticity merge when their distance relative to their radius, d/R-0l. is below...... a critical value, a(c). Using the Weiss-field, a(c) is estimated for vortex patches. Introducing an effective radius for vortices with distributed vorticity, we find that 3.3 ... is effectively producing small scale structures and the relation to the enstrophy "cascade" in developed 2D turbulence is discussed. The influence of finite viscosity on the merging is also investigated. Additionally, we examine vortex interactions on a finite domain, and discuss the results in connection...
Quantum vacuum energy in two dimensional space-times
Davies, P.C.W.; Fulling, S.A.
1977-01-01
The paper presents in detail the renormalization theory of the energy-momentum tensor of a two dimensional massless scalar field which has been used elsewhere to study the local physics in a model of black hole evaporation. The treatment is generalized to include the Casimir effect occurring in spatially finite models. The essence of the method is evaluation of the field products in the tensor as functions of two points, followed by covariant subtraction of the discontinuous terms arising as the points coalesce. In two dimensional massless theories, conformal transformations permit exact calculations to be performed. The results are applied here to some special cases, primarily space-times of constant curvature, with emphasis on the existence of distinct 'vacuum' states associated naturally with different conformal coordinate systems. The relevance of the work to the general problems of defining observables and of classifying and interpreting states in curved-space quantum field theory is discussed. (author)
Explorative data analysis of two-dimensional electrophoresis gels
Schultz, J.; Gottlieb, D.M.; Petersen, Marianne Kjerstine
2004-01-01
of gels is presented. First, an approach is demonstrated in which no prior knowledge of the separated proteins is used. Alignment of the gels followed by a simple transformation of data makes it possible to analyze the gels in an automated explorative manner by principal component analysis, to determine......Methods for classification of two-dimensional (2-DE) electrophoresis gels based on multivariate data analysis are demonstrated. Two-dimensional gels of ten wheat varieties are analyzed and it is demonstrated how to classify the wheat varieties in two qualities and a method for initial screening...... if the gels should be further analyzed. A more detailed approach is done by analyzing spot volume lists by principal components analysis and partial least square regression. The use of spot volume data offers a mean to investigate the spot pattern and link the classified protein patterns to distinct spots...
Tuning spin transport across two-dimensional organometallic junctions
Liu, Shuanglong; Wang, Yun-Peng; Li, Xiangguo; Fry, James N.; Cheng, Hai-Ping
2018-01-01
We study via first-principles modeling and simulation two-dimensional spintronic junctions made of metal-organic frameworks consisting of two Mn-phthalocyanine ferromagnetic metal leads and semiconducting Ni-phthalocyanine channels of various lengths. These systems exhibit a large tunneling magnetoresistance ratio; the transmission functions of such junctions can be tuned using gate voltage by three orders of magnitude. We find that the origin of this drastic change lies in the orbital alignment and hybridization between the leads and the center electronic states. With physical insight into the observed on-off phenomenon, we predict a gate-controlled spin current switch based on two-dimensional crystallines and offer general guidelines for designing spin junctions using 2D materials.
Logarithmic Superdiffusion in Two Dimensional Driven Lattice Gases
Krug, J.; Neiss, R. A.; Schadschneider, A.; Schmidt, J.
2018-03-01
The spreading of density fluctuations in two-dimensional driven diffusive systems is marginally anomalous. Mode coupling theory predicts that the diffusivity in the direction of the drive diverges with time as (ln t)^{2/3} with a prefactor depending on the macroscopic current-density relation and the diffusion tensor of the fluctuating hydrodynamic field equation. Here we present the first numerical verification of this behavior for a particular version of the two-dimensional asymmetric exclusion process. Particles jump strictly asymmetrically along one of the lattice directions and symmetrically along the other, and an anisotropy parameter p governs the ratio between the two rates. Using a novel massively parallel coupling algorithm that strongly reduces the fluctuations in the numerical estimate of the two-point correlation function, we are able to accurately determine the exponent of the logarithmic correction. In addition, the variation of the prefactor with p provides a stringent test of mode coupling theory.
Two-dimensional Simulations of Correlation Reflectometry in Fusion Plasmas
Valeo, E.J.; Kramer, G.J.; Nazikian, R.
2001-01-01
A two-dimensional wave propagation code, developed specifically to simulate correlation reflectometry in large-scale fusion plasmas is described. The code makes use of separate computational methods in the vacuum, underdense and reflection regions of the plasma in order to obtain the high computational efficiency necessary for correlation analysis. Simulations of Tokamak Fusion Test Reactor (TFTR) plasma with internal transport barriers are presented and compared with one-dimensional full-wave simulations. It is shown that the two-dimensional simulations are remarkably similar to the results of the one-dimensional full-wave analysis for a wide range of turbulent correlation lengths. Implications for the interpretation of correlation reflectometer measurements in fusion plasma are discussed
Directional detection of dark matter with two-dimensional targets
Hochberg, Yonit; Kahn, Yonatan; Lisanti, Mariangela; Tully, Christopher G.; Zurek, Kathryn M.
2017-09-01
We propose two-dimensional materials as targets for direct detection of dark matter. Using graphene as an example, we focus on the case where dark matter scattering deposits sufficient energy on a valence-band electron to eject it from the target. We show that the sensitivity of graphene to dark matter of MeV to GeV mass can be comparable, for similar exposure and background levels, to that of semiconductor targets such as silicon and germanium. Moreover, a two-dimensional target is an excellent directional detector, as the ejected electron retains information about the angular dependence of the incident dark matter particle. This proposal can be implemented by the PTOLEMY experiment, presenting for the first time an opportunity for directional detection of sub-GeV dark matter.
Quantum vacuum energy in two dimensional space-times
Davies, P C.W.; Fulling, S A [King' s Coll., London (UK). Dept. of Mathematics
1977-04-21
The paper presents in detail the renormalization theory of the energy-momentum tensor of a two dimensional massless scalar field which has been used elsewhere to study the local physics in a model of black hole evaporation. The treatment is generalized to include the Casimir effect occurring in spatially finite models. The essence of the method is evaluation of the field products in the tensor as functions of two points, followed by covariant subtraction of the discontinuous terms arising as the points coalesce. In two dimensional massless theories, conformal transformations permit exact calculations to be performed. The results are applied here to some special cases, primarily space-times of constant curvature, with emphasis on the existence of distinct 'vacuum' states associated naturally with different conformal coordinate systems. The relevance of the work to the general problems of defining observables and of classifying and interpreting states in curved-space quantum field theory is discussed.
