The Symplectic System for the Analytical Solutions of Skew Plate

2012 ◽  
Vol 619 ◽  
pp. 306-309
Author(s):  
Y.C. Wang ◽  
Y.Z. Yang
Keyword(s):  
Hamiltonian Systems ◽  
Analytical Solutions ◽  
Analytic Solutions ◽  
Speed Of Convergence ◽  
Skew Plate ◽  
Stress Components ◽  
Simple Support ◽  
Dual Variables ◽  
As Stress ◽  
Symplectic System

The Hamiltonian Systems is applied for the bending of skew plate.In contrast to the traditional technique using only one kind of variables, the symplectic dual variables include displacement components as well as stress components. The analytic solutions are obtained under simple support which shows the effectiveness of the symplectic dual and indicates that this method is good in speed of convergence and reliability.

scholarly journals On the feasibility of saltational evolution

2018 ◽  
Author(s):  
Mikhail I. Katsnelson ◽  
Yuri I. Wolf ◽  
Eugene V. Koonin
Keyword(s):  
Evolutionary Biology ◽  
Fitness Landscape ◽  
Evolutionary Process ◽  
Analytic Solutions ◽  
Population Bottlenecks ◽  
Effective Population ◽  
Evolutionary Transitions ◽  
Evolutionary Changes ◽  
Saltational Evolution ◽  
As Stress

One of the key tenets of Darwin’s theory that was inherited by the Modern Synthesis of evolutionary biology is gradualism, that is, the notion that evolution proceeds gradually, via accumulation of “infinitesimally small” heritable changes 1,2. However, some of the most consequential evolutionary changes, such as, for example, the emergence of major taxa, seem to occur abruptly rather than gradually, as captured in the concepts of punctuated equilibrium 3,4 and evolutionary transitions 5,6. We examine a mathematical model of an evolutionary process on a rugged fitness landscape 7,8 and obtain analytic solutions for the probability of multi-mutational leaps, that is, several mutations occurring simultaneously, within a single generation in one genome, and being fixed all together in the evolving population. The results indicate that, for typical, empirically observed combinations of the parameters of the evolutionary process, namely, effective population size, mutation rate, and distribution of selection coefficients of mutations, the probability of a multi-mutational leap is low, and accordingly, their contribution to the evolutionary process is minor at best. However, such leaps could become an important factor of evolution in situations of population bottlenecks and elevated mutation rates, such as stress-induced mutagenesis in microbes or tumor progression, as well as major evolutionary transitions and evolution of primordial replicators.

scholarly journals Symplectic Exact Solution for Stokes Flow in the Thin Film Coating Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Yan Wang ◽  
Zi-Chen Deng ◽  
Wei-Peng Hu
Keyword(s):  
Thin Film ◽  
Hamiltonian System ◽  
Analytical Solutions ◽  
Stokes Flow ◽  
Separation Of Variables ◽  
Hamiltonian Function ◽  
Film Coating ◽  
Thin Film Coating ◽  
Flow Problems ◽  
Dual Variables

The symplectic analytical method is introduced to solve the problem of the stokes flow in the thin film coating applications. Based on the variational principle, the Lagrangian function of the stokes flow is established. By using the Legendre transformation, the dual variables of velocities and the Hamiltonian function are derived. Considering velocities and stresses as the basic variables, the equations of stokes flow problems are transformed into Hamiltonian system. The method of separation of variables and expansion of eigenfunctions are developed to solve the governing equations in Hamiltonian system, and the analytical solutions of the stokes flow are obtained. Several numerical simulations are carried out to verify the analytical solutions in the present study and discuss the effects of the driven lids of the square cavity on the dynamic behavior of the flow structure.

Enriched Analytical Solutions for Additive Manufacturing Modeling and Simulation

2018 ◽  
Author(s):  
John C. Steuben ◽  
Andrew J. Birnbaum ◽  
Athanasios P. Iliopoulos ◽  
John G. Michopoulos
Keyword(s):  
Additive Manufacturing ◽  
Modeling And Simulation ◽  
Analytical Solutions ◽  
Analytic Solutions ◽  
Computational Effort ◽  
Infinite Domain ◽  
Underlying Assumption ◽  
Simulation Tools ◽  
Computational Performance ◽  
Am Processes

Additive Manufacturing (AM) is an increasingly widespread family of technologies for the fabrication of objects based on successive depositions of mass and energy. A strong need for modeling and simulation tools for AM exists, in order to predict thermal histories, residual stresses, microstructure, and various other aspects of the resulting components. In this paper we explore the use of analytic solutions to model the thermal aspects of AM, in an effort to achieve high computational performance and enable “in the loop” use for feedback control of AM processes. It is shown that the utility of existing analytical solutions is limited due to their underlying assumption of a homogeneous semi-infinite domain. These solutions must therefore be enriched from their exact form in order to capture the relevant thermal physics associated with AM processes. Such enrichments include the handling of strong nonlinear variations in material properties, finite non-convex solution domains, behavior of heat sources very near boundaries, and mass accretion coupled to the thermal problem. The enriched analytic solution method (EASM) is shown to produce results equivalent to those of numerical methods which require six orders of magnitude greater computational effort.

