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When our body is immersed in water, we experience weightlessness. The degree of weightlessness that we experience varies depending on the proportion of the body immersed in water, being governed by the relationship between the weight of body and the buoyant force acting on the body. Human body during the performance of swimming in no exception to these influences. Swimmers body is subject to a time and position dependent force system. Even the magnitude of the buoyant force acting on the swimmers body at every given instant and the corresponding position of the CB change continuously. The findings of this study support the following conclusions. The buoyancy torque was the primary source of bodyroll exhibited by front crawl swimmers performing at distance pace, accounting for 88 % of the bodyroll. Faster swimmers used buoyancy more effectively to generate bodyroll, partially supporting the postulation that an effective use of buoyancy for bodyroll may reduce the generated hydrodynamic forces to be wasted in non-propulsive directions and maximize forward propulsion.

A new class of quasi-exactly solvable potentials with a variable mass in the Schrodinger equation is presented. We have derived a general expression for the potentials, including Natanzon confluent potentials. The general solution of the Schrodinger equation is determined and the eigenstates are expressed in terms of the orthogonal polynomials.

We present the analysis of a deep colour-magnitude diagram (CMD) of NGC 1831, a rich star cluster in the LMC. The data were obtained with HST/WFPC2 in the F555W (~V) and F814W (~I) filters, reaching m_555 ~ 25. We discuss and apply a method of correcting the CMD for sampling incompleteness and field star contamination. Efficient use of the CMD data was made by means of direct comparisons of the observed to model CMDs. The model CMDs are built by an algorithm that generates artificial stars from a single stellar population, characterized by an age, a metallicity, a distance, a reddening value, a present day mass function and a fraction of unresolved binaries. Photometric uncertainties are empirically determined from the data and incorporated into the models as well. Statistical techniques are presented and applied as an objective method to assess the compatibility between the model and data CMDs. By modelling the CMD of the central region in NGC 1831 we infer a metallicity Z = 0.012, 8.75 < log(tau) < 8.80, 18.54 < (m-M)_0 < 18.68 and 0.00 < E(B-V) < 0.03. For the position dependent PDMF slope (alpha = -dlog(Phi(M))/dlog(M)), we clearly observe the effect of mass segregation in the system: for projected distances R < 30 arcsec, alpha ~ 1.7, whereas 2.2 < alpha < 2.5 in the outer regions of NGC 1831., 12 pages, 14 figures

Kinematical invariance groups of the 3d Schrodinger equations with position dependent masses and arbitrary potentials are classified. All non-equivalent classes of such equations are presented together with the corresponding symmetry algebras. The specific symmetries connected with the presence of the ordering-ambiguity parameters are discussed, and an extended class of systems which keep their forms for arbitrary or particular changes of these parameters is specified.

For the two-dimensional Schr\"odinger equation, the general form of the point transformations such that the result can be interpreted as a Schr\"odinger equation with effective (i.e. position dependent) mass is studied. A wide class of such models with different forms of mass function is obtained in this way. Starting from the solvable two-dimensional model, the variety of solvable partner models with effective mass can be built. Several illustrating examples not amenable to the conventional separation of variables are given., Comment: 18 pages

We solve the Schrödinger equation with a position-dependent mass (PDM) charged particle interacted via the superposition of the Morse-plus-Coulomb potentials and is under the influence of external magnetic and Aharonov–Bohm (AB) flux fields. The nonrelativistic bound state energies together with their wave functions are calculated for two spatially-dependent mass distribution functions. We also study the thermal quantities of such a system. Further, the canonical formalism is used to compute various thermodynamic variables for second choosing mass by using the Gibbs formalism. We give plots for energy states as a function of various physical parameters. The behavior of the internal energy, specific heat, and entropy as functions of temperature and mass density parameter in the inverse-square mass case for different values of magnetic field are shown.