CORPORATE VALUATION USING TWO-DIMENSIONAL MONTE CARLO SIMULATION
Toth Reka
2010-12-01
Full Text Available In this paper, we have presented a corporate valuation model. The model combine several valuation methods in order to get more accurate results. To determine the corporate asset value we have used the Gordon-like two-stage asset valuation model based on the calculation of the free cash flow to the firm. We have used the free cash flow to the firm to determine the corporate market value, which was calculated with use of the Black-Scholes option pricing model in frame of the two-dimensional Monte Carlo simulation method. The combined model and the use of the two-dimensional simulation model provides a better opportunity for the corporate value estimation.
Two-dimensional superconductivity in ultrathin disordered thin films
Beasley, M.R.
1992-01-01
The status of the understanding of two-dimensional superconductivity in ultrathin, disordered thin films is reviewed. The different consequences of microscopic versus macroscopic disorder are stressed. It is shown that microscopic disorder leads to a rapid suppression of the mean-field transition temperature. The consequences of macroscopic disorder are not well understood, but a universal behavior of the zero-bias resistance as a function of field and temperature has been observed. (orig.)
Two-dimensional heat conducting simulation of plasma armatures
Huerta, M.A.; Boynton, G.
1991-01-01
This paper reports on our development of a two-dimensional MHD code to simulate internal motions in a railgun plasma armature. The authors use the equations of resistive MHD, with Ohmic heating, and radiation heat transport. The authors use a Flux Corrected Transport code to advance all quantities in time. Our runs show the development of complex flows, subsequent shedding of secondary arcs, and a drop in the acceleration of the armature
Topological field theories and two-dimensional instantons
Schaposnik, F.A.
1990-01-01
In this paper, the author discusses some topics related to the recently developed Topological Field Theories (TFTs). The first part is devoted to a discussion on how a TFT can be quantized using techniques which are well-known from the study of gauge theories. Then the author describes the results that we have obtained in collaboration with George Thompson in the study of a two-dimensional TFT related to the Abelian Higgs model
Two-dimensional color-code quantum computation
Fowler, Austin G.
2011-01-01
We describe in detail how to perform universal fault-tolerant quantum computation on a two-dimensional color code, making use of only nearest neighbor interactions. Three defects (holes) in the code are used to represent logical qubits. Triple-defect logical qubits are deformed into isolated triangular sections of color code to enable transversal implementation of all single logical qubit Clifford group gates. Controlled-NOT (CNOT) is implemented between pairs of triple-defect logical qubits via braiding.
Collision dynamics of two-dimensional non-Abelian vortices
Mawson, Thomas; Petersen, Timothy C.; Simula, Tapio
2017-09-01
We study computationally the collision dynamics of vortices in a two-dimensional spin-2 Bose-Einstein condensate. In contrast to Abelian vortex pairs, which annihilate or pass through each other, we observe non-Abelian vortex pairs to undergo rungihilation—an event that converts the colliding vortices into a rung vortex. The resulting rung defect subsequently decays to another pair of non-Abelian vortices of different type, accompanied by a magnetization reversal.
An energy principle for two-dimensional collisionless relativistic plasmas
Otto, A.; Schindler, K.
1984-01-01
Using relativistic Vlasov theory an energy principle for two-dimensional plasmas is derived, which provides a sufficient and necessary criterion for the stability of relativistic plasma equilibria. This energy principle includes charge separating effects since the exact Poisson equation was taken into consideration. Applying the variational principle to the case of the relativistic plane plasma sheet, the same marginal wave length is found as in the non-relativistic case. (author)
Graphene – A Two-Dimensional Dirac Material
Liu, Danny; Wicklund, Johan
2014-01-01
Graphene is a two-dimensional material, whose popularity has soared in both condensedmatter physics and material science the past decade. Due to its unique properties, graphene can be used in a vast array of new and interesting applications that could fundamentally change the material industry. This report reviews the current research and literature in order to trace the historical development of graphene. Then, in order to better understand the material, the unique properties of graphene are...
Resistive-strips micromegas detectors with two-dimensional readout
Byszewski, M.; Wotschack, J.
2012-02-01
Micromegas detectors show very good performance for charged particle tracking in high rate environments as for example at the LHC. It is shown that two coordinates can be extracted from a single gas gap in these detectors. Several micromegas chambers with spark protection by resistive strips and two-dimensional readout have been tested in the context of the R&D work for the ATLAS Muon System upgrade.
Hall effect in the two-dimensional Luttinger liquid
Anderson, P.W.
1991-01-01
The temperature dependence of the Hall effect in the normal state is a commom theme of all the cuprate superconductors and has been one of the more puzzling observations on these puzzling materials. We describe a general scheme within the Luttinger liquid theory of these two-dimensional quantum fluids which corrrelates the anomalous Hall and resistivity observations on a wide variety of both pure and doped single crystals, especially the data in the accompanying Letter of Chien, Wang, and Ong
Theory of a Nearly Two-Dimensional Dipolar Bose Gas
2016-05-11
order to be published, he sent the paper to Einstein to translate it. The other contributing scientist is world famous physicist Albert Einstein , maybe...mechanical state, a Bose- Einstein condensate (BEC), where the atoms cease to behave like distinguishable entities, and instead form a single macroscopic...model in both three- and two-dimensional geometries. 15. SUBJECT TERMS Bose Einstein condensation, ultracold physics, condensed matter, dipoles 16
SU(1,2) invariance in two-dimensional oscillator
Krivonos, Sergey [Bogoliubov Laboratory of Theoretical Physics,Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation); Nersessian, Armen [Yerevan State University,1 Alex Manoogian St., Yerevan, 0025 (Armenia); Tomsk Polytechnic University,Lenin Ave. 30, 634050 Tomsk (Russian Federation)
2017-02-01
Performing the Hamiltonian analysis we explicitly established the canonical equivalence of the deformed oscillator, constructed in arXiv:1607.03756, with the ordinary one. As an immediate consequence, we proved that the SU(1,2) symmetry is the dynamical symmetry of the ordinary two-dimensional oscillator. The characteristic feature of this SU(1,2) symmetry is a non-polynomial structure of its generators written in terms of the oscillator variables.
Decaying Two-Dimensional Turbulence in a Circular Container
Schneider, Kai; Farge, Marie
2005-01-01
We present direct numerical simulations of two-dimensional decaying turbulence at initial Reynolds number 5×104 in a circular container with no-slip boundary conditions. Starting with random initial conditions the flow rapidly exhibits self-organization into coherent vortices. We study their formation and the role of the viscous boundary layer on the production and decay of integral quantities. The no-slip wall produces vortices which are injected into the bulk flow and tend to compensate the...
