Multiple Occupancy Research Articles

Cellular Automaton Model for Random Walkers.

A new stochastic discrete space-time model of multiple random walkers is proposed to simulate one-and two-dimensional many body interacting lattice gas systems. A very simple rule set which prohibits the multiple occupancy of lattice sites by the random walkers while conserving their number is used to define the dynamics of the walkers. We found a linear time dependence for the mean squared end-to-end distances of the two-dimensional random walkers system. Extensions of the model to a wide variety of diffusive systems are noted.

Monte Carlo and analytical modeling of the effects of grain boundaries on diffusion kinetics

We examine quantitatively the impact of a grain boundary on the kinetics of diffusion in a concentrated lattice gas. In our model the lattice gas particles move via Kawasaki dynamics on the sites of a simple cubic lattice in which a high-diffusivity slab (i.e. grain boundary) has been embedded. Their motion is constrained such that multiple occupancy of a site is forbidden. By examining various subsets of particles, it is found that a temporal bias exists and can be explained in terms of approximate rate equations which embody the dynamical inhomogeneity of the system. It is observed that particles tend to migrate toward the grain boundary region for a definite period of time. As it has been useful experimentally to relate bulk and grain boundary diffusivities from an analysis of concentration profiles, we identify analogous quantities here which relate these diffusivities in our simulations. In particular, by identifying correlations between particle position and site transition frequencies, we have constructed an accurate analytical model of diffusion kinetics that is applicable both near to and far from grain boundaries. It is found that a volume-weighted diffusivity is not appropriate normal to the boundary due to dynamical correlations.

Low-temperature specific heat of the degenerate supersymmetric t-J model in one dimension

We consider the one-dimensional SU(N)-invariant t-J model, which consists of electrons with N spin components on a lattice with nearest-neighbor hopping t constrained by the excluded multiple occupancy of the sites and spin-exchange J between neighboring lattice sites. The model is integrable and has been diagonalized in terms of nested Bethe ansatze at the supersymmetric point t=J. The low-T specific heat is proportional to T. The γ-coefficient is extracted from the thermodynamic Bethe-ansatz equations and is expressed in terms of the spin wave velocities and the group velocity of the charges for arbitrary N, band filling, and splitting of the levels (magnetic and crystalline fields). Our results contain the following special cases: (i) For N=2 the traditional spin-1/2 supersymmetric t-J model, (ii) for exactly one electron per site the SU(N)-Heisenberg chain, and (iii) for N=4 the two-band supersymmetric t-J model with crystalline field splitting.

A spider population in flux: selection and abandonment of artificial web-sites and the importance of intraspecific interactions in Lephthyphantes tenuis (Araneae: Linyphiidae) in wheat.

Lepthyphantes tenuis, a small sheet-webbuilding linyphiid spider is one of the most abundant spider species of cereal fields in Europe. In the present study we examined the process of web-site selection and web-site tenacity by adult females of this species in a winter wheat field. Spiders were selective in their choice of web-site. Different immigration rates into various manipulated web-sites, in field and laboratory, suggested that structural support and suitable micro-climate (high humidity) are the most important factors in the selection. Small holes dug in the ground were the most favoured web-sites. Web-site occupation was influenced by the presence of other conspecific spiders. Territorial contests occurred between spiders attempting to occupy the same web, these almost invariably led to the take-over of the web when the intruder was heavier. Interference, but also a certain level of tolerance, between spiders within the same web-site but in different webs was suggested by direct and indirect evidence. Many holes supported two or even three spiders in vertically stratified webs. Leaving probability of marked spiders was significantly higher in multiply occupied holes than in holes with a single web. Comparison with the results of a no-interference stochastic model showed that multiple occupancy in nature is less frequent than predicted by the model. There was further evidence for weak extra-web-interference between spiders in that multiple occupancy was even less frequent and overall occupancy was lower in web-sites which were packed close to each other. However, a level of tolerance for crowding is shown by the fact that closely packed hole colonies supported a spider density 13 times higher than in natural web-sites in the field. A marking experiment was carried out to gain information on web-site tenacity (i.e. the length of time a spider spends in a web-site) and abandonment. The average duration of tenacity was less than 2 days. A random loss function gave a good fit to the tenacity distribution and suggested that spiders abandoned web-sites randomly with a fixed leaving probability of c. 0.5. Individual webs were often used consecutively by more than one spider, and some spiders built more than one web in the same web-site. Calculations showed that abandonment is the most frequent leaving mode, while take-over by contest between spiders and disappearance due to destruction were some-what less frequent and equally likely modes of ending tenacity. It is suggested that the apparent contradiction between the selectiveness and competitiveness of spiders for web-sites and the relatively short tenacity observed can be resolved by hypothesising that spiders leave websites soon because they apply the strategy of spreading risk: spiders by frequently moving from one web-site to another distribute their reproductive efforts across several localities. This hypothesis is further supported by changes in web-site preference and ballooning behaviour at the onset of the reproductive stage in L. tenuis.