In this paper, the wave equation corresponding to the [Formula: see text]-rigid version of Bohr Hamiltonian for the modified Davidson potential is investigated in the position-dependent mass formalism. By solving the related differential equation, the wave function, energy spectra and transition rates are obtained. In order to evaluate our results, they are compared with experimental data through the standard error.

The relativistic problem of fermions subject to a PT-symmetric potential in the presence of position-dependent mass is reinvestigated. The influence of the PT-symmetric potential in the continuity equation and in the orthonormalization condition are analyzed. In addition, a misconception diffused in the literature on the interaction of neutral fermions is clarified., 8 pages

Second order integrals of motion for 3d quantum mechanical systems with position dependent masses (PDM) are classified. Namely, all PDM systems are specified which, in addition to their rotation invariance, admit at least one second order integral of motion. All such systems appear to be also shape invariant and exactly solvable. Moreover, some of them possess the property of double shape invariance and can be solved using two different superpotentials. Among them there are systems with double shape invariance which present nice bridges between the Coulomb and isotropic oscillator systems. A simple algorithm for calculation the discrete spectrum and the corresponding state vectors for the considered PDM systems is presented and applied to solve five of the found systems., misprints are corrected and discussion is extended

The position dependence of obstructive sleep apnea is an important facet of the complex phenotypic disease spectrum. The implications are important for understanding the pathophysiology, accurately diagnosing the presence and severity during overnight testing, and predicting the utility of certain treatment modalities. A thorough understanding of position dependence is critical in achieving an optimal approach to patients with obstructive sleep apnea, with implications for clinical care as well as clinical research.

The electrophoretic force on a single DNA molecule inside a glass nanocapillary depends on the opening size and varies with the distance along the symmetrical axis of the nanocapillary. Using optical tweezers and DNA-coated beads, we measured the stalling forces and mapped the position-dependent force profiles acting on DNA inside nanocapillaries of different sizes. We showed that the stalling force is higher in nanocapillaries of smaller diameters. The position-dependent force profiles strongly depend on the size of the nanocapillary opening, and for openings smaller than 20 nm, the profiles resemble the behavior observed in solid-state nanopores. To characterize the position-dependent force profiles in nanocapillaries of different sizes, we used a model that combines information from both analytical approximations and numerical calculations.

In the present work a dynamical system is investigated, in which the particles’ mass depends on their position in space. The first case study is that of a single point-like particle in one dimension, whose Hamiltonian is numerically integrated with a first-order, energy-conserving algorithm; subsequently, the model is extended to a Lennard-Jones fluid in three dimensions. The features of both setups are examined, and a simple, exact method is devised to obtain, from a system of particles with position-dependent mass, the same equilibrium observables that would be measured in a conventional simulation. The properties of these dynamical systems are explored, with possible applications in the development of efficient sampling strategies.

We examined how letter position coding is achieved in a script (Arabic) in which the different letter forms (i.e., allographs) may vary depending on their position within the letter string (e.g., compare the same-ligation pair and vs. the different-ligation pair and . To that end, we conducted an experiment in Uyghur, an agglutinative language from the Turkic family that employs an Arabic-based script in which both consonants and vowels are explicitly written. Participants had to reproduce the correct word forms in rapid serial visual presentation sentences that either contained jumbled words (with the same ligation or different ligation) or were intact. The results revealed that readers had more difficulty correctly reporting the target words in the jumbled sentences when the letter transposition involved changes in the ligation pattern, thus demonstrating that position-dependent allography affects letter position coding. This finding poses constraints to a universal model of letter position encoding.

In many visual interaction applications the user needs to explore a scene by moving with respect to the virtual environment. Using a fixed camera viewpoint leads to visual inconsistencies, which can be avoided only if the exact pose of the user head is known and can be used to produce a perspective correct rendering. To this end, tracking devices are often used, however many of them are relatively expensive or require the user to wear special apparel. With this paper we present a tracking system that can be implemented with a simple and very low cost modification of standard shutter glasses. The accuracy of such approach has been evaluated quantitatively with a specially crafted experimental setup.