Two-dimensional readout in a liquid xenon ionisation chamber
Solovov, V; Ferreira-Marques, R; Lopes, M I; Pereira, A; Policarpo, Armando
2002-01-01
A two-dimensional readout with metal strips deposited on both sides of a glass plate is investigated aiming to assess the possibility of its use in a liquid xenon ionisation chamber for positron emission tomography. Here, we present results obtained with an alpha-source. It is shown that position resolution of <=1 mm, fwhm, can be achieved for free charge depositions equivalent to those due to gamma-rays with energy from 220 down to 110 keV.
Stochastic and collisional diffusion in two-dimensional periodic flows
Doxas, I.; Horton, W.; Berk, H.L.
1990-05-01
The global effective diffusion coefficient D* for a two-dimensional system of convective rolls with a time dependent perturbation added, is calculated. The perturbation produces a background diffusion coefficient D, which is calculated analytically using the Menlikov-Arnold integral. This intrinsic diffusion coefficient is then enhanced by the unperturbed flow, to produce the global effective diffusion coefficient D*, which we can calculate theoretically for a certain range of parameters. The theoretical value agrees well with numerical simulations. 23 refs., 4 figs
The Convergence Acceleration of Two-Dimensional Fourier Interpolation
Anry Nersessian
2008-07-01
Full Text Available Hereby, the convergence acceleration of two-dimensional trigonometric interpolation for a smooth functions on a uniform mesh is considered. Together with theoretical estimates some numerical results are presented and discussed that reveal the potential of this method for application in image processing. Experiments show that suggested algorithm allows acceleration of conventional Fourier interpolation even for sparse meshes that can lead to an efficient image compression/decompression algorithms and also to applications in image zooming procedures.
Two-dimensional correlation spectroscopy in polymer study
Park, Yeonju; Noda, Isao; Jung, Young Mee
2015-01-01
This review outlines the recent works of two-dimensional correlation spectroscopy (2DCOS) in polymer study. 2DCOS is a powerful technique applicable to the in-depth analysis of various spectral data of polymers obtained under some type of perturbation. The powerful utility of 2DCOS combined with various analytical techniques in polymer studies and noteworthy developments of 2DCOS used in this field are also highlighted. PMID:25815286
Spatial Discrete Soliton in Two dimensional with Kerr medium
Aghdami, M.; Mostafavi, D.; Mokhtari, F.; Keradmand, R.
2012-01-01
In this theoretical work propagation of the Gaussian beam through a two dimensional waveguides array is numerically investigated, in which each waveguide contains medium with Kerr nonlinearity considering coupling to vertical, horizontal and diagonal neighbor through light electric field. Different values of intensity, nonlinear coefficient Kerr and Gaussian beam width of incident Gaussian beam are examined and finally suitable parameters for providing central spatial solitons are obtained.
GEPOIS: a two dimensional nonuniform mesh Poisson solver
Quintenz, J.P.; Freeman, J.R.
1979-06-01
A computer code is described which solves Poisson's equation for the electric potential over a two dimensional cylindrical (r,z) nonuniform mesh which can contain internal electrodes. Poisson's equation is solved over a given region subject to a specified charge distribution with either Neumann or Dirichlet perimeter boundary conditions and with Dirichlet boundary conditions on internal surfaces. The static electric field is also computed over the region with special care given to normal electric field components at boundary surfaces
Acoustic transparency in two-dimensional sonic crystals
Sanchez-Dehesa, Jose; Torrent, Daniel [Wave Phenomena Group, Department of Electronic Engineering, Polytechnic University of Valencia, C/ Camino de Vera s/n, E-46022 Valencia (Spain); Cai Liangwu [Department of Mechanical and Nuclear Engineering, Kansas State University, Manhattan, KS 66506 (United States)], E-mail: jsdehesa@upvnet.upv.es
2009-01-15
Acoustic transparency is studied in two-dimensional sonic crystals consisting of hexagonal distributions of cylinders with continuously varying properties. The transparency condition is achieved by selectively closing the acoustic bandgaps, which are governed by the structure factor of the cylindrical scatterers. It is shown here that cylindrical scatterers with the proposed continuously varying properties are physically realizable by using metafluids based on sonic crystals. The feasibility of this proposal is analyzed by a numerical experiment based on multiple scattering theory.
Two-dimensional manifolds with metrics of revolution
Sabitov, I Kh
2000-01-01
This is a study of the topological and metric structure of two-dimensional manifolds with a metric that is locally a metric of revolution. In the case of compact manifolds this problem can be thoroughly investigated, and in particular it is explained why there are no closed analytic surfaces of revolution in R 3 other than a sphere and a torus (moreover, in the smoothness class C ∞ such surfaces, understood in a certain generalized sense, exist in any topological class)
Warranty menu design for a two-dimensional warranty
Ye, Zhi-Sheng; Murthy, D.N. Pra
2016-01-01
Fierce competitions in the commercial product market have forced manufacturers to provide customer-friendly warranties with a view to achieving higher customer satisfaction and increasing the market share. This study proposes a strategy that offers customers a two-dimensional warranty menu with a number of warranty choices, called a flexible warranty policy. We investigate the design of a flexible two-dimensional warranty policy that contains a number of rectangular regions. This warranty policy is obtained by dividing customers into several groups according to their use rates and providing each group a germane warranty region. Consumers choose a favorable one from the menu according to their usage behaviors. Evidently, this flexible warranty policy is attractive to users of different usage behaviors, and thus, it gives the manufacturer a good position in advertising the product. When consumers are unaware about their use rates upon purchase, we consider a fixed two-dimensional warranty policy with a stair-case warranty region and show that it is equivalent to the flexible policy. Such an equivalence reveals the inherent relationship between the rectangular warranty policy, the L-shape warranty policy, the step-stair warranty policy and the iso-probability of failure warranty policy that were extensively discussed in the literature. - Highlights: • We design a two-dimensional warranty menu with a number of warranty choices. • Consumers can choose a favorable one from the menu as per their usage behavior. • We further consider a fixed 2D warranty policy with a stair-case warranty region. • We show the equivalence of the two warranty policies.
Two-dimensional analysis of trapped-ion eigenmodes
Marchand, R.; Tang, W.M.; Rewoldt, G.