Geometric and analytical aspects of anyons

We consider quantum systems ofn indistinguishable spinless particles, constrained to closed compact surfaces and satisfying fractional statistics (anyons). We question the traditional choice of a configuration space, and show that a theory maintaining the diagonal is possible. Such a theory leads naturally to questions in algebraic geometry involving desingularizations of certain algebraic varieties. The desingularizations induce the possibility of an “exotic exclusion principle” for anyons, wherein multiple occupancy is not excluded in general.

Response functions for quasi- n-dimensional ( n = 2, 1, 0) electron systems

We present an exact analytical method to calculate the inverse dielectric functions for quasi-two-dimensional electron systems (quantum wells), quasi-one-dimensional electron systems (quantum wires) and quasi-zero-dimensional electron systems (quantum dots). This is done for multiple subband occupancy within the random-phase approximation. The resulting expessions for the inverse dielectric functions pave the way to a simpler means of investigating the collective (both intraand intersubband) excitations and constitute a legitimate basis for studying, for example, the energy loss by a fast charged particle to the respective systems.

Adsorption and energetics of xenon in mordenite: A Monte Carlo simulation study

Grand canonical Monte Carlo (GCMC) simulations were used to calculate energy contour maps, isodensity surfaces and adsorption isotherms of xenon in purely siliceous mordenite at 300 K using previously published potential parameters. Then, in order to understand the effect of aluminum content, Al-containing mordenites were modeled by adding the appropriate negative charge to each of the oxygen atoms in the mordenite framework and by inserting Na+ ions at fixed extra-framework positions previously identified from x-ray crystallographic data. GCMC simulations were again performed using these structure models. Both main channel and sidepocket xenon adsorption were observed in all mordenite structures. The sidepockets were found to be only singly occupied whereas the main channel allowed multiple occupancy. Sidepocket xenon adsorption became more favorable when cations (and aluminum) were introduced. In the main channel, xenon adsorbed into localized sites that were distributed in an octahedral arrangement within each unit cell with two apices in front of opposing sidepockets. These sites remained at the same location over the entire range of loading (0–16 Xe/unit cell) and cation (and aluminum) content.

Search for small violations of the symmetrization postulate in an excited state of helium.

We have searched for the existence of the permutation symmetric $1s2s^{1}S$ state of helium in an atomic beam. Such a state directly violates the symmetrization postulate (SP) of quantum mechanics and implies a breakdown of the Pauli exclusion principle. Our data constrain recent SP-violating models at the 5 ppm level. This is the first experiment to look systematically for an SP-violating state with no multiple occupancy of a quantum state.

Ionic conduction in (1 − x)B2O3 + xLi2O

Abstract A model of ionic conduction in glasses is developed, in which the transport of classical particles takes place by hopping between negatively charged sites with possible multiple occupancy. This relates the ionic conductivity of (1 − x)B2O3 + xLi2O with the structural changes in the glass due to the addition of the alkali metal oxide, which give the nature of the negative traps as a function of x. A mean field calculation based on these ideas correctly predicts the behaviour of the activation energy and explains the surprisingly simple Arrhenius behaviour of the conductivity.

Multi-ion pore behaviour in the CFTR chloride channel.

Cystic fibrosis transmembrane conductance regulator (CFTR) is a non-rectifying, low-conductance channel regulated by ATP and phosphorylation, which mediates apical chloride conductance in secretory epithelia and malfunctions in cystic fibrosis (CF). Mutations at Lys 335 and Arg 347 in the sixth predicted transmembrane helix of CFTR alter its halide selectivity in whole-cell studies and its single channel conductance, but the physical basis of these alterations is unknown and permeation in CFTR is poorly understood. Here we present evidence that wild-type CFTR can contain more than one anion simultaneously. The conductance of CFTR passes through a minimum when channels are bathed in mixtures of two permeant anions. This anomalous mole fraction effect can be abolished by replacing Arg 347 with an aspartate and can be toggled on or off by varying the pH after the same residue is replaced with a histidine. Thus the CFTR channel should provide a convenient model in which to study multi-ion pore behaviour and conduction. The loss of multiple occupancy may explain how naturally occurring CF mutations at this site cause disease.

