Instability Collapse Research Articles

Density Instabilities in a Two-Dimensional Dipolar Fermi Gas

We study the density instabilities of a two-dimensional gas of dipolar fermions with aligned dipole moments. The random phase approximation (RPA) for the density-density response function is never accurate for the dipolar gas, and so we incorporate correlations beyond RPA via an improved version of the Singwi-Tosi-Land-Sjölander scheme. In addition to density-wave instabilities, our formalism captures the collapse instability that is expected from Hartree-Fock calculations but is absent from RPA. Crucially, we find that when the dipoles are perpendicular to the layer, the system spontaneously breaks rotational symmetry and forms a stripe phase, in defiance of conventional wisdom.

P-wave stabilization of three-dimensional Bose-Fermi solitons

We explore bright soliton solutions of ultracold Bose-Fermi gases, showing that the presence of $p$-wave interactions can remove the usual collapse instability and support stable soliton solutions that are global energy minima. A variational model that incorporates the relevant $s$- and $p$-wave interactions in the system is established analytically and solved to probe the dependencies of the soliton stationary states on key experimental parameters. Under attractive $s$-wave interactions, bright solitons exist only as metastable states susceptible to collapse. Remarkably, the presence of repulsive $p$-wave interactions alleviates this collapse instability. This dramatically widens the range of experimentally achievable soliton solutions and indicates greatly enhanced robustness. While we focus specifically on the boson-fermion pairing of ${}^{87}$Rb and ${}^{40}$K, the stabilization inferred by repulsive $p$-wave interactions should apply to the wider remit of ultracold Bose-Fermi mixtures.

Four-corner arthrodesis – Does the source of graft affect bony union rate? Iliac crest versus distal radius bone graft

Four-corner arthrodesis is an accepted surgical option for treatment of scapholunate advanced collapse, scaphoid non-union advanced collapse and midcarpal instability. A preferred source of bone graft for performing four-corner arthrodesis is the iliac crest. An alternative and more convenient donor site is the distal radius. The aim of this study was to investigate whether the union rate after four-corner arthrodesis is influenced by the source of bone graft, that is, iliac crest or distal radius. In a retrospective analysis, charts and radiographs of 180 patients were identified. In 109 patients, iliac crest bone grafts were used, whereas 71 patients received distal radius bone grafts. In the iliac crest bone graft group, 101 out of 109 patients obtained a solid radiographic union of the arthrodesis at an average of 10 weeks after surgery, and non-union in eight patients (7.3%). In the distal radius bone graft group, X-rays of 66 patients showed bone union after an average of 10 weeks after surgery as well and five patients with non-union (7.0%) respectively. There was no statistical difference in bone union. Our data show that distal radius bone graft compares equally to iliac crest bone graft in performing four-corner arthrodesis. The advantages of the distal radius bone graft include a minor surgical exposure and the avoidance of using a distant anatomic site with associated donor-site morbidity.

COLLAPSE PRESSURE ESTIMATES AND THE APPLICATION OF A PARTIAL SAFETY FACTOR TO CYLINDERS SUBJECTED TO EXTERNAL PRESSURE

The present paper investigates the collapse pressure of cylinders with intermediate thickness subjected to external pressure based on detailed elastic-plastic finite element (FE) analyses. The effect of the initial ovality of the tube on the collapse pressure was explicitly considered in the FE analyses. Based on the present FE results, the analytical yield locus, considering the interaction between the plastic collapse and local instability due to initial ovality, was also proposed. The collapse pressure values based on the proposed yield locus agree well with the present FE results; thus, the validity of the proposed yield locus for the thickness range of interest was verified. Moreover, the partial safety factor concept based on the structural reliability theory was also applied to the proposed collapse pressure estimation model, and, thus, the priority of importance of respective parameter constituting for the collapse of cylinders under external pressure was estimated in this study. From the application of the partial safety factor concept, the yield strength was concluded to be the most sensitive, and the initial ovality of tube was not so effective in the proposed collapse pressure estimation model. The present deterministic and probabilistic results are expected to be utilized in the design and maintenance of cylinders subjected to external pressure with initial ovality, such as the once-through type steam generator.

