An Analytical Poroelastic Model of a Nonhomogeneous Medium Under Creep Compression for Ultrasound Poroelastography Applications—Part II

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Md Tauhidul Islam ◽  
J. N. Reddy ◽  
Raffaella Righetti
Keyword(s):  
Normal Tissue ◽  
Soft Tissue Tumor ◽  
Fluid Pressure ◽  
Companion Paper ◽  
Finite Element Models ◽  
Nonhomogeneous Medium ◽  
Statistical Comparison ◽  
Poroelastic Model ◽  
The One ◽  
Analytical Expressions

An analytical theory for the unconfined creep behavior of a cylindrical inclusion (simulating a soft tissue tumor) embedded in a cylindrical background sample (simulating normal tissue) is presented and analyzed in this paper. Both the inclusion and the background are considered as fluid-filled, porous materials, each of them being characterized by a set of mechanical parameters. Specifically, in this derivation, the inclusion is assumed to have significantly higher interstitial permeability than the background. The formulations of the effective Poisson's ratio (EPR) and fluid pressure in the inclusion and in the background are derived for the case of a sample subjected to a creep compression. The developed analytical expressions are validated using finite element models (FEM). Statistical comparison between the results obtained from the developed model and the results from FEM demonstrates accuracy of the proposed theoretical model higher than 99.4%. The model presented in this paper complements the one reported in the companion paper (Part I), which refers to the case of an inclusion having less interstitial permeability than the background.

An Analytical Poroelastic Model of a Nonhomogeneous Medium Under Creep Compression for Ultrasound Poroelastography Applications—Part I

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Md Tauhidul Islam ◽  
J. N. Reddy ◽  
Raffaella Righetti
Keyword(s):  
Soft Tissue Tumor ◽  
Fluid Pressure ◽  
Cylindrical Sample ◽  
Surrounding Tissue ◽  
Finite Element Models ◽  
Mechanical Parameters ◽  
Poroelastic Model ◽  
The Impact ◽  
Analytical Expressions ◽  
Theoretical Results

An analytical theory for the unconfined creep behavior of a cylindrical inclusion (simulating a soft tissue tumor) embedded in a cylindrical background sample (simulating normal tissue) is presented and analyzed in this paper. Both the inclusion and the background are considered as fluid-filled, porous materials, each of them being characterized by a set of mechanical properties. Specifically, in this paper, the inclusion is considered to be less permeable than the background. The cylindrical sample is compressed using a constant pressure within two frictionless plates and is allowed to expand in an unconfined way along the radial direction. Analytical expressions for the effective Poisson's ratio (EPR) and fluid pressure inside and outside the inclusion are derived and analyzed. The theoretical results are validated using finite element models (FEMs). Statistical analysis shows excellent agreement between the results obtained from the developed model and the results from FEM. Thus, the developed theoretical model can be used in medical imaging modalities such as ultrasound poroelastography to extract the mechanical parameters of tissues and/or to better understand the impact of different mechanical parameters on the estimated displacements, strains, stresses, and fluid pressure inside a tumor and in the surrounding tissue.

scholarly journals APPLICATIONS OF DENSITY MATRICES IN A TRAPPED BOSE GAS

2006 ◽  
Vol 20 (15) ◽  
pp. 2189-2221 ◽  
Author(s):  
K. CH. CHATZISAVVAS ◽  
S. E. MASSEN ◽  
CH. C. MOUSTAKIDIS ◽  
C. P. PANOS
Keyword(s):  
Quantum Information ◽  
Bose Gas ◽  
Einstein Condensation ◽  
Density Distributions ◽  
Occupation Numbers ◽  
The One ◽  
Bose Einstein ◽  
Jensen Shannon Divergence ◽  
Analytical Expressions ◽  
Short Range Correlations

An overview of the Bose–Einstein condensation of correlated atoms in a trap is presented by examining the effect of interparticle correlations to one- and two-body properties of the above systems at zero temperature in the framework of the lowest order cluster expansion. Analytical expressions for the one- and two-body properties of the Bose gas are derived using Jastrow-type correlation function. In addition numerical calculations of the natural orbitals and natural occupation numbers are also carried out. Special effort is devoted for the calculation of various quantum information properties including Shannon entropy, Onicescu informational energy, Kullback–Leibler relative entropy and the recently proposed Jensen–Shannon divergence entropy. The above quantities are calculated for the trapped Bose gases by comparing the correlated and uncorrelated cases as a function of the strength of the short-range correlations. The Gross–Piatevskii equation is solved, giving the density distributions in position and momentum space, which are employed to calculate quantum information properties of the Bose gas.