1979-11-01
A fully two-dimensional eigenmode analysis of the trapped-ion instability in axisymmetric toroidal geometry is presented. The calculations also takes into account the basic dynamics associated with other low frequency modes such as the trapped-electron instability and the ion-temperature-gradient instability. The poloidal structure of the mode is taken into account by Fourier expanding the perturbed electrostatic potential, PHI, in theta
Analysis of two dimensional signals via curvelet transform
Lech, W.; Wójcik, W.; Kotyra, A.; Popiel, P.; Duk, M.
2007-04-01
This paper describes an application of curvelet transform analysis problem of interferometric images. Comparing to two-dimensional wavelet transform, curvelet transform has higher time-frequency resolution. This article includes numerical experiments, which were executed on random interferometric image. In the result of nonlinear approximations, curvelet transform obtains matrix with smaller number of coefficients than is guaranteed by wavelet transform. Additionally, denoising simulations show that curvelet could be a very good tool to remove noise from images.
Moussaoui, Ahmed; Bouziane, Touria
2016-01-01
The method LRPIM is a Meshless method with properties of simple implementation of the essential boundary conditions and less costly than the moving least squares (MLS) methods. This method is proposed to overcome the singularity associated to polynomial basis by using radial basis functions. In this paper, we will present a study of a 2D problem of an elastic homogenous rectangular plate by using the method LRPIM. Our numerical investigations will concern the influence of different shape parameters on the domain of convergence,accuracy and using the radial basis function of the thin plate spline. It also will presents a comparison between numerical results for different materials and the convergence domain by precising maximum and minimum values as a function of distribution nodes number. The analytical solution of the deflection confirms the numerical results. The essential points in the method are: •The LRPIM is derived from the local weak form of the equilibrium equations for solving a thin elastic plate.•The convergence of the LRPIM method depends on number of parameters derived from local weak form and sub-domains.•The effect of distributions nodes number by varying nature of material and the radial basis function (TPS).
Forming three-dimensional closed shapes from two-dimensional soft ribbons by controlled buckling
Aoki, Michio; Juang, Jia-Yang
2018-02-01
Conventional manufacturing techniques-moulding, machining and casting-exist to produce three-dimensional (3D) shapes. However, these industrial processes are typically geared for mass production and are not directly applicable to residential settings, where inexpensive and versatile tools are desirable. Moreover, those techniques are, in general, not adequate to process soft elastic materials. Here, we introduce a new concept of forming 3D closed hollow shapes from two-dimensional (2D) elastic ribbons by controlled buckling. We numerically and experimentally characterize how the profile and thickness of the ribbon determine its buckled shape. We find a 2D master profile with which various elliptical 3D shapes can be formed. More complex natural and artificial hollow shapes, such as strawberry, hourglass and wheel, can also be achieved via strategic design and pattern engraving on the ribbons. The nonlinear response of the post-buckling regime is rationalized through finite-element analysis, which shows good quantitative agreement with experiments. This robust fabrication should complement conventional techniques and provide a rich arena for future studies on the mechanics and new applications of elastic hollow structures.
Two-dimensional shielding benchmarks for iron at YAYOI, (1)
Oka, Yoshiaki; An, Shigehiro; Kasai, Shigeru; Miyasaka, Shun-ichi; Koyama, Kinji.
The aim of this work is to assess the collapsed neutron and gamma multigroup cross sections for two dimensional discrete ordinate transport code. Two dimensional distributions of neutron flux and gamma ray dose through a 70cm thick and 94cm square iron shield were measured at the fast neutron source reactor ''YAYOI''. The iron shield was placed over the lead reflector in the vertical experimental column surrounded by heavy concrete wall. The detectors used in this experiment were threshold detectors In, Ni, Al, Mg, Fe and Zn, sandwitch resonance detectors Au, W and Co, activation foils Au for neutrons and thermoluminescence detectors for gamma ray dose. The experimental results were compared with the calculated ones by the discrete ordinate transport code ANISN and TWOTRAN. The region-wise, coupled neutron-gamma multigroup cross-sections (100n+20gamma, EURLIB structure) were generated from ENDF/B-IV library for neutrons and POPOP4 library for gamma-ray production cross-sections by using the code system RADHEAT. The effective microscopic neutron cross sections were obtained from the infinite dilution values applying ABBN type self-shielding factors. The gamma ray production multigroup cross-sections were calculated from these effective microscopic neutron cross-sections. For two-dimensional calculations the group constants were collapsed into 10 neutron groups and 3 gamma groups by using ANISN. (auth.)
Electromagnetically induced two-dimensional grating assisted by incoherent pump
Chen, Yu-Yuan; Liu, Zhuan-Zhuan; Wan, Ren-Gang, E-mail: wrg@snnu.edu.cn
2017-04-25
We propose a scheme for realizing electromagnetically induced two-dimensional grating in a double-Λ system driven simultaneously by a coherent field and an incoherent pump field. In such an atomic configuration, the absorption is suppressed owing to the incoherent pumping process and the probe can be even amplified, while the refractivity is mainly attributed to the dynamically induced coherence. With the help of a standing-wave pattern coherent field, we obtain periodically modulated refractive index without or with gain, and therefore phase grating or gain-phase grating which diffracts a probe light into high-order direction efficiently can be formed in the medium via appropriate manipulation of the system parameters. The diffraction efficiency attainable by the present gratings can be controlled by tuning the coherent field intensity or the interaction length. Hence, the two-dimensional grating can be utilized as all-optical splitter or router in optical networking and communication. - Highlights: • Two-dimensional grating is coherently induced in four-level atoms. • Phase and gain-phase gratings are obtained assisted by incoherent pump. • The diffraction power is improved due to the enhanced refraction modulation. • The gratings can be utilized as multi-channel all-optical splitter and router.
Procedures for two-dimensional electrophoresis of proteins
Tollaksen, S.L.; Giometti, C.S.
1996-10-01
High-resolution two-dimensional gel electrophoresis (2DE) of proteins, using isoelectric focusing in the first dimension and sodium dodecyl sulfate/polyacrylamide gel electrophoresis (SDS-PAGE) in the second, was first described in 1975. In the 20 years since those publications, numerous modifications of the original method have evolved. The ISO-DALT system of 2DE is a high-throughput approach that has stood the test of time. The problem of casting many isoelectric focusing gels and SDS-PAGE slab gels (up to 20) in a reproducible manner has been solved by the use of the techniques and equipment described in this manual. The ISO-DALT system of two-dimensional gel electrophoresis originated in the late 1970s and has been modified many times to improve its high-resolution, high-throughput capabilities. This report provides the detailed procedures used with the current ISO-DALT system to prepare, run, stain, and photograph two-dimensional gels for protein analysis.