The preparation of two silylated cyclohexenes by using a Tsuji—Trost palladium-catalyzed cyclization is described.

The inhomogeneities in poly(acrylamide) (PAAm) gels and the formation mechanism of inhomogeneities were investigated using the results obtained by the mechanical measurements. The gels in the form of rods of 5.6 mm in diameter were prepared at various crosslinker (N,N'-methylene(bis)acrylamide) content. The initial monomer concentration was set to 5.1 w/v %. The results show that the elastic modulus of PAAm gels varies depending on the location, at which the mechanical measurements are carried out. The modulus increases with increasing distance from the bottom of the gel rod. The extent of modulus variation along the gel increases with increasing crosslinker content from 2.6 to 9 % BAAm.

In this paper, the effect of tooth wear on the vibration spectrum variation of a rotating spur gear pair is studied. In order to approximate the dynamic characteristics of an engaging spur gear pair, the load sharing alternation, position dependent mesh stiffness, damping factor and friction coefficient are considered in the mathematical model. The surface wear on the tooth is derived by Archard’s wear equation. The variation of the vibration spectra introduced from the interaction between the sliding wear and the dynamic load is simulated and analyzed. Numerical results indicate that the dynamic load histogram of an engaging spur gear pair may change greatly with the tooth wear. This finding implies that the variation of the gear vibration spectrum might be used to monitor the tooth wear of an engaging spur gear pair.

The bound-state solution of the position dependent mass Klein-Gordon equation including inversely linear potential is obtained with in the framework of the asymptotic iteration method. The relation between the scalar and vector potentials is considered to S(x) = V(x) (beta-1). In particular, it is shown that the corresponding method exactly reproduces the spectrum of linearly inversely potentials with spatially dependent mass.

We propose a transport mechanism for overdamped diffusing particles. The mechanism is based on a position-dependent mobility and on breaking detailed balance. Using a two-state model, we show that the transport direction is given by the phase shift between mobility and potential or mobility and transition rate. No symmetry breaking potential as employed in ratchet-type transport models is needed.

A new phenomenon of strain relaxation will be presented. In a series of In x Ga 1− x As graded composition buffer layers grown on well cut (001) GaAs substrates, a curvature of the epilayer lattice has been found, i.e. a tilt of the epilayer lattice orientation with respect to the substrate which varies coherently along the sample surface on the scale of several mm. The most recent data analysis performed on a buffer layer compositionally graded with a six-step profile shows also a thickness functional dependence of the curvature. The epilayer lattice curvature has been attributed to a coherent lateral distribution of the Burgers’ vectors. An analytical model has been developed in the framework of the continuum elasticity theory to compute the related strain field. The results show small but unexpected contributions to the parallel strain.

The behaviour of a model bidisperse suspension of colloidal particles undergoing the action of two effective physical fields is studied theoretically. Each of the two fields interacts exclusively with one of two particle populations but this ideal model can easily be extended to consider the application of one or more fields interacting with polydisperse colloidal species in a more complex manner. The conditions under which an equilibrium focusing phenomenon can appear are defined and the microscopic scale forces contributing to the resulting focusing force are analyzed. Whenever the sizes of two particle populations are commensurable, the focused particles can no longer be considered as being suspended in a continuum and the position dependent volume forces, resulting from the macroscopic density gradient established due to the concentration distribution of one of the particle populations, are no longer applicable. On the other hand, the microscopic approach allows one to demonstrate the role of surface forces, which can be the sole position dependent forces under these conditions and explains the incoherences between the existing particular theories and experimental observations.

The diffusion equation in physical space–time for a Brownian particle driven by an external force field has been derived by Smoluchowski in the two particular cases where the external field is uniform or varies linearly with position (elastic force). In more general cases, correction terms must be added to the Smoluchowski equation. We show here how to use a multi-scale Chapman–Enskog expansion to obtain, in the hydrodynamic limit, the first corrective terms to the Smoluchowski equation, without any restriction on the friction coefficient, and for any sufficiently small position-dependent constant force field. We also compare our approach with the works of Wilemski, Titulaer, and van Kampen.

