Equilibrium Deformation Research Articles

THE INTERNAL EXCITATION OF THE GAS OF INDEPENDENT PARTICLES IN A TIME DEPENDENT POTENTIAL

The order-to-chaos transition in the dynamics of independent classical and quantum gas of particles was studied by means of the computer simulations within the nuclear model based on the time-dependent mean-field approach. The excitation of the classical gas for containers whose surfaces are rippled according to Legendre polynomials P2, P3 is followed for twenty periods of oscillations. For different vibration frequencies of small amplitude vibrations of such a container near the spherical equilibrium shape we obtained for the classical gas much smaller excitation energies than those predicted by the wall formula. With increasing equilibrium deformation they become significantly larger and for P3 vibrations they are close to the wall formula limit. Notable shell effects were found in the excitation energies of the quantum gas in the Woods-Saxon potential with the corresponding relatively sharp (diffuseness equals to 0.1 fm) moving surfaces for small-amplitude slow vibrations.

ROTATIONAL STATES IN HEAVIEST ISOTOPES

Masses and rotational energies of even-even Fm - Hs isotopes are obtained using the Yukawa-folded single-particle potential and the Lublin Strasbourg Drop . The Strutinsky shell-correction method and the BCS approximation were used to evaluate the shell and pairing corrections. The paring force strength is adjusted to the experimental rotational states of the considered nuclei. The ground-state masses and the lowest rotational states obtained by using the cranking moments of inertia at the equilibrium deformations agree well with the experimental data.

A phase-field model for compliance shape optimization in nonlinear elasticity

Shape optimization of mechanical devices is investigated in the context of large, geometrically strongly nonlinear deformations and nonlinear hyperelastic constitutive laws. A weighted sum of the structure compliance, its weight, and its surface area are minimized. The resulting nonlinear elastic optimization problem differs significantly from classical shape optimization in linearized elasticity. Indeed, there exist different definitions for the compliance: the change in potential energy of the surface load, the stored elastic deformation energy, and the dissipation associated with the deformation. Furthermore, elastically optimal deformations are no longer unique so that one has to choose the minimizing elastic deformation for which the cost functional should be minimized, and this complicates the mathematical analysis. Additionally, along with the non-uniqueness, buckling instabilities can appear, and the compliance functional may jump as the global equilibrium deformation switches between different bluckling modes. This is associated with a possible non-existence of optimal shapes in a worst-case scenario. In this paper the sharp-interface description of shapes is relaxed via an Allen-Cahn or Modica-Mortola type phase-field model, and soft material instead of void is considered outside the actual elastic object. An existence result for optimal shapes in the phase field as well as in the sharp-interface model is established, and the model behavior for decreasing phase-field interface width is investigated in terms of Γ-convergence. Computational results are based on a nested optimization with a trust-region method as the inner minimization for the equilibrium deformation and a quasi-Newton method as the outer minimization of the actual objective functional. Furthermore, a multi-scale relaxation approach with respect to the spatial resolution and the phase-field parameter is applied. Various computational studies underline the theoretical observations.

Viscoelastic properties of a silica-filled styrene-butadiene rubber under uniaxial tension

A model composite — a silica-filled styrene-butadiene rubber with a various filler volume content — was tested for creep and creep recovery at different tensile load levels to evaluate the effect of viscoelasticity on the deformational properties of filled rubbers. A constitutive equation describing the diagram of equilibrium deformation of the composite in quasi-static loading was obtained from an analysis of creep test results. The equation was common for the filled rubber at different filler content. The existence of such a curve has been confirmed by experimental unloading diagrams registered in cyclic loading-unloading tests. It is shown that the phenomenological equations obtained from an analysis of creep recovery test results can be used successfully for describing the hysteresis loops of second and subsequent cycles for cyclic tests with a constant maximum stretch ratio.

Cell deformation cytometry using diode-bar optical stretchers

The measurement of cell elastic parameters using optical forces has great potential as a reagent-free method for cell classification, identification of phenotype, and detection of disease; however, the low throughput associated with the sequential isolation and probing of individual cells has significantly limited its utility and application. We demonstrate a single-beam, high-throughput method where optical forces are applied anisotropically to stretch swollen erythrocytes in microfluidic flow. We also present numerical simulations of model spherical elastic cells subjected to optical forces and show that dual, opposing optical traps are not required and that even a single linear trap can induce cell stretching, greatly simplifying experimental implementation. Last, we demonstrate how the elastic modulus of the cell can be determined from experimental measurements of the equilibrium deformation. This new optical approach has the potential to be readily integrated with other cytometric technologies and, with the capability of measuring cell populations, enabling true mechanical-property-based cell cytometry.