Experimental two-dimensional quantum walk on a photonic chip.
Tang, Hao; Lin, Xiao-Feng; Feng, Zhen; Chen, Jing-Yuan; Gao, Jun; Sun, Ke; Wang, Chao-Yue; Lai, Peng-Cheng; Xu, Xiao-Yun; Wang, Yao; Qiao, Lu-Feng; Yang, Ai-Lin; Jin, Xian-Min
2018-05-01
Quantum walks, in virtue of the coherent superposition and quantum interference, have exponential superiority over their classical counterpart in applications of quantum searching and quantum simulation. The quantum-enhanced power is highly related to the state space of quantum walks, which can be expanded by enlarging the photon number and/or the dimensions of the evolution network, but the former is considerably challenging due to probabilistic generation of single photons and multiplicative loss. We demonstrate a two-dimensional continuous-time quantum walk by using the external geometry of photonic waveguide arrays, rather than the inner degree of freedoms of photons. Using femtosecond laser direct writing, we construct a large-scale three-dimensional structure that forms a two-dimensional lattice with up to 49 × 49 nodes on a photonic chip. We demonstrate spatial two-dimensional quantum walks using heralded single photons and single photon-level imaging. We analyze the quantum transport properties via observing the ballistic evolution pattern and the variance profile, which agree well with simulation results. We further reveal the transient nature that is the unique feature for quantum walks of beyond one dimension. An architecture that allows a quantum walk to freely evolve in all directions and at a large scale, combining with defect and disorder control, may bring up powerful and versatile quantum walk machines for classically intractable problems.
Automated Processing of Two-Dimensional Correlation Spectra
Sengstschmid; Sterk; Freeman
1998-04-01
An automated scheme is described which locates the centers of cross peaks in two-dimensional correlation spectra, even under conditions of severe overlap. Double-quantum-filtered correlation (DQ-COSY) spectra have been investigated, but the method is also applicable to TOCSY and NOESY spectra. The search criterion is the intrinsic symmetry (or antisymmetry) of cross-peak multiplets. An initial global search provides the preliminary information to build up a two-dimensional "chemical shift grid." All genuine cross peaks must be centered at intersections of this grid, a fact that reduces the extent of the subsequent search program enormously. The program recognizes cross peaks by examining the symmetry of signals in a test zone centered at a grid intersection. This "symmetry filter" employs a "lowest value algorithm" to discriminate against overlapping responses from adjacent multiplets. A progressive multiplet subtraction scheme provides further suppression of overlap effects. The processed two-dimensional correlation spectrum represents cross peaks as points at the chemical shift coordinates, with some indication of their relative intensities. Alternatively, the information is presented in the form of a correlation table. The authenticity of a given cross peak is judged by a set of "confidence criteria" expressed as numerical parameters. Experimental results are presented for the 400-MHz double-quantum-filtered COSY spectrum of 4-androsten-3,17-dione, a case where there is severe overlap. Copyright 1998 Academic Press.
Quantum oscillations in quasi-two-dimensional conductors
Galbova, O
2002-01-01
The electronic absorption of sound waves in quasi-two-dimensional conductors in strong magnetic fields, is investigated theoretically. A longitudinal acoustic wave, propagating along the normal n-> to the layer of quasi-two-dimensional conductor (k-> = left brace 0,0,k right brace; u-> = left brace 0,0,u right brace) in magnetic field (B-> = left brace 0, 0, B right brace), is considered. The quasiclassical approach for this geometry is of no interest, due to the absence of interaction between electromagnetic and acoustic waves. The problem is of interest in strong magnetic field when quantization of the charge carriers energy levels takes place. The quantum oscillations in the sound absorption coefficient, as a function of the magnetic field, are theoretically observed. The experimental study of the quantum oscillations in quasi-two-dimensional conductors makes it possible to solve the inverse problem of determining from experimental data the extrema closed sections of the Fermi surface by a plane p sub z = ...
Compressible magma flow in a two-dimensional elastic-walled dike
Woods, A.W.; Bokhove, Onno; de Boer, A; Hill, B.E.
2006-01-01
The ascent of magma to the Earth's surface is commonly modeled by assuming a fixed dike or flow geometry from a deep subsurface reservoir to the surface. In practice, however, this flow geometry is produced by deformation of the crust by ascending overpressured magma. Here, we explore how this
Elastic-Plastic Fracture Mechanics Analysis of a CT-Specimen - a Two-Dimensional Approach
Larsen, Gunner Chr.
strain as well as a plane stress approximation. The results presented include applied loads and displacements at certain locations. Moreover, the J-integral and the crack opening displacement have been presented. The plane strain and the plane stress approximation have been compared and the plane stres......« approximation is believed to deliver the best results. The results have been obtained using the finiteelement code ADINA and the postprocessor code JINT....
Oblique propagation of nonlinear hydromagnetic waves: One- and two-dimensional behavior
Malara, F.; Elaoufir, J.
1991-01-01
The one- and two-dimensional behavior of obliquely propagating hydromagnetic waves is analyzed by means of analytical theory and numerical simulations. It is shown that the nonlinear evolution of a one-dimensional MHD wave leads to the formation of a rotational discontinuity and a compressive steepened quasi-linearly polarized pulse whose structure is similar to that of a finite amplitude magnetosonic simple wave. For small propagation angles, the pulse mode (fast or slow) depends on the value of β with respect to unity while for large propagation angles the wave mode is fixed by the sign of the initial density-field correlation. The two-dimensional evolution shows that an MHD wave is unstable against a small-amplitude long-wavelength modulation in the direction transverse to the wave propagation direction. A two-dimensional magnetosonic wave solution is found, in which the density fluctuation is driven by the corresponding total pressure fluctuation, exactly as in the one-dimensional simple wave. Along with the steepening effect, the wave experiences both wave front deformation and a self-focusing effect which may eventually lead to the collapse of the wave. The results compare well with observations of MHD waves in the Earth's foreshock and at comets
Forman, M B; Phelan, B K; Robertson, R M; Virmani, R
1985-02-01
Two-dimensional echocardiographic findings in porcine valve dysfunction were compared with pathologic findings in 10 patients (12 valves). Three specific echocardiographic findings were identified in patients with regurgitant lesions: prolapse, fracture and flail leaflets. Prolapse was associated pathologically with thinning of the leaflets, longitudinal tears close to the ring margin and acid mucopolysaccharide accumulation. Valve fracture was seen with and without prolapse and was accompanied pathologically by small pinpoint perforations or tears of the leaflet. A flail leaflet was seen with a linear tear of the free margin and was associated with calcific deposits. Mild degrees of fracture seen pathologically were missed on the echocardiographic study in five patients. Thickening or calcification, when present in moderate or severe amounts, was correctly identified by echocardiography. When all abnormal features were considered collectively, two-dimensional echocardiography correctly identified at least one of them in all patients. Therefore, two-dimensional echocardiography may prove useful in assessing the source of valvular regurgitation in patients with bioprosthetic valves.