Elasto-plastic instability of single-layer reticulated shells under dynamic actions

This paper addresses the issue on dynamic collapse mechanism of single-layer reticulated shells subjected to harmonic load, sudden load and seismic load. The method for failure mechanism has reviewed the relationship between the response of the reticulated shell and the peak acceleration of dynamic action. Besides, the steel damage accumulation is considered in the method by compiling a user subroutine based on the computing program ABAQUS. An example is introduced to describe dynamic instability collapse resulting from geometric nonlinearity of the shell and the other example is presented to describe strength failure resulting from excessive development of plastic deformation, for it is discovered that the structure is not only to be prone to instability collapse in dynamic action. According to the responses of the single-layer reticulated shell under dynamic loads, this study discusses the relationship between the failure model and the corresponding dynamic load parameters. Then, the method for distinguishing failure modes is proposed based on the fuzzy synthetic evaluation theory and the structural responses of sufficient samples at the failure state. The technique feasible to be used to distinguish different failure modes of single-layer reticulated shells under different dynamic loads is validated.

Collapse instability of solitons in the nonpolynomial Schrödinger equation with dipole–dipole interactions

A model of the Bose–Einstein condensate (BEC) of dipolar atoms, confined in a combination of a cigar-shaped trap and optical lattice acting in the axial direction, is studied in the framework of the one-dimensional (1D) nonpolynomial Schrödinger equation (NPSE) with additional terms describing long-range dipole–dipole (DD) interactions. The NPSE makes it possible to describe the collapse of localized modes, which was experimentally observed in the self-attractive BEC confined in tight traps, in the framework of the 1D description. We study the influence of the DD interactions on the dynamics of bright solitons, especially concerning their collapse-induced instability. Both attractive and repulsive contact and DD interactions are considered. The results are summarized in the form of stability/collapse diagrams in a respective parametric space. In particular, it is shown that the attractive DD interactions may prevent the collapse instability in the condensate with attractive contact interactions.

Modeling and Simulations of Collapse Instabilities of Microbeamsdue to Capillary Forces

We present modeling and analysis for the static behavior and collapse instabilities of doubly‐clamped and cantilever microbeams subjected to capillary forces. These forces can be as a result of a volume of liquid trapped underneath the microbeam during the rinsing and drying process in fabrication. The model considers the microbeam as a continuous medium, the capillary force as a nonlinear function of displacement, and accounts for the mid‐plane stretching and geometric nonlinearities. The capillary force is assumed to be distributed over a specific length underneath the microbeam. The Galerkin procedure is used to derive a reduced‐order model consisting of a set of nonlinear algebraic and differential equations that describe the microbeams static and dynamic behaviors. We study the collapse instability, which brings the microbeam from its unstuck configuration to touch the substrate and gets stuck in the so‐called pinned configuration. We calculate the pull‐in length that distinguishes the free from the pinned configurations as a function of the beam thickness and gap width for both microbeams. Comparisons are made with analytical results reported in the literature based on the Ritz method for linear and nonlinear beam models. The instability problem, which brings the microbeam from a pinned to adhered configuration is also investigated. For this case, we use a shooting technique to solve the boundary‐value problem governing the deflection of the microbeams. The critical microbeam length for this second instability is also calculated.

Transverse nonlinear optics in heavy-metal-oxide glass

We investigate beam propagation in a heavy-metal-oxide glass of the group ${\text{Nb}}_{2}{\text{O}}_{5}--\text{PbO}--{\text{GeO}}_{2}$ using picosecond pulses in the near infrared. We observe a wavelength-dependent self-focusing, with beam collapse and modulation instability in the Kerr regime at $1.064\text{ }\ensuremath{\mu}\text{m}$ and stable spatial solitons at 820 nm where multiphoton absorption is present. We report near-infrared beam self-confinement and solitons, filamentation, interactions, and conical emission in the ps regime and discuss them with the aid of a numerical model.

