Longitudinal Impact of Semi-Infinite Elastic Bars: Plane Any Time Solution

2013 ◽  
Vol 81 (5) ◽  
Author(s):  
M. A. Malkov
Keyword(s):  
Analytical Solution ◽  
Exact Analytical Solution ◽  
The Other ◽  
Longitudinal Impact ◽  
Infinite Plane ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
Contact Surfaces ◽  
The One ◽  
The Impact

Using the Sobolev–Smirnov method, we have found the exact analytical solution of a longitudinal impact of semi-infinite plane elastic bars for any time after the impact. After collision, there are loading waves from contact surfaces of bars and unloading waves from lateral surfaces. Then the unloading waves reach the opposite surface of the bars and create the reflected loading waves. These loading waves reach the other surface of the bars and generate new unloading waves. The number of waves grows exponentially. The sum of waves tends to the wave of the one-dimensional approximation.

LOCALIZED BREATHER-LIKE EXCITATIONS IN THE HELICOIDAL PEYRARD–BISHOP MODEL OF DNA

2009 ◽  
Vol 02 (04) ◽  
pp. 405-417 ◽  
Author(s):  
CONRAD BERTRAND TABI ◽  
ALIDOU MOHAMADOU ◽  
TIMOLEON CREPIN KOFANE
Keyword(s):  
Analytical Solution ◽  
Continuous Wave ◽  
Exact Analytical Solution ◽  
Modulational Instability ◽  
Elliptic Functions ◽  
Instability Criterion ◽  
Dna Dynamics ◽  
Jacobian Elliptic Functions ◽  
One Dimensional ◽  
The One

We consider the one-dimensional helicoidal Peyrard–Bishop (PB) model of DNA dynamics. By means of a method based on the Jacobian elliptic functions, we obtain the exact analytical solution which describes the modulational instability and the propagation of a bright solitary wave on a continuous wave background. It is shown that these solutions depend on the modulational (or Benjamin-Feir) instability criterion. Numerical simulations of their propagation show these excitations to be long-lived and suggest that they are physically relevant for DNA.

Thermochemical Response of Honeycomb Sandwich Panels

1983 ◽  
Vol 1 (5) ◽  
pp. 379-395
Author(s):  
Kumar Ramohalli
Keyword(s):  
Thermal Conductivity ◽  
Analytical Solution ◽  
Thermal Conductivity Coefficient ◽  
Sandwich Panels ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
Honeycomb Sandwich ◽  
The One

A simple study aimed at predicting the Thermochemical Response of honey comb sandwich panels is presented. The overall thermal conductivity coefficient for the panel is obtained through a consideration of the convective gas move ment within the cell spaces. The earlier correlations of Catton and Edwards are used. The analytical solution for the one-dimensional approximation is quoted from an earlier study.

The transport equation with plane symmetry and isotropic scattering

1964 ◽  
Vol 60 (4) ◽  
pp. 909-921 ◽  
Author(s):  
M. G. Smith
Keyword(s):  
Integral Equation ◽  
Analytical Solution ◽  
Point Sources ◽  
The Other ◽  
Isotropic Scattering ◽  
Dimensional Problem ◽  
Plane Symmetry ◽  
Double Integral ◽  
One Dimensional ◽  
The One

AbstractThe double integral equation, which takes the place of the Milne equation in the one-dimensional problem, is derived from the governing partial differentio-integral equations. An analytical solution of the problem of a distribution of point sources on a plane, when the other boundaries are at infinity, is then found. The possibility of more complicated boundary conditions is discussed.

scholarly journals The Generalized OTOC from Supersymmetric Quantum Mechanics—Study of Random Fluctuations from Eigenstate Representation of Correlation Functions

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 44
Author(s):  
Kaushik Y. Bhagat ◽  
Baibhab Bose ◽  
Sayantan Choudhury ◽  
Satyaki Chowdhury ◽  
Rathindra N. Das ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Quantum Statistical Mechanics ◽  
Supersymmetric Quantum Mechanics ◽  
The Other ◽  
Potential Well ◽  
One Dimensional ◽  
Quantum Randomness ◽  
The One ◽  
The Impact

