scholarly journals Shapes of a filament on the surface of a bubble

2021 ◽  
Vol 477 (2253) ◽  
pp. 20210353
Author(s):  
S. Ganga Prasath ◽  
Joel Marthelot ◽  
Rama Govindarajan ◽  
Narayanan Menon
Keyword(s):  
Phase Space ◽  
Simple Model ◽  
Theoretical Analysis ◽  
Geometric Parameter ◽  
Elastic Energy ◽  
Energy Minimization ◽  
Bubble Radius ◽  
Quantitative Agreement ◽  
Gravitational Energy ◽  
Spherical Bubble

The shape assumed by a slender elastic structure is a function both of the geometry of the space in which it exists and the forces it experiences. We explore, by experiments and theoretical analysis, the morphological phase space of a filament confined to the surface of a spherical bubble. The morphology is controlled by varying bending stiffness and weight of the filament, and its length relative to the bubble radius. When the dominant considerations are the geometry of confinement and elastic energy, the filament lies along a geodesic and when gravitational energy becomes significant, a bifurcation occurs, with a part of the filament occupying a longitude and the rest along a curve approximated by a latitude. Far beyond the transition, when the filament is much longer than the diameter, it coils around the selected latitudinal region. A simple model with filament shape as a composite of two arcs captures the transition well. For better quantitative agreement with the subcritical nature of bifurcation, we study the morphology by numerical energy minimization. Our analysis of the filament’s morphological space spanned by one geometric parameter, and one parameter that compares elastic energy with body forces, may provide guidance for packing slender structures on complex surfaces.

scholarly journals Interference Phenomena in Deformed Single Crystals of Ice

1971 ◽  
Vol 10 (59) ◽  
pp. 269-286 ◽  
Author(s):  
G. J. Readings ◽  
J. T. Bartlett
Keyword(s):  
Optical Properties ◽  
Simple Model ◽  
Single Crystals ◽  
Uniaxial Compression ◽  
Basal Plane ◽  
Quantitative Agreement ◽  
Optic Axis ◽  
Interference Fringes ◽  
Alternative Hypotheses ◽  
Active Contribution

AbstractWhen rectangular single crystals of ice were subjected to uniaxial compression parallel to their Long axes and viewed between crossed polarizers, interference fringes were often observed. Some of these interference bands were associated with grain boundaries formed as a result of “kinking”. These can be explained in terms of the known anisotropic optical properties of ice and the change in the orientation of the optic axis across the boundary. This case has been analysed in detail with the aid of Jones’ calculus and good quantitative agreement exists between the theory and the experimental observations.Other interference bands were observed parallel to the trace of the basal plane on the surface of some deformed crystals. Alternative hypotheses for the explanation of this phenomenon have been considered and it seems probable that these bands are a result of slight random misorientations between adjacent slip lamellae. Applying Jones’ calculus to a simple model of such a deformed crystal indicates that the required misorientations are of the order of 1º If this explanation is correct, it implies that dislocations with non-basal Burgers vectors (probablyc[0001]) make an active contribution to the deformation.

scholarly journals Vacuum Energy Decay from a q-Bubble

Physics ◽  
2019 ◽  
Vol 1 (3) ◽  
pp. 321-338 ◽  
Author(s):  
Frans R. Klinkhamer ◽  
Osvaldo P. Santillán ◽  
Grigory E. Volovik ◽  
Albert Zhou
Keyword(s):  
Cosmological Constant ◽  
Time Evolution ◽  
Gravitational Collapse ◽  
Vacuum Energy ◽  
Finite Size ◽  
Energy Scale ◽  
Gravitational Energy ◽  
Numerical Results ◽  
Field Energy ◽  
Spherical Bubble

We consider a finite-size spherical bubble with a nonequilibrium value of the q-field, where the bubble is immersed in an infinite vacuum with the constant equilibrium value q 0 for the q-field (this q 0 has already cancelled an initial cosmological constant). Numerical results are presented for the time evolution of such a q-bubble with gravity turned off and with gravity turned on. For small enough bubbles and a q-field energy scale sufficiently below the gravitational energy scale E Planck , the vacuum energy of the q-bubble is found to disperse completely. For large enough bubbles and a finite value of E Planck , the vacuum energy of the q-bubble disperses only partially and there occurs gravitational collapse near the bubble center.