Symmetry breaking in linearly coupled dynamical lattices

We examine one- and two-dimensional models of linearly coupled lattices of the discrete-nonlinear-Schrödinger type. Analyzing ground states of the system with equal powers (norms) in the two components, we find a symmetry-breaking phenomenon beyond a critical value of the total power. Asymmetric states, with unequal powers in their components, emerge through a subcritical pitchfork bifurcation, which, for very weakly coupled lattices, changes into a supercritical one. We identify the stability of various solution branches. Dynamical manifestations of the symmetry breaking are studied by simulating the evolution of the unstable branches. The results present the first example of spontaneous symmetry breaking in two-dimensional lattice solitons. This feature has no counterpart in the continuum limit because of the collapse instability in the latter case.

A comparison of open cell and closed cell properties for low-density materials

The stiffness and strength properties for open cell and closed cell low-density materials are collected and compared. These are the theoretical predictions for the Kelvin cell type and the oct-tet cell type of open cell forms and of the closed cell form from the generalized self-consistent method. The strength properties considered are those for plastic collapse and elastic instability, under both uniaxial stress and dilatational stress conditions.

Global structures in a composite system of two scale-free discs with a coplanar magnetic field

We investigate a theoretical magnetohydrodynamic (MHD) disc problem involving a composite disc system of gravitationally coupled stellar and gaseous discs with a coplanar magnetic field in the presence of an axisymmetric dark matter halo. The two discs are expediently approximated as razor-thin, with a barotropic equation of state, a power-law surface mass density, a ring-like magnetic field, and a power-law rotation curve of radius r. By imposing the scale-free condition, we construct analytically stationary global MHD perturbation configurations for both aligned and logarithmic spiral patterns, using our composite MHD disc model. MHD perturbation configurations in a composite system of partial discs in the presence of an axisymmetric dark matter halo are also considered. Our study generalizes the previous analyses of Lou & Shen and Shen & Lou on the unmagnetized composite system of two gravitationally coupled isothermal and scale-free discs, of Lou and Shen et al. on the cases of a single coplanarly magnetized isothermal and scale-free disc, and of Lou & Zou on magnetized two coupled singular isothermal discs. We derive analytically the stationary MHD dispersion relations for both aligned and unaligned perturbation structures and analyse the corresponding phase relationships between surface mass densities and the magnetic field. Compared with earlier results, we obtain three solution branches corresponding to superfast MHD density waves (sFMDWs), fast MHD density waves (FMDWs) and slow MHD density waves (SMDWs), respectively. We examine the m = 0 cases for both aligned and unaligned MHD perturbations. By evaluating the unaligned m = 0 case, we determine the marginal stability curves where the two unstable regimes corresponding to Jeans collapse instability and ring fragmentation instability are identified. We find that the aligned m = 0 case is simply the limit of the unaligned m = 0 case with the radial wavenumber ξ → 0 (i.e. the breathing mode) which does not merely represent a rescaling of the equilibrium state. We further show that a composite system of partial discs behaves much differently from a composite system of full discs in certain aspects. We provide numerical examples by varying dimensionless parameters β (rotation velocity index), η (ratio of effective sound speeds of the two discs), δ (ratio of surface mass densities of the two discs), q (a measure of coplanar magnetic field strength), F (gravitational potential ratio), ξ (radial wavenumber). Our formalism provides a useful theoretical framework in the study of stationary global perturbation configurations for MHD disc galaxies with bars, spirals and barred spirals.

압력과 모멘트의 복합하중을 받는 곡관의 소성 붕괴하중 예측식 개발

Based on three-dimensional (3-D) FE limit analyses, this paper provides plastic limit, collapse and instability load solutions for pipe bends under combined pressure and in-plane bending. The plastic limit loads are determined from FE limit analyses based on elastic-perfectly plastic materials using the small geometry change option, and the FE limit analyses using the large geometry change option provide plastic collapse loads (using the twice-elastic-slope method) and instability loads. For the bending mode, both closing bending and opening bending are considered, and a wide range of parameters related to the bend geometry is considered. Based on the FE results, closed-form approximations of plastic limit and collapse load solutions for pipe bends under combined pressure and bending are proposed.