Groundstate properties of the degenerate supersymmetric t−J model with crystalline field splitting in one dimension

The one-dimensional t−J model is considered, consisting of electrons with four spin-components on a lattice with nearest neighbor hopping t constrained by the excluded multiple occupancy of the sites, exchange J between neighboring sites and a crystal field splitting Δ. This model is integrable at the supersymmetric point. The exact solution is presented via Bethe’s ansatz and groundstate properties as a function of Δ are discussed. The model could correspond to a two-band situation with one band being the z2 and the other one the x2−y2 orbitals of Cu2+.

Degenerate supersymmetric t− J model in one dimension

The ground-state Bethe ansatz equations of the 1D SU( N)-invariant supersymmetric t− J model, which consists of electrons with N spin components on a lattice with nearest-neighbor hopping t constrained by the excluded multiple occupancy of the sites and spin exchange J( = t) between neighboring sites are solved numerically for arbitrary band-filling and N = 4. The elemental excitations are calculated.

The permeation properties of small organic cations in gramicidin A channels

The conductance properties of organic cations in single gramicidin A channels were studied using planar lipid bilayers. From measurements at 10 mM and at 27 mV the overall selectivity sequence was found to be NH4+ > K+ > hydrazinium > formamidinium > Na+ > methylammonium, which corresponds to Eisenman polyatomic cation sequence X'. Methylammonium and formamidinium exhibit self block, suggesting multiple occupancy and single filing. Formamidinium has an apparent dissociation constant (which is similar to those of alkali metal cations) for the first ion being 22 mM from the Eadie-Hofstee plot (G0 vs. G0/C), 12 mM from the rate constants of a three-step kinetic model. The rate-limiting step for formamidinium is translocation judging from supralinear I-V relations at low concentrations. 1 M formamidinium solutions yields exceptionally long single channel lifetimes, 20-fold longer than methylammonium, which yields lifetimes similar to those found with alkali metal cations. The average lifetime in formamidinium solution significantly decreases with increasing voltage up to 100 mV but is relatively voltage independent between 100 and 200 mV. At lower voltages (< or = 100 mV), the temperature and concentration dependences of the average lifetime of formamidinium were steep. At very low salt concentrations (0.01 M, 100 mV), there was no significant difference in average lifetime from that formed with 0.01 M methylammonium or hydrazinium. We conclude that formamidinium very effectively stabilizes the dimeric channel while inside the channel and speculate that it does so by affecting tryptophan-reorientation or tryptophan-lipid interactions at binding sites.

Ground state properties and excitation spectrum of the degenerate supersymmetric t-J model in one dimension

The authors considers the one-dimensional SU(N)-invariant t-J model which consists of electrons with N spin components on a lattice with nearest-neighbour hopping t constrained by the excluded multiple occupancy of the lattice sites and spin-exchange J between neighbouring lattice sites. The model is integrable at the supersymmetric point t=J. The ground state Bethe ansatz equations are analysed and solved numerically for arbitrary band filling and several values of N. The ground state energy, the chemical potential and the spin susceptibility are obtained as a function of band filling. The elemental charge and spin excitations are derived for arbitrary N and band filling. The energy of the charge excitations vanishes at the Fermi surface. The Fermi velocity has a maximum as a function of band filling, vanishing for the empty and full bands. The spinwave velocity is inversely proportional to the susceptibility. For exactly one electron per site the charge fluctuations are suppressed and the Bethe ansatz equations map onto those of the SU(N)-invariant Heisenberg chain.

Proton block of rat brain sodium channels. Evidence for two proton binding sites and multiple occupancy.

The acid titration function of bilayer-incorporated batrachotoxin (BTX)-modified sodium channels was examined in experiments in which the pH was decreased symmetrically, on both sides of the membrane, or asymmetrically, on only one side. In an attempt to minimize interpretational ambiguities, the experiments were done in 1.0 M NaCl (buffered to the appropriate pH) with channels incorporated into net neutral bilayers. When the pH was decreased symmetrically (from 7.4 to 4.5), the small-signal conductance (g) decreased in accordance with the predictions of a simple (single-site) titration function with a pK of approximately 4.9. As the pH was decreased below 6.5, the single-channel current-voltage (i-V) relation became increasingly rectifying, with the inward current being decreased more than the outward current. When the pH was decreased asymmetrically (with the pH of the other solution being held constant at 7.4), the titration behavior was different for extra- and intracellular acidification. With extracellular acidification, the reduction in g could still be approximated by a simple titration function with a pK of approximately 4.6, and there was a pronounced rectification at pHs < or = 6 (cf. Woodhull, A. M. 1973. Journal of General Physiology. 61:687-708). The voltage dependence of the block could be described by assuming that protons enter the pore and bind to a site with a pK of approximately 4.6 at an apparent electrical distance of approximately 0.1 from the extracellular entrance. With intracellular acidification there was only a slight reduction in g, and the g-pH relation could not be approximated by a simple titration curve, suggesting that protons can bind to several sites. The i-V relations were still rectifying, and the voltage-dependent block could be approximated by assuming that protons enter the pore and bind to a site with a pK of approximately 4.1 at an apparent electrical distance of approximately 0.2 from the intracellular entrance. Based on the difference between the three g-pH relations, we conclude that there are at least two proton binding sites in the pore and that they can be occupied simultaneously.