“War neurosis” and associated physical conditions: an exploratory statistical analysis

1992 ◽  
Vol 9 (1) ◽  
pp. 30-36 ◽  
Author(s):  
Ian P Burges Watson ◽  
George V Wilson ◽  
Helen Hornsby
Keyword(s):  
Vietnam Veterans ◽  
Military Service ◽  
Variance Component ◽  
Service Component ◽  
Independent Components ◽  
Physical Conditions ◽  
War Neurosis ◽  
Stress Components ◽  
Components Analysis ◽  
As Stress

AbstractRecords of the war service disability claims for Australian Vietnam veterans in Tasmania (n = 751) were analysed to establish patterns of interrelationships between categories of disability. The predicted relationship between psychiatric disability and stress related skin disabilities was strongly supported and relationships between psychiatric and other medical disabilities were found. An exploratory principal components analysis produced three independent components which accounted for 21.2 percent of total variance. Component 1 was interpreted as a general military service component and components 2 and 3 were labelled as stress components. The most likely interpretation of the two stress components was that they reflect differences in profiles of records for disability claims depending on the time when the disability presented. The relevance of the findings is discussed.

scholarly journals COSMOLOGICAL ANALYTIC SOLUTIONS WITH REDUCED RELATIVISTIC GAS

2012 ◽  
Vol 27 (33) ◽  
pp. 1250194 ◽  
Author(s):  
L. G. MEDEIROS
Keyword(s):  
Cosmological Constant ◽  
Analytical Solutions ◽  
Type A ◽  
Analytic Solutions ◽  
The Other ◽  
Hot Matter ◽  
Relativistic Gas ◽  
Cold Matter ◽  
Three Components

In this paper one examines analytical solutions for flat and non-flat universes composed by four components namely hot matter (ultra-relativistic), warm matter (WM) (relativistic), cold matter (CM) (non-relativistic) and cosmological constant. The WM is treated as a reduced relativistic gas (RRG) and the other three components are treated in the usual way. The solutions achieved contains one, two or three components of which one component is of WM type. A solution involving all the four components was not found.

Some Analytical Solutions of the Kamal Equation for Isothermal Curing With Applications to Composite Patch Repair

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
G. J. Tsamasphyros ◽  
Th. K. Papathanassiou ◽  
S. I. Markolefas
Keyword(s):  
Differential Equation ◽  
Analytical Solutions ◽  
Adhesive Bonding ◽  
Practical Importance ◽  
Engineering Application ◽  
Analytic Solutions ◽  
Patch Repair ◽  
Critical Duration ◽  
Composite Patch ◽  
Thermosetting Polymers

In this paper, we derive some analytical solutions of the Kamal cure rate differential equation. The Kamal model is a first order quasilinear ordinary differential equation, describing the progress of the curing reaction of several thermosetting polymers. All the examined cases refer to isothermal curing processes. The solutions obtained in this paper are all of implicit form. The derived solutions are applied to a repair technique based on the adhesive bonding of polymer matrix composite patches onto damaged or corroded areas. Critical duration times of realistic cure cycles corresponding to composite patch repair are estimated. The practical importance of the proposed analytic solutions is demonstrated through the presented engineering application.

scholarly journals Analytic solutions for Long's equation and its generalization

2017 ◽  
Vol 24 (4) ◽  
pp. 727-735
Author(s):  
Mayer Humi
Keyword(s):  
Steady State ◽  
Gravity Waves ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Analytic Solutions ◽  
Two Dimensional ◽  
Atmospheric Flow ◽  
Flow Over Topography ◽  
Isothermal Flows

Abstract. Two-dimensional, steady-state, stratified, isothermal atmospheric flow over topography is governed by Long's equation. Numerical solutions of this equation were derived and used by several authors. In particular, these solutions were applied extensively to analyze the experimental observations of gravity waves. In the first part of this paper we derive an extension of this equation to non-isothermal flows. Then we devise a transformation that simplifies this equation. We show that this simplified equation admits solitonic-type solutions in addition to regular gravity waves. These new analytical solutions provide new insights into the propagation and amplitude of gravity waves over topography.