Static deformation of a heavy spring due to gravity and centrifugal force

The static equilibrium deformation of a heavy spring due to its own weight is calculated for two cases: first for a spring hanging in a constant gravitational field, and then for a spring which is at rest in a rotating system where it is stretched by the centrifugal force. Two different models are considered: first a discrete model assuming a finite number of point masses connected by springs of negligible weight, and then the continuum limit of this model. In the second case, the differential equation for the deformation is obtained by demanding that the potential energy is minimized. In this way a simple application of the variational calculus is obtained.

ROTATIONAL BANDS IN HEAVY AND SUPERHEAVY NUCLEI WITHIN THE LUBLIN STRASBOURG DROP + YUKAWA FOLDED MODEL

The potential energies of heavy and superheavy even even nuclei were found within the macroscopic–microscopic method with LSD model, Yukawa–folded mean field, Strutinsky shell correction and BCS pairing theory in order to calculate the rotational state with cranking moments of inertia. The calculations were performed for a couple of nuclei: 250 No - 264 Hs on a deformation grid c = 0.8 up to 1.6 with step length 0.05 and h = -0.4 to 0.4 with step length 0.1. The equilibrium deformations were found and the masses compared to the experimental ones. Rotational energies of No isotopes for L/ħ = 2, 4, 6, 8, 10, 12 agree well with the data when a pairing strengths [Formula: see text] and a pairing window of [Formula: see text] levels is used. A prediction of the E2+ rotational states for all the investigated nuclei is given.

Cell Elastic Modulus Cytometry using Diode-Bar Optical Stretchers

The mechanical deformation of biological cells using optical forces is an efficient experimental method to study cellular mechanical properties that may identify cell types and detect disease states. However, the low throughput has significantly limited its utility and application due to the need to sequentially isolate and probe individual cells. We have implemented a pseudo steady-state high-throughput optical stretcher in which anisotropic forces from an inexpensive laser diode stretch osmotically swollen bovine erythrocytes in a continuous microfluidic flow at a rate of ∼ 1 cell/second. This measurement rate is a factor of 10-100 higher than previous demonstrations of optical stretching. We also simulate the deformation of elastic capsules induced by single diode-bar optical stretcher with and without flow. Finally, we demonstrate how theory can be applied to determine the elastic modulus of individual cells from experimental measurements of the equilibrium deformation. Analysis of the deformed cells results in a shear modulus in the range of reported values from 2.5x10−3 dyne/cm to 1.3x10−2 dyne/cm for swollen human erythrocytes. This new optical approach has the potential to be readily integrated with other cytometric technologies, and with the capability of measuring cell populations, thus enabling true mechanical-property based cytometry.

Level density parameter dependence of the fission cross sections of some subactinide nuclei induced by protons with the incident energy up to 250 MeV

This study aims to show the dependence on the choice of the ratio of the level density parameters a f and a n corresponding to the saddle point of fission and equilibrium deformation of nucleus, respectively, of the proton induced fission cross sections of some subactinide targets. The method was employed using different level density parameter ratios for each fission cross section calculation in ALICE/ASH computer code. The ALICE/ASH code calculations were compared both with the available experimental data and with the Prokofiev systematics data. It is found that the fission cross sections dependent heavily on the choice of level density parameter ratio in the fission and neutron emission channels, a f / a n , for some subactinide nuclei. To get a good description of the measured fission cross sections for subactinide nuclei, we used a ratio of the level density parameters in the fission and neutron emission channels, a f / a n , depending both on the target-nucleus and on the energy of the projectile, in agreement with results published in literature.

Circular closed DNA. Topology, energy, and stress at different equilibrium configurations and deformation conditions

The topology of ring closed DNA at different equilibrium configurations and deformation conditions has been investigated. The distribution of energy and bending and torsional stress has been studied. It is shown that the relationship between the torsional and flexural rigidity of DNA molecule qualitatively influences the deformation of ring DNA.

