A Method of Numerical Evaluation of a Large Determinant

1960 ◽  
Vol 27 (2) ◽  
pp. 350-351
Author(s):  
F. R. E. Crossley ◽  
U¨stu¨n Germen
Keyword(s):  
Numerical Evaluation ◽  
Computer Programming ◽  
Numerical Procedure ◽  
Coupled System

When solving problems in the vibration of a close-coupled system, there arises the need to expand a tridiagonal determinant of the type of equation (1). A very quick and accurate means of accomplishing this expansion is provided by the following numerical procedure, which can readily be adapted to computer programming.

A Model For Diffusion and Competition in Cancer Growth and Metastasis

1997 ◽  
Vol 489 ◽  
Author(s):  
G. P. Pescarmona ◽  
M. Scalerandi ◽  
P. P. Delsanto ◽  
C. A. Condat
Keyword(s):  
Numerical Procedure ◽  
Local Environment ◽  
Coupled System ◽  
Cancer Growth ◽  
C Cells ◽  
Simulation Approach ◽  
Multiple Tumor ◽  
Suitable Parameter ◽  
Interaction Simulation ◽  
Stochastic Mechanism

AbstractA master equation formalism is used to model the growth and metastasis of a tumor as a function of the diffusion and absorption of a nutrient. Healthy and cancerous (C-) cells compete to bind the nutrient, which is allowed to diffuse starting from a prescribed region. Two thresholds are defined for the quantity of nutrient bound by the C-cells. If this quantity falls below the lower threshold, the cell dies, while if it increases above the upper threshold, the cell divides according to a predefined stochastic mechanism. C-cells migrate when they record a low concentration of free nutrient in the local environment. The model is formulated in terms of a coupled system of equations for the cell populations and the free and bound nutrient. This system can be solved by using the Local Interaction Simulation Approach (LISA), a numerical procedure that permits an efficient and detailed solution and is easily adaptable to parallel processing. With suitable parameter variation, the model can describe multiple tumor configurations, ranging from the classical spheroid with a necrotic core favored by mathematicians to very anisotropic shapes with inhomogeneous concentrations of the various populations. This is important because the nature of the anisotropy may be crucial in determining whether and how the cancer metastasizes. The effects of stochasticity and the presence of additional nutrients or inhibitors can be easily incorporated.

NUMERICAL EVALUATION OF FEM WITH APPLICATION TO THE 1-D ADVECTION–DIFFUSION PROBLEM

2002 ◽  
Vol 12 (02) ◽  
pp. 205-228 ◽  
Author(s):  
GIANCARLO SANGALLI
Keyword(s):  
Finite Element ◽  
Numerical Methods ◽  
General Framework ◽  
Numerical Evaluation ◽  
Numerical Procedure ◽  
Diffusion Problem ◽  
Empirical Justification ◽  
Eigenvalue Computation ◽  
Advection Diffusion

In this paper we present a numerical procedure to evaluate the efficiency of finite element numerical methods. We improve some of the ideas proposed in previous works and give a partly theoretical, partly empirical justification in a general framework. The proposed procedure performs an eigenvalue computation, and requires the knowledge of the behavior of the exact operator in order to choose proper norms for the evaluations. In the experiments we focus our attention on the 1-D advection–diffusion problem: we show that our numerical procedure actually gives very sharp indications about the optimality of the tested numerical methods.

scholarly journals On a Crucial Role of Gravity in the Formation of Elementary Particles

Universe ◽  
2020 ◽  
Vol 6 (11) ◽  
pp. 193
Author(s):  
Ahmed Alharthy ◽  
Vladimir V. Kassandrov
Keyword(s):  
Elementary Particle ◽  
Energy Requirement ◽  
Numerical Procedure ◽  
Coupled System ◽  
Scalar Fields ◽  
Boson Stars ◽  
Electromagnetic Interactions ◽  
Klein Gordon ◽  
First Time

We consider the model of minimally interacting electromagnetic, gravitational and massive scalar fields free of any additional nonlinearities. In the dimensionless form, the Lagranginan contains only one parameter γ=(mG/e)2 which corresponds to the ratio of gravitational and electromagnetic interactions and, for a typical elementary particle, is about 10−40 in value. However, regular (soliton-like) solutions can exist only for γ≠0, so that gravity would be necessary to form the structure of an (extended) elementary particle. Unfortunately (in the stationary spherically symmetrical case), the numerical procedure breaks in the range γ≤0.9 so that whether the particle-like solutions actually exist in the model remains unclear. Nonetheless, for γ∼1 we obtain, making use of the minimal energy requirement, a discrete set of (horizon-free) electrically charged regular solutions of the Planck’s range mass and dimensions (“maximons”, “planckeons”, etc.). In the limit γ→∞, the model reduces to the well-known coupled system of the Einstein and Klein–Gordon equations. We obtain—to our knowledge—for the first time, the discrete spectrum of neutral soliton-like solutions (“mini-boson stars”, “soliton stars”, etc.)

scholarly journals Examination of the Effect of a Sound Source Location on the Steady-State Response of a Two-Room Coupled System

2011 ◽  
Vol 36 (4) ◽  
pp. 761-775 ◽  
Author(s):  
Mirosław Meissner
Keyword(s):  
Steady State ◽  
Sound Source ◽  
Computer Modelling ◽  
Numerical Procedure ◽  
Coupled System ◽  
Expansion Method ◽  
Source Location ◽  
Steady State Response ◽  
Modal Expansion ◽  
State Response