Kinematic Geometry of Wheeled Vehicle Systems

1996 ◽  
Author(s):  
S. V. Sreenivasan ◽  
P. Nanua
Keyword(s):  
Geometric Approach ◽  
Companion Paper ◽  
Kinematic Chains ◽  
Uneven Terrain ◽  
Geometric Conditions ◽  
Kinematic Study ◽  
Vehicle Systems ◽  
Motion Characteristics ◽  
The One ◽  
Wheeled Vehicles

Abstract This paper addresses instantaneous motion characteristics of wheeled vehicles systems on even and uneven terrain. A thorough kinematic geometric approach which utilizes screw system theory is used to investigate vehicle-terrain combinations as spatial mechanisms that possess multiple closed kinematic chains. It is shown that if the vehicle-terrain combination satisfies certain geometric conditions, for instance when the vehicle operates on even terrain, the system becomes singular or non-Kutzbachian — it possesses finite range mobility that is different from the one obtained using Kutzbach criterion. An application of this geometric approach to the study of rate kinematics of various classes of wheeled vehicles is also included. This approach provides an integrated framework to study the kinematic effects of varying the vehicle and/or terrain geometric parameters from their nominal values. In addition, design enhancements of existing vehicles are suggested using this approach. This kinematic study is closely related to the force distribution characteristics of wheeled vehicles which is the subject of the companion paper [SN96].

scholarly journals Semi-Analytic Evaluation of 1, 2 and 3-Electron Coulomb Integrals with Gaussian Expansion of Distance Operators W= RC1-nRD1-M, RC1-Nr12-M, R12-Nr13-M

2019 ◽  
Author(s):  
Sandor Kristyan
Keyword(s):  
Gaussian Function ◽  
Approximate Solutions ◽  
Equation System ◽  
Least Square ◽  
Position Vector ◽  
Least Square Fit ◽  
Analytic Expressions ◽  
The One ◽  
Analytical Expressions ◽  
Coulomb Integrals

The equations derived help to evaluate semi-analytically (mostly for k=1,2 or 3) the important Coulomb integrals Int rho(r1)…rho(rk) W(r1,…,rk) dr1…drk, where the one-electron density, rho(r1), is a linear combination (LC) of Gaussian functions of position vector variable r1. It is capable to describe the electron clouds in molecules, solids or any media/ensemble of materials, weight W is the distance operator indicated in the title. R stands for nucleus-electron and r for electron-electron distances. The n=m=0 case is trivial, the (n,m)=(1,0) and (0,1) cases, for which analytical expressions are well known, are widely used in the practice of computation chemistry (CC) or physics, and analytical expressions are also known for the cases n,m=0,1,2. The rest of the cases – mainly with any real (integer, non-integer, positive or negative) n and m - needs evaluation. We base this on the Gaussian expansion of |r|^-u, of which only the u=1 is the physical Coulomb potential, but the u≠1 cases are useful for (certain series based) correction for (the different) approximate solutions of Schrödinger equation, for example, in its wave-function corrections or correlation calculations. Solving the related linear equation system (LES), the expansion |r|^-u about equal SUM(k=0toL)SUM(i=1toM) Cik r^2k exp(-Aik r^2) is analyzed for |r| = r12 or RC1 with least square fit (LSF) and modified Taylor expansion. These evaluated analytic expressions for Coulomb integrals (up to Gaussian function integrand and the Gaussian expansion of |r|^-u) are useful for the manipulation with higher moments of inter-electronic distances via W, even for approximating Hamiltonian.

scholarly journals Seismic deformation at the Alban Hills volcano during the 1989-1990 seismic sequence

1998 ◽  
Vol 41 (2) ◽  
Author(s):  
G. Selvaggi ◽  
F. D'Ajello Caracciolo
Keyword(s):  
Strain Rate ◽  
Fluid Pressure ◽  
Strain Rate Tensor ◽  
Seismic Structure ◽  
Fault Plane Solutions ◽  
Alban Hills ◽  
Shear Failures ◽  
One Year ◽  
The One ◽  
Seismic Moment Release

We analysed the one-year-long seismic swarm at the Alban Hills volcano which occurred during 1989-1990. We portray spatial distribution of seismic moment release, better delineating the activated volume during the swarm. The seismic structure is imaged as a 7-km long, 3-km wide, and 3-km thick volume, located between 2 and 5 km depth, and NW-SE striking. Fault plane solutions and scalar seismic moments for the largest earthquakes provide the description of the average strain rate tensor. The principal strain rate axes show a dominant extension in NE-SW direction, a SE-NW direction of compression and a negligible thickening rate. P and T axes direction of the smaller earthquakes suggests that the same mode of deformation is distributed all over the activated volume. These results are discussed in terms of seismic deforming processes active at the Alban Hills volcano, in the frame of magmatic inflation recently invoked to explain the rapid vertical uplift affecting part of the volcano. The observed average deformation is consistent with shear failures occurring on faults connecting stress-oriented dykes in response to an increasing fluid pressure.