Vorotnikov, K.; Starosvetsky, Y.
2018-01-01
The present study concerns two-dimensional nonlinear mechanisms of bidirectional and unidirectional channeling of longitudinal and shear waves emerging in the locally resonant acoustic structure. The system under consideration comprises an oscillatory chain of the axially coupled masses. Each mass of the chain is subject to the local linear potential along the lateral direction and incorporates the lightweight internal rotator. In the present work, we demonstrate the emergence of special resonant regimes of complete bi- and unidirectional transitions between the longitudinal and the shear waves of the locally resonant chain. These regimes are manifested by the two-dimensional energy channeling between the longitudinal and the shear traveling waves in the recurrent as well as the irreversible fashion. We show that the spatial control of the two dimensional energy flow between the longitudinal and the shear waves is solely governed by the motion of the internal rotators. Nonlinear analysis of the regimes of a bidirectional wave channeling unveils their global bifurcation structure and predicts the zones of their spontaneous transitions from a complete bi-directional wave channeling to the one-directional entrapment. An additional regime of a complete irreversible resonant transformation of the longitudinal wave into a shear wave is analyzed in the study. The intrinsic mechanism governing the unidirectional wave reorientation is described analytically. The results of the analysis of both mechanisms are substantiated by the numerical simulations of the full model and are found to be in a good agreement.
Rabinskiy, L. N.; Zhavoronok, S. I.
2018-04-01
The transient interaction of acoustic media and elastic shells is considered on the basis of the transition function approach. The three-dimensional hyperbolic initial boundary-value problem is reduced to a two-dimensional problem of shell theory with integral operators approximating the acoustic medium effect on the shell dynamics. The kernels of these integral operators are determined by the elementary solution of the problem of acoustic waves diffraction at a rigid obstacle with the same boundary shape as the wetted shell surface. The closed-form elementary solution for arbitrary convex obstacles can be obtained at the initial interaction stages on the background of the so-called “thin layer hypothesis”. Thus, the shell–wave interaction model defined by integro-differential dynamic equations with analytically determined kernels of integral operators becomes hence two-dimensional but nonlocal in time. On the other hand, the initial interaction stage results in localized dynamic loadings and consequently in complex strain and stress states that require higher-order shell theories. Here the modified theory of I.N.Vekua–A.A.Amosov-type is formulated in terms of analytical continuum dynamics. The shell model is constructed on a two-dimensional manifold within a set of field variables, Lagrangian density, and constraint equations following from the boundary conditions “shifted” from the shell faces to its base surface. Such an approach allows one to construct consistent low-order shell models within a unified formal hierarchy. The equations of the N th-order shell theory are singularly perturbed and contain second-order partial derivatives with respect to time and surface coordinates whereas the numerical integration of systems of first-order equations is more efficient. Such systems can be obtained as Hamilton–de Donder–Weyl-type equations for the Lagrangian dynamical system. The Hamiltonian formulation of the elementary N th-order shell theory is
Mercier, Sylvain; Gratton, Serge; Tardieu, Nicolas; Vasseur, Xavier
2017-12-01
Many applications in structural mechanics require the numerical solution of sequences of linear systems typically issued from a finite element discretization of the governing equations on fine meshes. The method of Lagrange multipliers is often used to take into account mechanical constraints. The resulting matrices then exhibit a saddle point structure and the iterative solution of such preconditioned linear systems is considered as challenging. A popular strategy is then to combine preconditioning and deflation to yield an efficient method. We propose an alternative that is applicable to the general case and not only to matrices with a saddle point structure. In this approach, we consider to update an existing algebraic or application-based preconditioner, using specific available information exploiting the knowledge of an approximate invariant subspace or of matrix-vector products. The resulting preconditioner has the form of a limited memory quasi-Newton matrix and requires a small number of linearly independent vectors. Numerical experiments performed on three large-scale applications in elasticity highlight the relevance of the new approach. We show that the proposed method outperforms the deflation method when considering sequences of linear systems with varying matrices.
Two-dimensional cross-section and SED uncertainty analysis for the Fusion Engineering Device (FED)
Embrechts, M.J.; Urban, W.T.; Dudziak, D.J.
1982-01-01
The theory of two-dimensional cross-section and secondary-energy-distribution (SED) sensitivity was implemented by developing a two-dimensional sensitivity and uncertainty analysis code, SENSIT-2D. Analyses of the Fusion Engineering Design (FED) conceptual inboard shield indicate that, although the calculated uncertainties in the 2-D model are of the same order of magnitude as those resulting from the 1-D model, there might be severe differences. The more complex the geometry, the more compulsory a 2-D analysis becomes. Specific results show that the uncertainty for the integral heating of the toroidal field (TF) coil for the FED is 114.6%. The main contributors to the cross-section uncertainty are chromium and iron. Contributions to the total uncertainty were smaller for nickel, copper, hydrogen and carbon. All analyses were performed with the Los Alamos 42-group cross-section library generated from ENDF/B-V data, and the COVFILS covariance matrix library. The large uncertainties due to chromium result mainly from large convariances for the chromium total and elastic scattering cross sections
Transport properties of diazonium functionalized graphene: chiral two-dimensional hole gases
Huang Ping; Jing Long; Zhu Huarui; Gao Xueyun
2012-01-01
The electric transport properties of diazonium functionalized graphene (DFG) were investigated. The temperature dependence of the resistivity (ρ-T) and the Shubnikov-de Haas oscillation of the DFG revealed two-dimensional hole gas (2DHG) behaviors. The DFGs exhibited unusual weak localization behaviors in which both inelastic and chirality-breaking elastic scattering processes should be taken into account, meaning that graphene chirality was maintained. Because of the giant decrease in the diffusion coefficient, the scattering rates remained relatively low in the presence of suppression of the scattering lengths. The decreases of both the mean free path and the Fermi velocity were responsible for the suppression of the diffusion coefficient and hence the charge mobility. (paper)
Magnetooscillations of the tunneling current between two-dimensional electron systems
Raichev, O.E.; Vasko, F.T.