AbstractIn this paper, the computer modelling application based on the modal expansion method is developed to study the influence of a sound source location on a steady-state response of coupled rooms. In the research, an eigenvalue problem is solved numerically for a room system consisting of two rectangular spaces connected to one another. A numerical procedure enables the computation of shape and frequency of eigenmodes, and allows one to predict the potential and kinetic energy densities in a steady-state. In the first stage, a frequency room response for several source positions is investigated, demonstrating large deformations of this response for strong and weak modal excitations. Next, a particular attention is given to studying how the changes in a source position influence the room response when a source frequency is tuned to a resonant frequency of a strongly localized mode.

scholarly journals Impact of train-induced vibration on railway cable-stayed bridges fatigue evaluation

2016 ◽  
Vol 11 (2) ◽  
pp. 102-110 ◽  
Author(s):  
Shiling Pei ◽  
Yongle Li ◽  
Yulong Bao ◽  
Xin Li ◽  
Shizhong Qiang
Keyword(s):  
Fatigue Damage ◽  
Welded Joints ◽  
Moving Load ◽  
Numerical Procedure ◽  
Coupled System ◽  
Accurate Estimation ◽  
Truss Bridges ◽  
Cumulative Fatigue Damage ◽  
Fatigue Evaluation ◽  
Critical Locations

Under repetitive heavy train traffic, railway steel truss bridges tend to have many fatigue related performance issues, especially at welded joints. Accurate estimation of the stress history at critical locations of welded joints under vehicle loading is important for joint fatigue design. Traditionally, vehicle loads were treated as moving static loads without considering their dynamic effects. In this study, a numerical procedure was introduced to incorporate the effect of dynamic response of the train–bridge coupled system on nodal fatigue damage. The proposed approach employs a twolevel modelling scheme which combines dynamic analysis for the full train-bridge system and detailed stress analysis at the joint. Miner rule was used to determine the cumulative fatigue damage at critical locations on the welded joint. A sensitivity analysis was conducted for different train loading configurations. It was determined that dynamic vibration negatively influences fatigue life. The calculated cumulative damage at investigated locations can more than the damage estimated using only static moving load method.

scholarly journals Efficient Series Expansions of the Temperature Field in Dry Surface Grinding for Usual Heat Flux Profiles

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Juan Luis González-Santander
Keyword(s):  
Heat Flux ◽  
Temperature Field ◽  
Numerical Evaluation ◽  
Numerical Procedure ◽  
Constant Heat Flux ◽  
Surface Grinding ◽  
Maximum Temperature ◽  
Series Expansions ◽  
Constant Heat ◽  
Flux Profile

In the framework of Jaeger’s model for heat transfer in dry surface grinding, series expansions for calculating the temperature field, assuming constant, linear, triangular, and parabolic heat flux profiles entering into the workpiece, are derived. The numerical evaluation of these series is considerably faster than the numerical integration of Jaeger’s formula and as accurate as the latter. Also, considering a constant heat flux profile, a numerical procedure is proposed for the computation of the maximum temperature as a function of the Peclet number and the depth below the surface. This numerical procedure has been used to evaluate the accuracy of Takazawa’s approximation.

Ad- and Desorption of Oxygen at Metal-Oxide Interfaces: Numerical Approach for Non-Homogeneous Oxide Distribution

2006 ◽  
Vol 249 ◽  
pp. 35-40 ◽  
Author(s):  
Andreas Öchsner ◽  
Michael Stasiek ◽  
José Grácio
Keyword(s):  
Finite Difference ◽  
Atomic Oxygen ◽  
Numerical Procedure ◽  
Coupled System ◽  
Numerical Approach ◽  
Time Dependent ◽  
Two Dimensional ◽  
General Boundary Conditions ◽  
Oxide Interfaces ◽  
One Dimensional

A numerical approach for the segregation of atomic oxygen at Ag/MgO interfaces is presented. A general segregation kinetics is considered and the coupled system of partial differential equations is solved due to a one-dimensional finite difference scheme. Based on a model oxide distribution, the influence of the oxide distribution is numerically investigated and compared with the solution for equidistant arrangements. The numerical approach allows for the consideration of general boundary conditions, specimen sizes and time-dependent material and process parameters. Furthermore, a numerical procedure to convert two-dimensional microstructures into representative one-dimensional distributions is described.

On the Green's functions for a layered half-space. Part II

1983 ◽  
Vol 73 (4) ◽  
pp. 931-951
Author(s):  
Randy J. Apsel ◽  
J. Enrique Luco
Keyword(s):  
Integral Representation ◽  
Half Space ◽  
Numerical Evaluation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Numerical Procedure ◽  
Number Of Solutions ◽  
Viscoelastic Media ◽  
Layered Half Space

abstract A numerical procedure to obtain the dynamic Green's functions for layered viscoelastic media is presented. The procedure is based on numerical evaluation of certain Hankel-type integrals which appear in an integral representation derived previously by the authors. Comparisons illustrating the accuracy and flexibility of the approach are made with a number of solutions obtained by other methods.

scholarly journals On the Numerical Evaluation of Stop-Loss Premiums

1979 ◽  
Vol 10 (3) ◽  
pp. 318-324 ◽  
Author(s):  
F. Covens ◽  
M. Van Wouwe ◽  
M. Goovaerts
Keyword(s):  
Poisson Process ◽  
Numerical Evaluation ◽  
Fourier Transforms ◽  
Numerical Procedure ◽  
Compound Poisson Process ◽  
Risk Process ◽  
Compound Poisson ◽  
Stop Loss

A numerical procedure is described to evaluate the stop-loss premium in case the risk process is a compound Poisson process. The method is mainly based on an algorithm of R. Piessens and M. Branders for the numerical evaluation of Fourier transforms.

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