As a measure of variation, total absolute deviation of job completion times (TADC) has received relatively little attention in scheduling literature. Minimizing TADC on a single machine was shown to have a polynomial time solution. In this note, we extend TADC in two directions: (i) we allow position-dependent processing times and (ii) we consider parallel identical machines. We show that each of these two more general problems, and TADC with both extensions remain polynomially solvable.

New theoretical methods are developed to analyze dynamical effects on the position-dependent, non-localized reaction transitions. Both time-dependent kinetics and average survival times are evaluated. Predicated on the steady-state Green's function formalism introduced in Part I (Spirina and Doktorov, Chem. Phys., 203 (1995) 117), a consistent decoupling series approximation is introduced for the solution of dynamic equations. The conditions of its applicability are thoroughly analyzed. The approximation works well in the case of moderately narrow transition regions with weak-to-moderate electronic coupling. To compliment the decoupling procedure, the absorbing boundary approximation is introduced to cover the case of wider transition regions with strong electronic coupling. It is demonstrated that in the latter case, slow dynamics assure formation of the absorbing walls emerging from the center of the transition regions. Both methods require only straightforward evaluations as they successfully separate the surface dynamics from the reactive transitions. We present a consistent analysis of the major qualitative changes in the reaction rates induced by widening reaction regions. Special attention is paid to dynamic effects in reactions initiated by non-equilibrium distributions. A simple model for the description of dynamically smeared transition regions is also suggested and tested.

The one-dimensional generalized Schrodinger equation for a system with smooth potential and mass step is resolved exactly. The wave function depends on the Heun’s function, which is a solution of a second-order Fuchsian equation with four singularities. The behavior of the transmission coefficient as a function of energy is compared to that of the case of an abrupt potential and mass step. Two limiting cases are also studied: when the width of the mass step is vanishing, and when the smooth potential and mass step tend to an abrupt potential and mass step.

By separating the matrix from the agglomerate it was possible to determine the nature of agglomerate breakdown during extrusion within a known geometry. Previous attempts at observing agglomerate breakdown have been unsuccessful at relating the properties of the paste to the properties of the agglomerate due to the indistinguishability of the paste and the agglomerates. By using well-characterized materials, it was found that the breakdown probabilities of the agglomerates during extrusion were independent of the position of the agglomerate. This indicated that as the shear strain rate was known to be highly position dependent, the agglomerate breakdown was shear strain rate independent. Following breakdown, the distributive mixing was observed to be position dependent.

We consider a free particle,V(r)=0, with position-dependent mass m(r)=1/(1+zeta^2*r^2)^2 in the d-dimensional schrodinger equation. The effective potential turns out to be a generalized Poschl-Teller potential that admits exact solution., 6 pages, no figures, to appear in Phys. Lett. A

This paper analyses the impact of armature slotting and magnetically nonlinear and anisotropic iron core on the trajectories of a kinematically controlled linear synchronous reluctance motor (LSRM). A new magnetically nonlinear dynamic two-axis LSRM model is introduced in order to perform the analysis. The magnetic nonlinearities and slotting effects are accounted for by the current and position-dependent characteristics of flux linkages.

Taking elastic anisotropy into consideration, we use a dislocation position dependent model to calculate the preferential formation site of noninterfacial 60° mixed dislocation segment in ellipsoid shaped InAs/GaAs quantum dots (QDs) which is observed in the experiment. From the result, it is clear that the positions near the right edge of the quantum dot are the energy favorable areas for the noninterfacial 60° mixed dislocations.

We obtain an analytical expression for position-dependent diffusion coefficient which adequately describes wave transport through 1D random medium in localized regime.