1995-08-01
We calculate electric current caused by electron tunnelling between two-dimensional layers in the magnetic field applied perpendicular to the layers. An elastic scattering of the electrons is taken into account. Analytical results are obtained for two regimes: i) small magnetic field, when the Landau quantization is suppressed by the scattering and the oscillatory part of the current shows nearly harmonic behaviour; ii) high magnetic field, when the Landau levels are well-defined and the conductivity shows series of sharp peaks corresponding to resonant magnetotunneling. In the last case, we used two alternative approaches: self-consistent Born approximation and path integral method, and compared obtained results. (author). 12 refs, 3 figs
Dinesh Kumar
2013-11-01
Full Text Available This paper deals with the study of two-dimensional Saigo-Maeda operators of Weyl type associated with Aleph function defined in this paper. Two theorems on these defined operators are established. Some interesting results associated with the H-functions and generalized Mittag-Leffler functions are deduced from the derived results. One dimensional analog of the derived results is also obtained.
Majumdar, S.; Kwasny, R.
1985-01-01
High-cycle fatigue tests using 5-mm-diameter smooth specimens were performed on the single crystal alloy PWA 1480 (001 axis) at 70F (room temperature) in air and at 100F (538C) in vacuum (10 to the -6 power torr). Tests were conducted at zero mean stress as well as at high tensile mean stress. The results indicate that, although a tensile mean stress, in general, reduces life, the reduction in fatigue strength, for a given mean stress at a life of one million cycles, is much less than what is predicted by the usual linear Goodman plot. Further, the material appears to be significantly more resistant to mean stress effects at 1000F than at 70F. Metallographic examinations of failed specimens indicate that failures in all cases are initiated from micropores of sizes of the order of 30 to 40 microns. Since the macroscopic stress-strain response in all cases was observed to be linear elastic, linear elastic fracture mechanics (LEFM) analyses were carried out to determine the crack growth curves of the material assuming that crack initiation from a micropore (a sub o = 40 microns) occurs very early in life. The results indicate that the calculated crack growth rates at an R (defined as the ratio between minimum stress to maximum stress) value of zero are approximately the same at 70F as at 1000F. However, the calculated crack growth rates at other R ratios, both positive and negative, tend to be higher at 70F than at 1000F. Calculated threshold effects at large R values tend to be independent of temperature in the temperature regime studied. They are relatively constant with increasing R ratio up to a value of about 0.6, beyond which the calculated threshold stress intensity factor range decreases rapidly with increasing R ratios.
Dai, Jian; Song, Xing-Chang
2001-07-01
One of the key ingredients of Connes's noncommutative geometry is a generalized Dirac operator which induces a metric (Connes's distance) on the pure state space. We generalize such a Dirac operator devised by Dimakis et al, whose Connes distance recovers the linear distance on an one-dimensional lattice, to the two-dimensional case. This Dirac operator has the local eigenvalue property and induces a Euclidean distance on this two-dimensional lattice, which is referred to as `natural'. This kind of Dirac operator can be easily generalized into any higher-dimensional lattices.
Raman scattering in a two-dimensional Fermi liquid with spin-orbit coupling
Maiti, Saurabh; Maslov, Dmitrii L.
2017-04-01
We present a microscopic theory of Raman scattering in a two-dimensional Fermi liquid (FL) with Rashba and Dresselhaus types of spin-orbit coupling and subject to an in-plane magnetic field (B ⃗). In the long-wavelength limit, the Raman spectrum probes the collective modes of such a FL: the chiral spin waves. The characteristic features of these modes are a linear-in-q term in the dispersion and the dependence of the mode frequency on the directions of both q ⃗ and B ⃗. All of these features have been observed in recent Raman experiments on Cd1 -xMnxTe quantum wells.
Status for the two-dimensional Navier-Stokes solver EllipSys2D
Bertagnolio, F.; Soerensen, N.; Johansen, J.
2001-08-01
This report sets up an evaluation of two-dimensional Navier-Stokes solver EllipSys2D in its present state. This code is used for blade aerodynamics simulations in the Aeroelastic Design group at Risoe. Two airfoils are investigated by computing the flow at several angles of attack ranging from the linear to the stalled region. The computational data are compared to experimental data and numerical results from other computational codes. Several numerical aspects are studied, as mesh dependency, convective scheme, steady state versus unsteady computations, transition modelling. Some general conclusions intended to help in using this code for numerical simulations are given. (au)
Analysis of two-dimensional microdischarge distribution in dielectric-barrier discharges
Chirokov, A; Gutsol, A; Fridman, A; Sieber, K D; Grace, J M; Robinson, K S
2004-01-01
The two-dimensional spatial distribution of microdischarges in atmospheric pressure dielectric-barrier discharges (DBDs) in air was studied. Experimental images of DBDs (Lichtenberg figures) were obtained using photostimulable phosphors. The storage phosphor imaging method takes advantage of the linear response of the phosphor for characterization of microdischarge intensity and position. A microdischarge interaction model in DBDs is proposed and a Monte Carlo simulation of microdischarge interactions in the discharge is presented. Comparison of modelled and experimental images indicates interactions and short-range structuring of microdischarge channels
Calculation of two-dimensional thermal transients by the method of finite elements
Fontoura Rodrigues, J.L.A. da.
1980-08-01
The unsteady linear heat conduction analysis throught anisotropic and/or heterogeneous matter, in either two-dimensional fields with any kind of geometry or three-dimensional fields with axial symmetry is presented. The boundary conditions and the internal heat generation are supposed time - independent. The solution is obtained by modal analysis employing the finite element method under Galerkin formulation. Optionally, it can be used with a reduced resolution method called Stoker Economizing Method wich allows a decrease on the program processing costs. (Author) [pt
Generalized perturbation theory using two-dimensional, discrete ordinates transport theory
Childs, R.L.