The concept of the out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness, using which one can study both chaotic and non-chaotic phenomena in the context of quantum statistical mechanics. In this paper, we define a general class of OTOC, which can perfectly capture quantum randomness phenomena in a better way. Further, we demonstrate an equivalent formalism of computation using a general time-independent Hamiltonian having well-defined eigenstate representation for integrable Supersymmetric quantum systems. We found that one needs to consider two new correlators apart from the usual one to have a complete quantum description. To visualize the impact of the given formalism, we consider the two well-known models, viz. Harmonic Oscillator and one-dimensional potential well within the framework of Supersymmetry. For the Harmonic Oscillator case, we obtain similar periodic time dependence but dissimilar parameter dependences compared to the results obtained from both micro-canonical and canonical ensembles in quantum mechanics without Supersymmetry. On the other hand, for the One-Dimensional Potential Well problem, we found significantly different time scales and the other parameter dependence compared to the results obtained from non-Supersymmetric quantum mechanics. Finally, to establish the consistency of the prescribed formalism in the classical limit, we demonstrate the phase space averaged version of the classical version of OTOCs from a model-independent Hamiltonian, along with the previously mentioned well-cited models.

scholarly journals Initial magnetic field distribution around high rectangular bus bars

2014 ◽  
Vol 11 (4) ◽  
pp. 523-534
Author(s):  
Grigore Cividjian
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Magnetic Fields ◽  
Analytical Solution ◽  
Exact Analytical Solution ◽  
One Dimensional ◽  
Transient Electromagnetic ◽  
The One ◽  
Two Sides ◽  
Initial Magnetic Field

The one-dimensional transient electromagnetic field in and around a system of two nonmagnetic homogenous rectangular high thin bars can be analytically evaluated if the ratio of average initial magnetic field on the two sides of thin bar, or of the ratio of initial magnetic fields in middle of the bar height is known. In this paper, using appropriate conformal mappings, an exact analytical solution for these ratios are proposed in the case of very thin bars. Obtained values are compared with FEM results for relatively thick bars.

Longitudinal Impact of Semi-Infinite Elastic Bars: Plane Short Time Solution

2012 ◽  
Vol 80 (1) ◽  
Author(s):  
M. A. Malkov
Keyword(s):  
Rayleigh Waves ◽  
Seismic Waves ◽  
Exact Analytical Solution ◽  
Approximate Solutions ◽  
Singular Points ◽  
Longitudinal Impact ◽  
Infinite Plane ◽  
Transverse Waves ◽  
Short Time ◽  
The Impact

Using the Sobolev-Smirnov method we find the exact analytical solution of the longitudinal impact of semi-infinite plane elastic bars. The solution allows us to investigate wave propagations shortly after the impact. The obtained results allow us to compare the exact and approximate solutions of impact problems. We show that approximate solutions are wrong in a short time. According to the exact solution five waves are created in the first time after impact: one longitudinal loading wave and two unloading longitudinal waves from the lateral surfaces of the bars and two unloading transverse waves, also from the surfaces. We find singular points of the solution. It can be used for other applications such as any impact of two elastic bodies since the same waves arise and the same singular points exist at the impact. One of the singular points moves along surfaces with the speed of Rayleigh waves. At this point the bar surface is perpendicular to the axis of the bars. Such a point arises at any impact. As the earth surface is also perpendicular to the direction of propagation of seismic waves, Rayleigh waves are especially destructive at earthquakes.