Super-equipartition fields in simulations of photospheric magnetoconvection

AbstractObservations of magnetic fields in the quiet Sun indicate that kilogauss-strength fields can be found in the intergranular lanes. Since the magnetic energy of these localised features greatly exceeds estimates of the kinetic energy of the surrounding granular convection, it is difficult to see how these features could be formed simply by convective flux concentration. Idealised, high-resolution simulations of three-dimensional compressible magnetoconvection are used to investigate the formation of these features numerically. Initially we take a fully developed non-magnetic convective state into which we insert a weak, uniform, vertical magnetic field. Magnetic flux is rapidly swept into the convective downflows, where it is concentrated into localised regions. As the field strength within these regions becomes dynamically significant, the high magnetic pressure leads to partial evacuation (via the convective downflows). Provided that the magnetic Reynolds number is large enough, the strength of the resulting magnetic fields significantly exceeds the (so called) “equipartition” value, with the dynamical effects of the surrounding convection playing an important role in confining these magnetic features to localised regions. These results can be related to the well-known convective collapse instability, although there are some important differences between the two models.

Closed-form plastic collapse loads of pipe bends under combined pressure and in-plane bending

Based on three-dimensional (3-D) FE limit analyses, this paper provides plastic limit, collapse and instability load solutions for pipe bends under combined pressure and in-plane bending. The plastic limit loads are determined from FE limit analyses based on elastic–perfectly-plastic materials using the small geometry change option, and the FE limit analyses using the large geometry change option provide plastic collapse loads (using the twice-elastic-slope method) and instability loads. For the bending mode, both closing bending and opening bending are considered, and a wide range of parameters related to the bend geometry is considered. Based on the FE results, closed-form approximations of plastic limit and collapse load solutions for pipe bends under combined pressure and bending are proposed.

Collisional oscillations of trapped boson-fermion mixtures in the approach to the collapse instability

We study the collective modes of a confined gaseous cloud of bosons and fermions with mutual attractive interactions at zero temperature. The cloud consists of a Bose-Einstein condensate and a spin-polarized Fermi gas inside a spherical harmonic trap and the coupling between the two species is varied by increasing either the magnitude of the interspecies s-wave scattering length or the number of bosons. The mode frequencies are obtained in the collisional regime by solving the equations of generalized hydrodynamics and are compared with the spectra calculated in the collisionless regime within a random-phase approximation. We find that, as the mixture is driven towards the collapse instability, the frequencies of the modes of fermionic origin show a blue shift which can become very significant for large numbers of bosons. Instead the modes of bosonic origin show a softening, which becomes most pronounced in the very proximity of collapse. Explicit illustrations of these trends are given for the monopolar spectra, but similar trends are found for the dipolar and quadrupolar spectra except for the surface (n=0) modes which are essentially unaffected by the interactions.

Mixed-isotope Bose-Einstein condensates in rubidium

We consider the ground state properties of mixed Bose-Einstein condensates of 87Rb and 85Rb atoms in the isotropic pancake trap, for both signs of the interspecies scattering length. In the case of repulsive interspecies interaction, there are the axially-symmetric and symmetry-breaking ground states. The threshold for the symmetry breaking transition, which is related to appearance of a zero dipole-mode, is found numerically. For attractive interspecies interactions, the two condensates assume symmetric ground states for the numbers of atoms up to the collapse instability of the mixture.

Werner syndrome protein, the MRE11 complex and ATR: menage-à-trois in guarding genome stability during DNA replication?

The correct execution of the DNA replication process is crucially import for the maintenance of genome integrity of the cell. Several types of sources, both endogenous and exogenous, can give rise to DNA damage leading to the DNA replication fork arrest. The processes by which replication blockage is sensed by checkpoint sensors and how the pathway leading to resolution of stalled forks is activated are still not completely understood. However, recent emerging evidence suggests that one candidate for a sensor of replication stress is ATR and that, together with a member of RecQ family helicases, Werner syndrome protein (WRN) and MRE11 complex, can collaborate to promote the restarting of DNA synthesis through the resolution of stalled replication forks. Here, we discuss how WRN, the MRE11 complex and the ATR kinase could work together in response to replication blockage to avoid DNA replication fork collapse and genome instability.