Response of Quasi-Integrable and Resonant Hamiltonian Systems to Fractional Gaussian Noise

2021 ◽  
Vol 144 (1) ◽  
Author(s):  
Q. F. Lü ◽  
W. Q. Zhu ◽  
M. L. Deng
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Analytical Solutions ◽  
Gaussian Noise ◽  
Nonlinear Dynamical Systems ◽  
Original System ◽  
System Response ◽  
Fractional Gaussian Noise

Abstract The major difficulty in studying the response of multi-degrees-of-freedom (MDOF) nonlinear dynamical systems driven by fractional Gaussian noise (fGn) is that the system response is not Markov process diffusion and thus the diffusion process theory cannot be applied. Although the stochastic averaging method (SAM) for quasi Hamiltonian systems driven by fGn has been developed, the response of the averaged systems still needs to be predicted by using Monte Carlo simulation. Later, noticing that fGn has rather flat power spectral density (PSD) in certain frequency band, the SAM for MDOF quasi-integrable and nonresonant Hamiltonian system driven by wideband random process has been applied to investigate the response of quasi-integrable and nonresonant Hamiltonian systems driven by fGn. The analytical solution for the response of an example was obtained and well agrees with Monte Carlo simulation. In the present paper, the SAM for quasi-integrable and resonant Hamiltonian systems is applied to investigate the response of quasi-integrable and resonant Hamiltonian system driven by fGn. Due to the resonance, the theoretical procedure and calculation will be more complicated than the nonresonant case. For an example, some analytical solutions for stationary probability density function (PDF) and stationary statistics are obtained. The Monte Carlo simulation results of original system confirmed the effectiveness of the analytical solutions under certain condition.

Simple Chaotic Systems with Specific Analytical Solutions

2019 ◽  
Vol 29 (09) ◽  
pp. 1950116 ◽  
Author(s):  
Zahra Faghani ◽  
Fahimeh Nazarimehr ◽  
Sajad Jafari ◽  
Julien C. Sprott
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Periodic Orbits ◽  
Analytical Solutions ◽  
Strange Attractor ◽  
Chaotic Systems ◽  
Analytic Solutions ◽  
Unstable Periodic Orbits ◽  
Chaotic Orbit ◽  
Dynamical Properties

In this paper, a new structure of chaotic systems is proposed. There are many examples of differential equations with analytic solutions. Chaotic systems cannot be studied with the classical methods. However, in this paper we show that a system that has a simple analytical solution can also have a strange attractor. The main goal of this paper is to show examples of chaotic systems with a simple analytical solution that is unstable so that the chaotic orbit does not track it. We believe the structures presented here are new. Two categories of chaotic systems are described, and their dynamical properties are investigated. The proposed systems have analytic solutions that exist far from the equilibrium. Of course, all strange attractors are dense in unstable periodic orbits, but mostly the equations that describe these orbits are unknown and difficult to calculate. The analytical solutions provide examples where the orbits can be calculated despite their instability.

Toward Feedback Control for Additive Manufacturing Processes Via Enriched Analytical Solutions

2019 ◽  
Vol 19 (3) ◽  
Author(s):  
John C. Steuben ◽  
Andrew J. Birnbaum ◽  
Athanasios P. Iliopoulos ◽  
John G. Michopoulos
Keyword(s):  
Additive Manufacturing ◽  
Feedback Control ◽  
Analytical Solutions ◽  
Analytic Solutions ◽  
Computational Effort ◽  
Infinite Domain ◽  
Underlying Assumption ◽  
Computational Performance ◽  
Process Feedback ◽  
Am Processes

Additive manufacturing (AM) enables the fabrication of objects using successive additions of mass and energy. In this paper, we explore the use of analytic solutions to model the thermal aspects of AM, in an effort to achieve high computational performance and enable “in the loop” use for feedback control of AM processes. It is shown that the utility of existing analytical solutions is limited due to their underlying assumption of a homogeneous semi-infinite domain. These solutions must, therefore, be enriched from their exact form in order to capture the relevant thermal physics associated with AM processes. Such enrichments include the handling of strong nonlinear variations in material properties, finite nonconvex solution domains, behavior of heat sources very near boundaries, and mass accretion coupled to the thermal problem. The enriched analytic solution method (EASM) is shown to produce results equivalent to those of numerical methods, which require six orders of magnitude greater computational effort. It is also shown that the EASM's computational performance is sufficient to enable AM process feedback control.

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