Laughter on the Fringes

2019 ◽  
Author(s):  
Anna Peterson
Keyword(s):  
The Other ◽  
Literary Canon ◽  
Autobiographical Writing ◽  
Treasure Trove ◽  
Old Comedy ◽  
Other Hand ◽  
Aggressive Humor ◽  
The One ◽  
The Individual ◽  
The Impact

This book examines the impact that Athenian Old Comedy had on Greek writers of the Imperial era. It is generally acknowledged that Imperial-era Greeks responded to Athenian Old Comedy in one of two ways: either as a treasure trove of Atticisms, or as a genre defined by and repudiated for its aggressive humor. Worthy of further consideration, however, is how both approaches, and particularly the latter one that relegated Old Comedy to the fringes of the literary canon, led authors to engage with the ironic and self-reflexive humor of Aristophanes, Eupolis, and Cratinus. Authors ranging from serious moralizers (Plutarch and Aelius Aristides) to comic writers in their own right (Lucian, Alciphron), to other figures not often associated with Old Comedy (Libanius) adopted aspects of the genre to negotiate power struggles, facilitate literary and sophistic rivalries, and provide a model for autobiographical writing. To varying degrees, these writers wove recognizable features of the genre (e.g., the parabasis, its agonistic language, the stage biographies of the individual poets) into their writings. The image of Old Comedy that emerges from this time is that of a genre in transition. It was, on the one hand, with the exception of Aristophanes’s extant plays, on the verge of being almost completely lost; on the other hand, its reputation and several of its most characteristic elements were being renegotiated and reinvented.

scholarly journals Analytical solution of one-dimensional Pennes’ bioheat equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1084-1092
Author(s):  
Hongyun Wang ◽  
Wesley A. Burgei ◽  
Hong Zhou
Keyword(s):  
Analytical Solution ◽  
Radiofrequency Energy ◽  
Bioheat Equation ◽  
Surface Cooling ◽  
One Dimensional ◽  
The Fourier Transform ◽  
The One ◽  
Parameter Values ◽  
Mathematical Derivation ◽  
Effect Of Surface

Abstract Pennes’ bioheat equation is the most widely used thermal model for studying heat transfer in biological systems exposed to radiofrequency energy. In their article, “Effect of Surface Cooling and Blood Flow on the Microwave Heating of Tissue,” Foster et al. published an analytical solution to the one-dimensional (1-D) problem, obtained using the Fourier transform. However, their article did not offer any details of the derivation. In this work, we revisit the 1-D problem and provide a comprehensive mathematical derivation of an analytical solution. Our result corrects an error in Foster’s solution which might be a typo in their article. Unlike Foster et al., we integrate the partial differential equation directly. The expression of solution has several apparent singularities for certain parameter values where the physical problem is not expected to be singular. We show that all these singularities are removable, and we derive alternative non-singular formulas. Finally, we extend our analysis to write out an analytical solution of the 1-D bioheat equation for the case of multiple electromagnetic heating pulses.

scholarly journals Assessing a Linear Nanosystem's Limiting Reliability from its Components

2008 ◽  
Vol 45 (03) ◽  
pp. 879-887 ◽  
Author(s):  
Nader Ebrahimi
Keyword(s):  
Present State ◽  
Size Range ◽  
Two Dimensions ◽  
The Other ◽  
One Dimension ◽  
Present Moment ◽  
One Dimensional ◽  
The One ◽  
Fixed Moment ◽  
Nanosized Systems

Nanosystems are devices that are in the size range of a billionth of a meter (1 x 10-9) and therefore are built necessarily from individual atoms. The one-dimensional nanosystems or linear nanosystems cover all the nanosized systems which possess one dimension that exceeds the other two dimensions, i.e. extension over one dimension is predominant over the other two dimensions. Here only two of the dimensions have to be on the nanoscale (less than 100 nanometers). In this paper we consider the structural relationship between a linear nanosystem and its atoms acting as components of the nanosystem. Using such information, we then assess the nanosystem's limiting reliability which is, of course, probabilistic in nature. We consider the linear nanosystem at a fixed moment of time, say the present moment, and we assume that the present state of the linear nanosystem depends only on the present states of its atoms.

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