1979-01-01
Perturbation theory for changes in linear and bilinear functionals of the forward and adjoint fluxes in a critical reactor has been implemented using two-dimensional discrete ordinates transport theory. The computer program DOT IV was modified to calculate the generalized functions Λ and Λ*. Demonstration calculations were performed for changes in a reaction-rate ratio and a reactivity worth caused by system perturbations. The perturbation theory predictions agreed with direct calculations to within about 2%. A method has been developed for calculating higher lambda eigenvalues and eigenfunctions using techniques similar to those developed for generalized functions. Demonstration calculations have been performed to obtain these eigenfunctions
A large area two-dimensional position sensitive multiwire proportional detector
Moura, M M D; Souza, F A; Alonso, E E; Fujii, R J; Meyknecht, A B; Added, N; Aissaoui, N; Cardenas, W H Z; Ferraretto, M D; Schnitter, U; Szanto, E M; Szanto de Toledo, A; Yamamura, M S; Carlin, N
1999-01-01
Large area two-dimensional position sensitive multiwire proportional detectors were developed to be used in the study of light heavy-ion nuclear reactions at the University of Sao Paulo Pelletron Laboratory. Each detector has a 20x20 cm sup 2 active area and consists of three grids (X-position, anode and Y-position) made of 25 mu m diameter gold plated tungsten wires. The position is determined through resistive divider chains. Results for position resolution, linearity and efficiency as a function of energy and position for different elements are reported.
Miranda, M; Dorrio, B V; Blanco, J; Diz-Bugarin, J; Ribas, F
2011-01-01
Two-stage phase shifting algorithms make possible to directly recover the sum or the difference of the encoded optical phase of two different fringe patterns. These algorithms can be constructed, for example, by combining known phase shifting algorithms in a non-linear way. In this work two-stage phase shifting algorithms are linked to a two-dimensional characteristic polynomial to qualitatively analyse their behaviour against the main systematic error sources in an analysis protocol like that used for phase shifting algorithms. This tool enables us to understand the propagation of properties from precursor phase shifting algorithms to new evaluation algorithms that can be built from them.
Diffraction of a plane wave on two-dimensional conductive structures and a surface wave
Davidovich, Mikhael V.
2018-04-01
We consider the structures type of two-dimensional electron gas in the form of a thin conductive, in particular, graphene films described by tensor conductivity, which are isolated or located on the dielectric layers. The dispersion equation for hybrid modes, as well as scattering parameters. We show that free wave (eigenwaves) problem follow from the problem of diffraction when linking the amplitude of the current of the linear equations are unsolvable, i.e., the determinant of this system is zero. As a particular case the dispersion equation follow from the conditions of matching (with zero reflection coefficient).
Polarization-selective transmission in stacked two-dimensional complementary plasmonic crystal slabs
Iwanaga, Masanobu
2010-02-01
It has been experimentally and numerically shown that transmission at near infrared wavelengths is selectively controlled by polarizations in two-dimensional complementary plasmonic crystal slabs (2D c-PlCSs) of stacked unit cell. This feature is naturally derived by taking account of Babinet's principle. Moreover, the slight structural modification of the unit cell has been found to result in a drastic change in linear optical responses of stacked 2D c-PlCSs. These results substantiate the feasibility of 2D c-PlCSs for producing efficient polarizers with subwavelength thickness.
On the exact spectra of two electrons confined by two-dimensional quantum dots
Soldatov, A.V.; Bogolubov Jr, N.N.
2005-12-01
Applicability of the method of intermediate problems to investigation of the energy spectrum and eigenstates of a two- electron two-dimensional quantum dot (QD) formed by a parabolic confining potential is discussed. It is argued that the method of intermediate problems, which provides convergent improvable lower bound estimates for eigenvalues of linear half-bound Hermitian operators in Hilbert space, can be fused with the classical Rayleigh-Ritz variational method and stochastic variational method thus providing an efficient tool of verification of the results obtained so far by various analytical and numerical methods being of current usage for studies of quantum dot models. (author)
Two-dimensional polyacrylamide gel electrophoresis of intracellular proteins
Ojima, N.; Sakamoto, T.; Yamashita, M.
1996-01-01
Since two-dimensional electrophoresis was established by O'Farrell for analysis of intracellular proteins of Escherichia coli, it has been applied to separation of proteins of animal cells and tissues, and especially to identification of stress proteins. Using this technique, proteins are separated by isoelectric focusing containing 8 m urea in the first dimension and by SDS-PAGE in the second dimension. The gels are stained with Coomassie Blue R-250 dye, followed by silver staining. In the case of radio-labeled proteins, the gels are dried and then autoradiographed. In order to identify a specific protein separated by two-dimensional electrophoresis, a technique determining the N-terminal amino acid sequence of the protein has been developed recently. After the proteins in the gel were electrotransferred to a polyvinylidene difluoride membrane, the membrane was stained for protein with Commassie Blue and a stained membrane fragment was applied to a protein sequencer. Our recent studies demonstrated that fish cells newly synthesized various proteins in response to heat shock, cold nd osmotic stresses. For example, when cellular proteins extracted from cold-treated rainbow trout cells were subjected to two-dimensional gel electrophoresis, the 70 kDa protein was found to be synthesized during the cold-treatment. N-Terminal sequence analysis showed that the cold-inducible protein was a homolog of mammalian valosin-containing protein and yeast cell division cycle gene product CDC48p. Furthermore, the sequence data were useful for preparing PCR primers and a rabbit antibody against a synthetic peptide to analyze a role for the protein in the function of trout cells and mechanisms for regulation
Statistical mechanics of two-dimensional and geophysical flows
Bouchet, Freddy; Venaille, Antoine
2012-01-01
The theoretical study of the self-organization of two-dimensional and geophysical turbulent flows is addressed based on statistical mechanics methods. This review is a self-contained presentation of classical and recent works on this subject; from the statistical mechanics basis of the theory up to applications to Jupiter’s troposphere and ocean vortices and jets. Emphasize has been placed on examples with available analytical treatment in order to favor better understanding of the physics and dynamics. After a brief presentation of the 2D Euler and quasi-geostrophic equations, the specificity of two-dimensional and geophysical turbulence is emphasized. The equilibrium microcanonical measure is built from the Liouville theorem. Important statistical mechanics concepts (large deviations and mean field approach) and thermodynamic concepts (ensemble inequivalence and negative heat capacity) are briefly explained and described. On this theoretical basis, we predict the output of the long time evolution of complex turbulent flows as statistical equilibria. This is applied to make quantitative models of two-dimensional turbulence, the Great Red Spot and other Jovian vortices, ocean jets like the Gulf-Stream, and ocean vortices. A detailed comparison between these statistical equilibria and real flow observations is provided. We also present recent results for non-equilibrium situations, for the studies of either the relaxation towards equilibrium or non-equilibrium steady states. In this last case, forces and dissipation are in a statistical balance; fluxes of conserved quantity characterize the system and microcanonical or other equilibrium measures no longer describe the system.