The dynamics of language

1999 ◽  
Vol 22 (2) ◽  
pp. 284-285
Author(s):  
Peter W. Culicover ◽  
Andrzej Nowak
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Simple Model ◽  
Syntactic Structure ◽  
Neural Assemblies ◽  
Systems Perspective ◽  
Model Based ◽  
Associative Structures

To deal with syntactic structure, one needs to go beyond a simple model based on associative structures, and to adopt a dynamical systems perspective, where each phrase and sentence of a language is represented as a trajectory in a syntactic phase space. Neural assemblies could possibly be used to produce dynamics that in principle could handle syntax along these lines.

Experimental and Theoretical Analysis of the Hall-Mobility in N-Type Bulk 6H- and 4H-SiC

1999 ◽  
Vol 572 ◽  
Author(s):  
S. T. G. Müller ◽  
D. Hofmann ◽  
A. Winnacker
Keyword(s):  
Theoretical Analysis ◽  
Hall Mobility ◽  
Phonon Scattering ◽  
Electron System ◽  
Quantitative Agreement ◽  
Coupling Constants ◽  
Effective Density ◽  
Iteration Algorithm ◽  
Bulk Crystals ◽  
Mobility Data

ABSTRACTThe electrical properties of nitrogen doped n-type 6H- and 4H-SiC bulk crystals grown by the Lely- or modified Lely-method have been characterized by Hall-measurements. The doping densities were determined by a fit of the neutrality equation to the experimental data, accounting for in-equivalent lattice sites and the temperature dependence of the effective density-of- states-mass extracted from recent results of ab-initio-calculations of the 6H- and 4H-SiC bandstructure [1]. The theoretical analysis of the Hall-mobility is based on an extended form of the Rode-Nag iteration algorithm [2]. The calculation scheme considers all relevant elastic and inelastic scattering mechanisms. the anisotropy of the crystal modifications and the possible effect of spatial inhomogeneities in the distribution of donors, acceptors or in the related electron system. Within these concepts it is possible to achieve a quantitative agreement between theoretical and experimental mobility data in 4H- and 6H-SiC over the whole temperature range of band conduction. New values for the acoustic deformation potentials Eac [15.0±0.5 eV (6H), 14.8±0.5 eV (4H)] and the coupling constants for intervalley phonon scattering Dint [2.3 ± 0.1 × 109eV/cm (6H), 2.6 ± 0.1 × 109eV/cm (4H)] are given.

Suppression of Cation Segregation in (La,Sr)CoO3−δ by Elastic Energy Minimization

2018 ◽  
Vol 10 (9) ◽  
pp. 8057-8065 ◽  
Author(s):  
Ja Yang Koo ◽  
Hyunguk Kwon ◽  
Minwoo Ahn ◽  
Mingi Choi ◽  
Ji-Won Son ◽  
...  
Keyword(s):  
Elastic Energy ◽  
Energy Minimization

LATTICE DYNAMICS OF THE BINARY APERIODIC CHAINS OF ATOMS III: PROPERTIES OF VIBRATIONAL EIGENVECTORS

1995 ◽  
Vol 09 (12) ◽  
pp. 1475-1501 ◽  
Author(s):  
WŁODZIMIERZ SALEJDA
Keyword(s):  
Elastic Energy ◽  
Lattice Dynamics ◽  
Quantitative Agreement ◽  
Model Parameters ◽  
Harmonic Model ◽  
Energy Field ◽  
Qualitative And Quantitative ◽  
Phonon Spectra ◽  
Multifractal Spectra ◽  
Optical Region