Black, Single, Working Mothers in Poverty: Preferences for Employment, Well-being, and Perceptions of Preschool-Age Children

Poor, single, black mothers have been largely excluded from research on the impact of maternal employment. This study examined the relationship between employment preferences and well-being in a sample of 111 black, single, employed mothers with a threeor four-year-old child and low income. Two competing views of multiple role occupancy were explored, using data from structured interviews in which mothers completed a questionnaire about role strain, life satisfaction, depression, and perceptions of children. Findings revealed that mothers whose employment status was consistent with their preference were lower in role strain and higher in overall life satisfaction. Having no education beyond high school and a male child predicted significantly higher strain, greater depressive symptomatology, and the least favorable perceptions of children. Overall, results suggest that parenting boys may be especially stressful for black single mothers balancing work and family roles in poverty, particularly when low education is also a factor. Implications for policy are considered in light of the Family Support Act of 1988.

Ground state and excitations of a one-dimensional two-band supersymmetric t-J model with crystalline field splitting.

We consider a one-dimensional two-band model of electrons on a lattice with nearest-neighbor hopping {ital t} constrained by the excluded multiple occupancy of the sites, an interband splitting, {Delta}, and intraband and interband exchange {ital J} between neighboring sites. This model is integrable at the supersymmetric point and reduces to the SU(4)-invariant supersymmetric {ital t}-{ital J} model with crystal field splitting. We present the exact solution via Bethe's ansatz and discuss ground-state properties and the excitation spectrum as a function of {Delta}.

Thermodynamics of the degenerate supersymmetric t-J model in one dimension

The one-dimensional SU(N)-invariant t-J model consists of electrons with N spin components on a lattice with nearest-neighbour hopping and spin exchange J. The multiple occupancy of the lattice sites is excluded. The model is integrable at the supersymmetric point, t=J. The discrete Bethe ansatz equations are analysed and the solutions are classified according to the string hypothesis. The thermodynamic Bethe ansatz equations are derived for arbitrary band filling in terms of thermodynamic energy potentials for the classes of eigenstates of the Hamiltonian. These equations are solved in limiting cases, e.g., S=1/2, the ground state and the high-temperature limit. If the charge fluctuations are suppressed the Bethe ansatz equations map onto those of the SU(N)-invariant Heisenberg chain.

Transverse magnetoresistance in quantum wells with multiple subband occupancy.

The low-field magnetotransport properties of a two-dimensional electron gas are calculated for a situation in which more than one subband is occupied. The theory is formulated in terms of a Boltzmann transport equation in which only elastic impurity scattering is taken into account. The possibility of intersubband scattering is included and its effect on the transverse magnetoresistance and Hall coefficient is determined. We find that intersubband scattering plays an important role and its neglect can lead to erroneous conclusions regarding the values of the subband mobilities extracted from fits to experimental data.

Mechanisms of protein solubilization in reverse micelles

Solubilization properties of alpha-chymotrypsin and alcohol dehydrogenase (LADH) in reverse micelles are reported for three different solubilization techniques. The solubilization properties for these two proteins depend on the method used for protein addition. The addition of a dry protein powder to a reverse-micelle-containing organic phase does not appreciably solubilize the protein until the diameter of the reverse micelle is similar to that of the protein. However, when an aqueous protein solution is injected an organic phase, protein solubilization is not strongly dependent on micelle size. For chymotrypsin, multiple protein occupancy occurs at large micelle size, with as many as 11 chymotrypsin molecules solubilized in one reverse micelle. The solubilization of chymotrypsin using a phase-transfer technique with a positively charged surfactant follows the expected trend based on protein-surfactant electrostatic interactions. When a negatively charged surfactants is used for phase transfer, at low pH the solubilization data do not fit this electrostatic interaction mechanism. In this case, protein-surfactant aggregation may be occurring at the aqueous-organic interface.