A new algorithm for numerical modelling of impurity transport in the frame of statistically homogeneous sharply contrasting media

2019 ◽  
Vol 34 (6) ◽  
pp. 339-351 ◽  
Author(s):  
Petr S. Kondratenko ◽  
Leonid V. Matveev ◽  
Alexander D. Vasiliev
Keyword(s):  
Numerical Modelling ◽  
Contaminant Transport ◽  
Integral Kernel ◽  
Time Intervals ◽  
One Dimensional ◽  
Time Representation ◽  
Impurity Transport ◽  
The One ◽  
Analytical Expressions ◽  
Good Agreement

Abstract A new method is developed to calculate characteristics of contaminant transport (including non-classical regimes) in statistically homogeneous sharply contrasting media. A transport integro-differential equation in the space-time representation is formulated on the basis of the model earlier proposed by one of the authors (L. M.). Analytical expressions for transport characteristics in limiting time intervals in the one-dimensional case are derived. An interpolation form is proposed for the integral kernel of the transport equation. On a basis of this expression, an algorithm is developed for numerical modelling the contaminant transport in statistically homogeneous sharply contrasting media. Trial numerical 1D calculations are performed based on this algorithm. Good agreement was found between the numerical simulation results and the asymptotic analytical expressions.

scholarly journals Parametrization of the Yukawa matrix in the scotogenic model and single-zero textures of the neutrino mass matrix

2019 ◽  
Vol 34 (19) ◽  
pp. 1950098 ◽  
Author(s):  
Teruyuki Kitabayashi
Keyword(s):  
Neutrino Mass ◽  
Mass Matrix ◽  
Branching Ratio ◽  
Neutrino Mass Matrix ◽  
Neutrino Masses ◽  
Neutrino Sector ◽  
The One ◽  
Relic Abundance ◽  
Analytical Expressions ◽  
Data Group

As the first topic, we propose a new parametrization of the complex Yukawa matrix in the scotogenic model. The new parametrization is compatible with the particle data group parametrization of the neutrino sector. Some analytical expressions for the neutrino masses with the new parametrization are shown. As the second topic, we consider the phenomenology of the scotogenic model with the one-zero-textures of the neutrino flavor mass matrix. One of the six patterns of the neutrino mass matrix is favorable for the real Yukawa matrix. On the other hand, for the complex Yukawa matrix, five of the six patterns are compatible with observations of the neutrino oscillations, dark matter relic abundance and branching ratio of the [Formula: see text] process.

Considerations of a classical model for spontaneous emission in a nonhomogeneous medium

1992 ◽  
Vol 70 (8) ◽  
pp. 631-636
Author(s):  
André Reid ◽  
Michel Piché
Keyword(s):  
General Solution ◽  
Frequency Shift ◽  
Spontaneous Emission ◽  
Transition Rate ◽  
Classical Model ◽  
Nonhomogeneous Medium ◽  
Effective Polarizability ◽  
Analytical Expressions

The classical model for spontaneous emission from a source embedded in a nonhomogeneous medium is examined in a new light. It is shown that the general solution may be expressed in terms of an effective polarizability associated with the transition being modeled. The case of a transition occurring in the vicinity of a perfect mirror is then studied as an illustration. Analytical expressions for the frequency shift and changes in the transition rate as a function of distance are found.

Sinusoidal input-based visual control for nonholonomic vehicles

Robotica ◽  
2013 ◽  
Vol 31 (5) ◽  
pp. 811-823 ◽  
Author(s):  
M. Aranda ◽  
G. López-Nicolás ◽  
C. Sagüés
Keyword(s):  
Kinematic Model ◽  
Visual Control ◽  
State Feedback Control ◽  
Control Approach ◽  
Vehicle Trajectories ◽  
Control Scheme ◽  
Sinusoidal Input ◽  
The One ◽  
Nonholonomic Vehicles ◽  
Analytical Expressions

SUMMARYThis paper proposes a new visual control approach based on sinusoidal inputs to be used on a nonholonomic robot. We present several contributions: In our method, developed considering a unicycle kinematic model, sinusoids are used in such a way that the generated vehicle trajectories are feasible, smooth and versatile. Our technique improves previous sinusoidal-based control works in terms of efficiency and flexibility. As further contributions, we present analytical expressions for the evolution of the robot's state, and propose a new state-feedback control law based on these expressions. All the information used in the control scheme is obtained from omnidirectional vision by means of the one-dimensional trifocal tensor. Stability analysis of the proposed approach is presented, and its performance is illustrated through experiments.

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