One-dimensional Continuum Research Articles

A continuum model of lipid bilayers

We study a one-dimensional continuum model for lipid bilayers. The system consists of water and lipid molecules; lipid molecules are represented by two ‘beads’, a head bead and a tail bead, connected by a rigid rod. We derive a simplified model for such a system, in which we only take into account the effects of entropy and hydrophilic/hydrophobic interactions. We show that for this simple model membrane-like structures exist for certain choices of the parameters, and numerical calculations suggest that they are stable.

Compact interface property for symbiotic branching

A process which we call symbiotic branching, is suggested covering three well-known interacting models: mutually catalytic branching, the stepping stone model, and the Anderson model. Basic tools such as self-duality, particle system moment duality, measure case moment duality, and moment equations are still available in this generalized context. As an application, we show that in the setting of the one-dimensional continuum the compact interface property holds: starting from complementary Heaviside states, the interface is compact at each time almost surely and propagates at most with a linear speed.

Dysthymia and Major Depression: Distinct Conditions or Different Stages Along a One-Dimensional Continuum?

Dysthymia and Major Depression: Distinct Conditions or Different Stages Along a One-Dimensional Continuum?

Integrability and soliton in a classical one-dimensional site-dependent biquadratic Heisenberg spin chain and the effect of nonlinear inhomogeneity

The integrability of one-dimensional classical continuum inhomogeneous biquadratic Heisenberg spin chain and the effect of nonlinear inhomogeneity on the soliton of an underlying completely integrable spin model are studied. The dynamics of the spin system is expressed in terms of a higher order generalized nonlinear Schrodinger equation through a differential geometric approach which becomes integrable for a particular choice of the biquadratic exchange interaction and for linear inhomogeneity. The effect of nonlinear inhomogeneity on the spin soliton is studied by carrying out a multiple scale perturbation analysis.

Dysthymia and Major Depression: Distinct Conditions or Different Stages Along a One-Dimensional Continuum?

Until recently researchers have discussed whether dysthymia and major depression represent distinct conditions or rather different stages along a one-dimensional continuum. This study addresses this question by examining the belief systems of normal, dysthymic, and depressed participants. We explored participants’ beliefs and differentiated between positive and negative as well as between core and peripheral beliefs. Normal participants showed fewer negative beliefs and negative peripheral beliefs than the dysthymic group, whereas normal participants had more positive beliefs and positive core beliefs as well as fewer negative core beliefs than the depressed group. The hypothesized one-dimensional continuum could not be demonstrated for the belief systems. Instead, the data point to the conclusion that our idea of a one-dimensional continuum reaching from normal to dysthymic to depressed was too simple. Apparently, the differences in the belief systems reported here are related to the chronic character and severity of the mood disorder.

Polarization-dependent photoluminescence-excitation spectra of one-dimensional exciton and continuum states in T-shaped quantum wires

We measured polarization-dependent photoluminescence-excitation spectra of highly uniform T-shaped quantum wires at 5 K. We attribute one peak to the one-dimensional- (1D-) exciton ground state and the continuous absorption band to 1D continuum states. These had similar polarization dependences. We also observed some other peaks above the 1D-exciton ground state and attribute them to exciton states consisting of excited hole subbands. These results show good agreement with a model calculation of a single electron–hole pair in T-shaped geometry with exact diagonalizations of the Coulomb interaction.

Wavelet-based spatial and temporal multiscaling: Bridging the atomistic and continuum space and time scales

A wavelet-based multiscale methodology is presented that naturally addresses time scaling in addition to spatial scaling. The method combines recently developed atomistic-continuum models and wavelet analysis. An atomistic one-dimensional harmonic crystal is coupled to a one-dimensional continuum. The methodology is illustrated through analysis of the dispersion relation, which is highly dispersive at small spatial scales and, as usual, nondispersive at large (continuum) scales. It is feasible to obtain the complete dispersion relation through the combination of the atomistic and the continuum analyses. Wavelet analysis in this work is not only used for bridging the atomistic and continuum scales but also for efficiently extracting the dispersion relation from the solution of wave propagation problems.

Continuum Self-Organized-Criticality Model of Turbulent Heat Transport in Tokamaks

A simple generic one-dimensional continuum model of driven dissipative systems is proposed to explain self-organized bursty heat transport in tokamaks. Extensive numerical simulations of this model reproduce many features of present day tokamaks such as submarginal temperature profiles, intermittent transport events, 1/f scaling of the frequency spectra, propagating fronts, etc. This model utilizes a minimal set of phenomenological parameters, which may be determined from experiments and/or simulations. Analytical and physical understanding of the observed features has also been attempted.