Resection of the distal pole of the scaphoid for scaphoid nonunion with radioscaphoid and intercarpal arthritis

Purpose: The treatment of scaphoid nonunion with degenerative arthritis poses a clinical problem that is particularly challenging in cases of associated dorsal intercalated segmental instability collapse, radiocarpal and intercarpal degenerative changes, and poor scaphoid bone quality. The purpose of this study was to report our clinical experience performing a distal scaphoid resection for symptomatic scaphoid nonunion in patients with either radioscaphoid or intercarpal arthritis who have had multiple surgeries. Methods: Nine patients with recalcitrant scaphoid nonunion and associated degenerative arthritis treated by resection of the distal scaphoid fragment were evaluated both clinically and radiographically. Eight patients were male and one patient was female; the average follow-up period was 28.6 months (range, 12–52 mo). Results: Seven patients reported pain with daily use and the remaining 2 patients reported mild pain with light work before surgery, whereas after surgery 4 of the 9 patients had no wrist pain and the remaining 5 patients had only mild pain with strenuous activity. The wrist range of motion improved from 70° (51.4% of the opposite wrist) to 140° (94% of the opposite wrist) and grip strength improved from 18 kg (40% of the opposite wrist) to 30 kg (77% of the opposite wrist). Clinical results were excellent in 6 patients and good in 3 patients based on a modified Mayo wrist-scoring chart. Radiographically neither additional degeneration nor progress of degenerative changes was noted after surgery in 8 patients. Newly developed degenerative arthritis occurred at the proximal scapholunate capitate articulation in the remaining patient who has a type II lunate, which had a facet (medial facet) articulation with the hamate. Conclusions: The results of this study showed that distal scaphoid resection produces a satisfactory clinical outcome, requires only a short period of immobilization, and should be considered one of the surgical options for long-standing scaphoid nonunion with either radioscaphoid or intercarpal degenerative arthritis. Nevertheless care must be taken in performing this procedure on patients whose preoperative radiograph show a type II lunate.

Simulation of the thermal response of self-heating power transistors using a time step adaption method

An implementation of the Rosenbrock-Wanner scheme with embedded time-step adaption in the thermal simulation of AlGaAs-GaAs heterojunction bipolar transistors (HBT) is presented. The simulations are based on discrete 3-D models of the device using the finite integration technique for the solution of the thermal equation. The thermally coupled current response of the device in DC operation is obtained by a nonlinear EM/sub 3/ model. Several simulations featuring the thermal crosstalk and the current collapse instability demonstrates the utility of time-step adaption in simulating the alternating slow-fast transients in multifinger HBTs.

Electrohydrodynamic wave-packet collapse and soliton instability for dielectric fluids in (2 + 1)-dimensions

A weakly nonlinear theory of wave propagation in two superposed dielectric fluids in the presence of a horizontal electric field is investigated using the multiple scales method in (2+1)-dimensions. The equation governing the evolution of the amplitude of the progressive waves is obtained in the form of a two-dimensional nonlinear Schrodinger equation. We convert this equation for the evolution of wave packets in (2+1)-dimensions, using the function transformation method, into an exponentional and a Sinh-Gordon equation, and obtain classes of soliton solutions for both the elliptic and hyperbolic cases. The phenomenon of nonlinear focusing or collapse is also studied. We show that the collapse is direction-dependent, and is more pronounced at critical wavenumbers, and dielectric constant ratio as well as the density ratio. The applied electric field was found to enhance the collapsing for critical values of these parameters. The modulational instability for the corresponding one-dimensional nonlinear Schrodinger equation is discussed for both the travelling and standing waves cases. It is shown, for travelling waves, that the governing evolution equation admits solitary wave solutions with variable wave amplitude and speed. For the standing wave, it is found that the evolution equation for the temporal and spatial modulation of the amplitude and phase of wave propagation can be used to show that the monochromatic waves are stable, and to determine the amplitude dependence of the cutoff frequencies.