Inelastic axial-flexure–shear coupling in a mixed formulation beam finite element

In this paper a beam element that accounts for inelastic axial-flexure–shear coupling is presented. The mathematical model is derived from a three-field variational form. The finite element approximation for the beam uses shape functions for section forces that satisfy equilibrium and discontinuous section deformations along the beam. No approximation for the beam displacement field is necessary in the formulation. The coupling of the section forces is achieved through the numerical integration of an inelastic multi-axial material model over the cross-section. The proposed element is free from shear-locking. Examples confirm the accuracy and numerical robustness of the proposed element and showcase the interaction between axial force, shear, and bending moment.

Mechanical Response of an Alumina-filled Epoxy at Various Strain Rates

The compressive response of an alumina-filled epoxy composite material was characterized at various strain rates using a Kolsky bar and universal testing frame (MTS). In the Kolsky-bar experiments, dynamic stress equilibrium and constant strain-rate deformation in specimens were achieved using pulse-shaping techniques. The effects of specimen aspect ratio and interfacial friction on the dynamic response of the material were examined. Compressive stress-strain curves for the composite were obtained at strain rates ranging from 9.4 × 10-4 to 1.35 × 103 s-1 which exhibited strong strain-rate sensitivity. A material response model, which agrees well with the experimental measurements for the strain rates examined in this study, is also described.

Mechanical Response of an Alumina-Filled Epoxy at Various Strain Rates

The compressive response of an alumina-filled epoxy composite material was characterized at various strain rates using a Kolsky bar and universal testing frame (MTS). In the Kolsky-bar experiments, dynamic stress equilibrium and constant strain-rate deformation in specimens were achieved using pulse-shaping techniques. The effects of specimen aspect ratio and interfacial friction on the dynamic response of the material were examined. Compressive stress-strain curves for the composite were obtained at strain rates ranging from 9.4 × 10-4 to 1.35 × 103 s-1 which exhibited strong strain-rate sensitivity. A material response model, which agrees well with the experimental measurements for the strain rates examined in this study, is also described.

Electric quadrupole moments of17/2−and13/2−subsequent isomers inPo209

The electric quadrupole interaction of $^{209}\mathrm{Po}$ high spin isomers in a Bi single crystal has been investigated by the time-differential perturbed angular distribution (TDPAD) technique. A two-level analysis procedure for the $17/{2}^{\ensuremath{-}}$and $13/{2}^{\ensuremath{-}}$ subsequent isomers was employed. The spectroscopic electric quadrupole moments were measured as $|Q(17/{2}^{\ensuremath{-}})|=65.9(7)e {\mathrm{fm}}^{2}$ and $|Q(13/{2}^{\ensuremath{-}})|=12.6(5)e {\mathrm{fm}}^{2}$. The experimental values of equilibrium deformations were extracted.

Doubly magic properties in superheavy nuclei

A systematic study of global properties of superheavy nuclei in the framework of the Liquid Drop Model and the Strutinsky shell correction method is performed. The evolution equilibrium deformations, TRS graphs and α-decay energies are calculated using the TRS model. The analysis covers a wide range of even-even superheavy nuclei from Z = 102 to 122. Magic numbers and their observable influence occurring in this region have been investigated. Shell closures appear at proton number Z = 114 and at neutron number N = 184.

1401 気泡変形による分散気泡流れの実効粘度変化(OS14-1 分散系混相流のダイナミクス,オーガナイズドセッション)

In order to obtain effective viscosity in bubbly liquid, which changes with transient bubble deformation, spatio-temporal velocity distributions of transient shear flows in a rotating cylinder is measured by using Ultrasonic Velocity Profiling (UVP) synchronizing of bubble deformation measurement. For Silicone oil of 1000 cSt as a test liquid, velocity distribution during spinning up has been found to be different from the liquid without bubbles. We have compared the circumferential acceleration of liquid with time serial images of bubble deformation to reach the conclusion that the maximal stretched bubbles the strongest drive the shear flow contrastively to the conventional equilibrium deformation theory of effective viscosity.