This paper describes the design and construction of a static and dynamic gear transmission test rig to analyse the position dependent elasticity, losses and transmission errors under varying circumstances. These data is important for system simulations and development of health monitoring algorithms predicting system behaviour with faults. A detailed description of the test rig is given. Example measurements of gear elasticity and losses are presented.

We introduce a general model for single machine scheduling problems, in which the actual processing times of jobs are subject to a combination of positional and time-dependent effects, that are job-independent but additionally depend on certain activities that modify the processing rate of the machine, such as, maintenance. We focus on minimizing two classical objectives: the makespan and the sum of the completion times. The traditional classification accepted in this area of scheduling is based on the distinction between the learning and deterioration effects on one hand, and between the positional effects and the start-time dependent effects on the other hand. Our results show that in the framework of the introduced model such a classification is not necessary, as long as the effects are job-independent. The model introduced in this paper covers most of the previously known models. The solution algorithms are developed within the same general framework and their running times are no worse than those available earlier for problems with less general effects.

A product's position on the shop shelf relative to other products in the category is an important yet understated factor affecting product demand. We present a parametric demand model that interprets the location of shelf facings as a set of (potentially irregular) lattice data and thereafter deploy spatial econometric techniques to (a) jointly estimate shelf position dependent demand parameters for all the stock keeping units (SKUs) in the focal category, and (b) develop an understanding of the nature of position-effects on SKU sales. In particular, we empirically investigate the (a) existence, (b) source, (c) range, (d) directionality, and (e) monetary value of spatial externalities in product demand.

Starting from the coherent state representation of the evolution operator with the help of the path-integral, we derive a formula for the low-lying levels E = ffl0 Gamma 24ffl cos(s + ,)ss of a quantum spin system. The quenching of macroscopic quantum coherence is understood as the vanishing of cos(s + ,)ss in disagreement with the suppression of tunneling (i.e. 4ffl = 0) as claimed in the literature. A new configuration called the macroscopic Fermi-particle is suggested by the character of its wave function. The tunne- ling rate ( 24fflss ) does not vanish, not for integer spin s nor for a half-integer value of s, and is calculated explicitly (for the position dependent mass) up to the one-loop approximation.

A procedure for calculating the complex susceptibility, χ = χ ′ − j χ ′', of granular superconductors with any given field and position dependent critical-current density J c is introduced. As an example of its application, the field-amplitude, H m , dependent χ of a sintered and oxidized YBa 2 Cu 3 O 7− δ before and after air annealing at temperature T a = 150−550°C is measured and fitted by the calculated curves. The results show that with increasing T a , the intergranular J c decreases quickly between 150 and 250°C and above 450°C. The decreased J c is strongly position dependent, being greater at the center than on the surface. However, the fitting is never perfect; after χ′ versus H m is well fitted, the measured χ′' is always greater than the calculated one.

The electrophoresis of a pH-regulated, zwittterionic nanoparticle, taking account of its self-induced nonuniform surface charge, the presence of multiple ionic species, and the effect of double-layer polarization, is modeled. This extends previous models to a case closer to reality because the charged properties of a particle can be influenced by both its physicochemical nature and the solution conditions. We show that the nonuniform surface charge distribution induces a local electric field having the direction either opposite to or the same as that of the applied electric field, thereby either reducing or raising the particle velocity. This effect is most important when both the surface potential and the degree of nonuniformality are high. The competition of the effects of the position dependent double layer thickness, the surface proton distribution, and the double-layer polarization yields complicated and interesting behaviors. Depending upon the level of pH, the influence of the types of background salt on the particle mobility can be significant.

In this paper, we analyse the two identical parallel processor makespan minimization problem with the learning effect, which is modelled by position dependent job/task processing times. We construct an exact pseudopolynomial time algorithm for the considered problem that takes into consideration the learning ability of the processors. Moreover, we analyse the efficiency of the exact algorithm dedicated for the classical problem with constant job/task processing times, if it is used to provide a schedule of jobs/tasks for the learning system.