Effects of quasiactive membrane on multiply periodic traveling waves in integrate-and-fire systems.

We consider the dynamics of a one-dimensional continuum of synaptically interacting integrate-and-fire neurons with realistic forms of axodendritic interaction. The speed and stability of traveling waves are investigated as a function of discrete communication delays, distributed synaptic delays, and axodendritic delays arising from the spatially extended nature of the model neuron. In particular, dispersion curves for periodic traveling waves are constructed. Nonlinear ionic channels in the dendrite responsible for a so-called quasiactive bandpass response are shown to significantly influence the shape of dispersion curves. Moreover, a kinematic theory of spike train propagation suggests that period-doubling bifurcations of a singly periodic wave can occur in dendritic systems with a quasiactive membrane. The explicit construction of period-doubled solutions is used to confirm this prediction.

Quantum wire lasers with high uniformity formed by cleaved-edge overgrowth with growth-interrupt anneal

High-quality T-shaped quantum wire lasers are fabricated by cleaved-edge overgrowth with the molecular beam epitaxy on the interface improved by a growth-interrupt high-temperature anneal. Micro-photoluminescence (PL) and PL excitation spectroscopy reveals unprecedented high quality of the wires, and structures of one-dimensional (1D) free excitons and 1D continuum states. At high pumping levels, PL evolves from a sharp free exciton peak via a biexciton peak to a red-shifted broad band. Lasing has been achieved with low lasing threshold. The lasing energy is on the red-shifted broad band and is about 5 meV below the free exciton. The observed shift excludes free excitons in lasing, and suggests contribution of highly Coulomb-correlated electron–hole plasma.

A one-dimensional continuum model for ferroelectric ceramics

Abstract In this article, we introduce a one-dimensional continuum model for ferroelectric ceramics within a thermodynamical framework. The model consists of a free energy potential, a switching criterion, and a kinetic relation. The free energy potential is given as a function of polarization, strain, and two internal variables – remanent polarization and remanent strain. A polarization switching is described by evolutions of the two internal variables and evolution laws called kinetics are proposed based on the second law of thermodynamics. The predictions of the model are compared with experimental observations. It is suggested to model unpoled domains in the fully poled state for improved model responses.

One-dimensional continuum and exciton states in quantum wires

High-quality T-shaped quantum wires are fabricated by cleaved-edge overgrowth with molecular-beam epitaxy on the interface improved by a growth-interrupt high-temperature anneal. Characterization by micro-photoluminescence (PL) and PL excitation (PLE) spectroscopy at 5 K reveals high uniformity, a sharp spectral width, and a small Stokes shift of one-dimensional (1D) excitons. The PLE spectrum for 1D states shows a large peak of ground-state excitons and a small absorption band ascribed to 1D continuum states with an onset at 11 meV above the exciton peak.

Hydrodynamic Continuum Model for Gas–Liquid Fixed Beds Operating in Trickle Flow and Pre-Loading Regimes

A one-dimensional two-fluid continuum model based on the volume-average mass and momentum balance equations was developed for the prediction of the two-phase pressure drop and the total liquid hold-up in co-current down-flow and counter-current fixed-bed reactors operating respectively in the trickle flow regime and in the pre-loading zone. The slit model drag force closures, as well as the drag closures derived from the modified Kozeny–Carman theory based on a two-dimensional tortuosity model, were adapted. The inertial term in the drag force expressions was corrected to predict satisfactorily the two-phase pressure drops at high pressures. Wall effect functions were incorporated into the drag force equations. Associating the drag forces based on the modified Kozeny–Carman theory and the presently developed continuum model resulted in a fully predictive tool with no adjustable parameter both in co-current down-flow and counter-current flow.

Polarization switching of ferroelectric ceramics with grain boundary effect: A simple continuum model

A one-dimensional continuum model is proposed to simulate the polarization switching of ferroelectric ceramics and investigate the effects of the presence of grain boundaries on the switching behavior. A ceramic bar is modeled as a composite system of grains and grain boundaries. A grain element consists of a material characterized by a Helmholtz free energy function and a grain boundary element consists of a linear dielectric material. A polarization switching in a grain element starts and proceeds according to a switching criterion and a kinetic relation, respectively. Electric conduction effects in both grain and grain boundary elements are included in the model. A system of differential equations is derived from the law of charge conservation and solved using the finite difference method. The predicted change of hysteresis loops with electrical loading rates is qualitatively consistent with experiments. The effects of the grain boundary on polarization switching are also calculated and discussed.