Conformation and deformation of linear macromolecules in concentrated solutions and melts in the self‐avoiding random walks statistics

AbstractA strict statistics of self‐avoiding random walks in the d‐measured lattice and continuous space for intertwining chains in the concentrated solutions and melts was proposed. On the basis of this statistics the thermodynamics of conformation and isothermal and adiabatic deformation of intertwining chains was described. The equation of conformational state has been obtained. It was shown that in the field of chains overlap they are stretched increasing its conformational volume. In this volume there are other chains with the formation of m‐ball. Free energy of a chain conformation does not depend upon the fact, if the chains intertwined or they are isolated in the m‐ball. Mixing entropy is responsible to the chains interweaving in the m‐ball. Dependencies of the conformational radius, free energy, and conformation pressure on respective concentration of polymeric chains have been determined. Using the thermodynamics of intertwining polymeric chains of m‐ball conformational state and also the laws of isotropic media deformation into linear differential form the theoretical expressions for elasticity modules (namely, volumetric volume, Young's module and shift's module) and for the main tensions appearing at the equilibrium deformation of the m‐ball were obtained. Poisson's coefficient is a function only on the Euclidean's space and for the real three‐dimensional space is equal to 3/8. A simple model explaining the tensile strength of the m‐ball by the chains intertwining effect and, thereafter by the loss of the mixing entropy, but not by the chemical bonds breaking was proposed. Calculations of the elastic properties, the main tensions, and tensile strength of natural rubber carried out without using the empirical adjusting parameters are in good agreement with the experimental data. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008

Deformation of a Sheet with Coupling between Elasticity and Concentration

We investigate a simple model for equilibrium deformation of a sheet with concentration-dependent elasticity. The model is motivated by several physical situations where deformation of a sheet is modulated by concentration of a mobile species, for example, a quasi-2D array of carbon nanotubes. Elasticity of the sheet is modeled using a free energy functional that includes concentration-dependent potential energies, and a free energy of mixing. We show that the sheet responds to imposed distortion by rearranging its constituents and can do so in a smooth and stable manner only for sufficiently small distortion. For larger distortions, through phase plane and numerical analysis, we consider how the system can meet boundary conditions through nonsmooth solutions.

High-spin states inAu191,193andPt192: Evidence for oblate deformation and triaxial shapes

High-spin states of $^{191,193}\mathrm{Au}$ and $^{192}\mathrm{Pt}$ have been populated in the $^{186}\mathrm{W}$($^{11}\mathrm{B}$, xn) and $^{186}\mathrm{W}$($^{11}\mathrm{B}$, p4n) reactions, respectively, at a beam energy of 68 MeV and their \ensuremath{\gamma} decay was studied using the YRAST Ball detector array at the Wright Nuclear Structure Laboratory at Yale University. The level scheme of $^{193}\mathrm{Au}$ has been extended up to ${I}^{\ensuremath{\pi}}=55/{2}^{+}$. New transitions were observed also in $^{191}\mathrm{Au}$ and $^{192}\mathrm{Pt}$. Particle-plus-Triaxial-Rotor (PTR) and Total Routhian Surface (TRS) calculations were performed to determine the equilibrium deformations of the Au isotopes. The predictions for oblate deformations in these nuclei are in agreement with the experimental data. Development of nonaxial shapes is discussed within the framework of the PTR model.

Numerical study of equilibrium shapes and deformation of single-wall carbon nanotubes

A method is proposed for constructing equilibrium shapes and studying the energetics of perfect single-wall carbon nanotubes in terms of five geometrical parameters including the twist, radial expansion, axial stretch, and two components of the inner displacement of the interwoven Bravais lattices defining the unrolled, planar, hexagonal graphene sheet. Values of these quintuplets at equilibrium are computed over an extensive range of chiralities by solving an unconstrained energy minimization problem using Brenner’s interatomic potential. An analogous formulation for computing the parameters defining the deformed tube shape under the auspices of molecular membrane mechanics is discussed. Three fundamental modes of deformation that preserve the cylindrical shape are identified describing extension that allows for expansion and twist, and their two cyclic permutations. The tube response is studied in each case by solving constrained energy minimization problems in four scalar variables. The results demonstrate the coupling between the elementary modes of deformation, and reveal topological transitions when the deformation exceeds certain thresholds. Under these critical conditions, a change in neighbors occurs signaling reconstruction and plastic deformation. Graphene rolling and tube deformation are shown to have a significant effect on the electronic band gap.