We numerically study the localization and multifractal properties of normalized vibrational eigenvectors (NVEV), denoted by U, of the microscopic harmonic model of lattice dynamics in Thue-Morse (TM), generalized Fibonacci, octagonal, dodecagonal, Severin, circle and Rudin-Shapiro (RS) binary chain of atoms. Eigenvalues and NVEV are determined with the help of the Dean and Wu-Zheng algorithm, respectively, with free end boundary conditions for chains containing 103<N<104 atoms. The first FM(L) and second SM(L) moment, and the reduced participation ratios Λ red (L) are derived at 1≤L≤N for varying model parameters. All the chains studied show sinusoidal-like and packet-like extended NVEV with Λred(L)≃1, FM(L)≃N/2 and [Formula: see text] The new extended eigenstates called dimmerized NVEV have been found out in the case of the TM chain. The surface localized NVEV with Λred(L)≪1, FM(L)≃1 or FM(L)≃N and the strong tendency to localization of NVEV in RS chain have been observed. The critical NVEV, which dominate in the optical region of phonon spectra, are objects with a broad multifractal (αmin, αmax) spectra. If magnitudes of model parameters are increased then, first, [Formula: see text] and [Formula: see text] at L≪N and, second, [Formula: see text] and [Formula: see text] at L≃N. It is numerically shown that the multifractal spectra α′—f′ characterizing the curdling of the elastic energy field ε(L) are in excellent qualitative and quantitative agreement with the multifractal spectra of the critical NVEV.

Method of elastic energy minimization for evaluation of transition parameters in oxidation kinetics of Zr alloys

2012 ◽  
Vol 61 ◽  
pp. 143-147 ◽  
Author(s):  
V.V. Likhanskii ◽  
T.N. Aliev ◽  
Mikhail Y. Kolesnik ◽  
I.A. Evdokimov ◽  
V.G. Zborovskii
Keyword(s):  
Elastic Energy ◽  
Oxidation Kinetics ◽  
Energy Minimization ◽  
Kinetics Of ◽  
Zr Alloys

Simple Approximate Solutions for Dynamic Response of Suspension System

2022 ◽  
Vol 21 ◽  
pp. 20-31
Author(s):  
Jacob Nagler
Keyword(s):  
Analytic Solution ◽  
Approximate Solutions ◽  
Quantitative Agreement ◽  
Gravitational Energy ◽  
Suspension System ◽  
Approximate Analytic Solution ◽  
Stiffness Properties ◽  
Coupling Case ◽  
The One ◽  
The Impact

An approximate simplified analytic solution is proposed for the one DOF (degree of freedom) static and dynamic displacements alongside the stiffness (dynamic and static) and damping coefficients (minimum and maximum/critical values) of a parallel spring-damper suspension system connected to a solid mass-body gaining its energy by falling from height h. The analytic solution for the prescribed system is based on energy conservation equilibrium, considering the impact by a special G parameter. The formulation is based on the works performed by Timoshenko (1928), Mindlin (1945), and the U. S. army-engineering handbook (1975, 1982). A comparison between the prescribed studies formulations and current development has led to qualitative agreement. Moreover, quantitative agreement was found between the current prescribed suspension properties approximate value - results and the traditionally time dependent (transient, frequency) parameter properties. Also, coupling models that concerns the linkage between different work and energy terms, e.g., the damping energy, friction work, spring potential energy and gravitational energy model was performed. Moreover, approximate analytic solution was proposed for both cases (friction and coupling case), whereas the uncoupling and the coupling cases were found to agree qualitatively with the literature studies. Both coupling and uncoupling solutions were found to complete each other, explaining different literature attitudes and assumptions. In addition, some design points were clarified about the wire mounting isolators stiffness properties dependent on their physical behavior (compression, shear tension), based on Cavoflex catalog. Finally, the current study aims to continue and contribute the suspension, package cushioning and containers studies by using an initial simple pre – design analytic evaluation of falling mass- body (like cushion, containers, etc.).

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