We study some basic and interesting quantum mechanical systems in dynamical noncommutative spaces in which the space- space commutation relations are position dependent. It is observed that the fundamental objects in the dynamical noncommutative space introduced here are stringlike. We show that the Stark effect can be employed to determine whether the noncommutativity of space is dynamical or non-dynamical. It appears that unlike non-dynamical case there is a fundamental energy $\dfrac{\tau\hbar^{2}}{m}$ in this dynamical space.}, Comment: 11 pages, no figures, replaced with the version accepted for publication in "Journal of Physics A: Mathematical and Theoretical"

Energy losses of 12.5–30 keV He + ions are measured at glancing-angle incidence on the (001) surface of SnTe. Position-dependent stopping powers of the surfaces for the ions are derived from the observed losses. It is shown that the stopping power is explained by the single collision of a neutral He atom with valence electrons outside the surface.

We consider theoretically the gels crosslinked in the early stage of spinodal decomposition. A weakly crosslinked and homogeneous gel is brought into the thermodynamically unstable state, and additional crosslinks are introduced while the spinodal decomposition takes place. The inhomogenization of gel is ‘‘recorded’’ as position dependent distribution of chain conformations. The model is based on the theory of permanent set and that of nonequilibrium thermodynamics of gels. We investigate the effect of the rate of crosslinking on the process of spinodal decomposition. We also analyze the stability of the inhomogeneous gel thus processed. Our study shows that the spinodal instability may still occur in an inhomogeneous ‘‘opaque’’ gel, and a possible experimental test is proposed.

In N-methyl amino acids, the hydrogen of the N-H group is replaced with a bulky methyl group. While this change is expected to destabilize helical structures, the amount of destabilization is not known. Here the N-methyl group is placed into several positions of the helical peptides, acetyl-WGG(EAAAR)4A-amide and acetyl-WGG(RAAAA)4R-amide, and the melting of the peptides followed using CD. When analyzed using a simple two-state model, the destabilization associated with the H to CH3 substitution at 0 degree C is between 0.3 to 1.7 kcal/mole and is position dependent. The melting data may also be analyzed using a modified form of the Lifson-Roig statistics that should more correctly model the helix-coil transition in this small peptide. This analysis fails, however, apparently because the destabilization energy is greater than the energy that can be attributed to a single residue in this model.

During asymmetric cell division, cytoplasmic components are segregated to opposite sides of the cell. We discuss how the observed segregation can be achieved by a position-dependent phase separation mechanism controlled by a protein concentration gradient. We show that effects of even a weak gradient can be amplified by the phase transition to achieve strong segregation. We compare our theory to the segregation of germ granules observed during the divisions in the C. elegans embryo. Our study demonstrates how liquid-liquid phase separation can play a key role in the organization of the cytoplasm.

Characterizing the chemotactic motility of slowly migrating cells as a function of time is still challenging. In this paper, we use a microfluidic device for investigating the chemotactic activity of HFF-1 fibroblasts in a sigmoidal concentration profile of epidermal growth factor (EGF). Sigmoidal concentration profiles are very common in biological systems but, in contrast to linear gradients, are much less studied in microfluidic systems. We monitored cell migration for up to 10 hours and found that chemotaxis is strongest where the absolute EGF concentration is below 25 pM (K D of EGF is 1 nM). Calculating the fraction of receptor occupancy (FRO) at the front and rear of the cells showed that the chemotactic activity of HFF-1 cells scaled with the difference in FRO between both ends of the cell normalized by the average FRO av of the cell. Interestingly, the mean chemotactic index of the cells was found to be a function of the gradient at the starting position and did not change when cells were entering into other regions of the highly non-linear concentration profile. Our studies demonstrate the usefulness of stable sigmoidal concentration profiles produced in microfluidic channels for a detailed analysis of the chemotactic response of slowly migrating cells.