The fundamental groups of one-dimensional spaces and spatial homomorphisms

Let X be a one-dimensional metric space and H be the Hawaiian earring. (1) Each homomorphism from π 1( H) to π 1( X) is induced from a continuous map up to the base-point-change isomorphism on π 1( X). (2) Let X be a one-dimensional Peano continuum. Then X has the same homotopy type as that of H if and only if π 1( X) is isomorphic to π 1( H) , if and only if X has a unique point at which X is not semi-locally simply connected. (3) Let X and Y be one-dimensional Peano continua which are not semi-locally simply connected at any point. Then, X and Y are homeomorphic if and only if π 1( X) and π 1( Y) are isomorphic. Moreover, each isomorphism from π 1( X) to π 1( Y) is induced by a homeomorphism from X to Y up to the base-point-change-isomorphism.

Two-level linear paired comparison models: estimation and identifiability issues

The method of paired comparisons became popular in psychological research with Thurstone’s [Psychometrika 65 (1927) 233] demonstration that attitudes can be scaled along a one-dimensional continuum. Despite a large number of applications of this method over the years, it has been noted only recently that paired comparison data do not only contain information about item mean differences but are also useful for studying how individuals differ in their evaluative judgments. We show that a mixed-effects, generalized linear model is well-suited for investigating such individuals differences and present a Monte Carlo EM algorithm for parameter estimation. In addition, we discuss identification issues in the specifications of different covariance structures because they impose important constraints on the interpretation of model parameters. An extensive analysis of a value study employing ordinal paired comparison illustrates the proposed statistical framework.

FRICTION-INDUCED VIBRATION IN PERIODIC LINEAR ELASTIC MEDIA

For a one-dimensional finite elastic continuum with distributed contacts and periodic boundary conditions, the presence of unstable waves is investigated. The stability of the waves is evaluated and explanations for instabilities under a constant coefficient of friction are provided. A negative slope in the coefficient of friction as a function of sliding speed is not a necessary condition for the occurrence of dynamic instability. Dynamic instability occurs in the form of self-excited, unstable, travelling waves. The stabilizing effects of external and internal damping were studied. Low- and high-frequency terms of the travelling waves are stabilized by adding external and internal damping respectively. Responses corresponding to unstable eigenvalues can dominate the system response. It is presumed that this can lead to squeaking or squealing noise in applications.

On repeated adiabatic shear band formation during high-speed machining1

Abstract We compare the repeated adiabatic shear band formation that takes place at sufficiently large cutting speeds in a number of materials during high-speed machining operations with the more well-known formation of a single shear band that often takes place at sufficiently large strain rates in dynamic torsion tests on these materials. We show that there are several major differences in the physics of the two deformation processes. In particular, the shear stress in machining over the tool-material contact length is not even approximately homogeneous. Additionally, in high-speed machining, the material flow can become convection-dominated, so that the tool can “outrun” the thermal front generated in the workpiece material by the high-strain-rate cutting process. We demonstrate by means of a one-dimensional continuum model that these differences can lead to repeated oscillations in the plastic flow of the workpiece material during high-speed machining, leading to the repeated formation of adiabatic shear bands.

Propagation of small waves in inextensible strings

The model of an inextensible uniform string subject to constant gravitation is used to study the propagation of transversal waves in one-dimensional continua. Perturbation analysis of the equations of motion yields as a result the local representation of small waves in terms of a normalized Riemann function. By means of the latter, shape and speed of propagating waves may be discussed. A refined analysis confirms that on first order, small waves travel along characteristics of the unperturbed equilibrium configuration. An explicit power law for the waves’ amplitudes is given, and the findings are supported by the numerical results.

Dynamics of Geometrically Nonlinear Rods: I. Mechanical Models and Equations of Motion

Slender thread like bodies (like cables, ropes, textilethreads or belts) are often used in technical applications. Becauseof their dimensions the one-dimensional continuum is the appropriatemechanical model for bodies of this type. Making use of the basicrelations of three-dimensional continua as a starting point the paperdevelops the general kinematic and kinetic relations of one-dimensionalcontinua for the case that the cross-sections will remain plane (Bernoullihypothesis), that large deflections are possible but the strains remainsmall and that the material is homogeneous and isotropic and behaveslinearly elastic. This results in the equations of motion of shearableand extensible rods (Timoshenko-beams). By neglection of shear deformationand of the rotational inertia of the cross-sections (assumptions thatcan be done in most technical applications) the equations of motionof Euler–Bernoulli-beams are derived in standard and concentratedform. The Euler–Bernoulli-beam equations contain the equations ofmotion of threads with zero bending and torsional stiffness. It isshown that the neglection of bending and torsional stiffness is onlyvalid if the tension is always positive. The second part of this paper[1] selects and develops appropriate numerical solution methods.The derived algorithms are used to solve problems from space and marineengineering.