Local Exchange Model Research Articles

A Local-Exchange Model of Folding Chain Surface of Polymer Crystal Based on Worm-Like Chain Model within Single-Chain in Mean-Field Theory.

The structure of amorphous layer of folding surface controls the properties of the polymer lamellar crystal, which consists of chains with a loop conformation. The surface tension depends on the length and the distance between two injection points of the loop which involving the reptation motion and lateral exchange motion of the stems. In the present work, a local-exchange motion model based on the worm-like chain model is developed to investigate the effects of lateral motion of stems on the release the surface tension. The optimal distance between two injection points is determined by the balance of chain bending energy and conformational entropy. The numerical results provide evidences to the adjacent re-entry model for various loop lengths. A possible explanation involving density of injection points is proposed to interpret the mechanism.

Turbulent particle transport in streams: Can exponential settling be reconciled with fluid mechanics?

Most ecological studies of particle transport in streams that focus on fine particulate organic matter or benthic invertebrates use the Exponential Settling Model (ESM) to characterize the longitudinal pattern of particle settling on the bed. The ESM predicts that if particles are released into a stream, the proportion that have not yet settled will decline exponentially with transport time or distance and will be independent of the release elevation above the bed. To date, no credible basis in fluid mechanics has been established for this model, nor has it been rigorously tested against more-mechanistic alternative models. One alternative is the Local Exchange Model (LEM), which is a stochastic advection–diffusion model that includes both longitudinal and vertical spatial dimensions and is based on classical fluid mechanics. The LEM predicts that particle settling will be non-exponential in the near field but will become exponential in the far field, providing a new theoretical justification for far-field exponential settling that is based on plausible fluid mechanics. We review properties of the ESM and LEM and compare these with available empirical evidence. Most evidence supports the prediction of both models that settling will be exponential in the far field but contradicts the ESM's prediction that a single exponential distribution will hold for all transport times and distances.

Dispersion of freshwater mussel larvae in a lowland river

We examined the dispersal of larvae (glochidia) of a common unionid mussel species, Actinonaias ligamentina, which need to attach to a host fish in order to develop into juveniles, in a lowland river (Sydenham River, Ontario, Canada). Generally, the decline in the number of glochidia captured with distance from release was best described by an inverse power function. The highest proportion was found in the first net 4 m downstream (range 0.1–3.6%), but a small proportion of glochidia was captured 96 m downstream (0–0.03%). This indicates that infestation of host fish may occur several tens to hundreds of meters downstream of the adults’ location, even at relatively low flow conditions (mean velocity, 15 cm s−1). Dispersal distances increased with velocity, but the number of glochidia sampled at a given location can vary considerably due to stochastic effects of turbulence, especially at shorter distances. Individual trials could, therefore, deviate considerably from the predictions of an existing turbulent transport model (local exchange model), but overall there was a good correlation between measured data and model prediction. However, model predictions were quantitatively much higher than measured values (i.e., > 50 fold in some cases), which could be in part due to several simplifying assumptions of the model.

Probabilistic settling in the Local Exchange Model of turbulent particle transport

The Local Exchange Model (LEM) is a stochastic diffusion model of particle transport in turbulent flowing water. It was developed mainly for application to particles of near-neutral buoyancy that are strongly influenced by turbulent eddies. Turbulence can rapidly transfer such particles to the bed, where settlement can then occur by, for example, sticking to biofilms (e.g., fine particulate organic matter, or FPOM) or attaching to the substrate behaviorally (e.g., benthic invertebrates). Previous papers on the LEM have addressed the problems of how long (time) and far (distance) a suspended particle will be transported before hitting the bed for the first time. These are the hitting-time and hitting-distance problems, respectively. Hitting distances predicted by the LEM for FPOM in natural streams tend to be much shorter than the distances at which most particles actually settle, suggesting that particles usually do not settle the first time they hit the bed. The present paper extends the LEM so it can address probabilistic settling, where a particle encountering the bed can either remain there for a positive length of time (i.e., settle) or immediately reflect back into the water column, each with positive probability. Previous results for the LEM are generalized by deducing a single set of equations governing the probability distribution and moments of a broad class of quantities that accumulate during particle trajectories terminated by hitting or settling on the bed (e.g., transport time, transport distance, cumulative energy expenditure during transport). Key properties of the settling-time and settling-distance distributions are studied numerically and compared with the observed FPOM settling-distance distribution for a natural stream. Some remaining limitations of the LEM and possible means of overcoming them are discussed.

Temperature-dependent magnetization in diluted magnetic semiconductors

We calculate magnetization in magnetically doped semiconductors assuming a local exchange model of carrier-mediated ferromagnetic mechanism and using a number of complementary theoretical approaches. In general, we find that the results of our mean-field calculations, particularly the dynamical mean field theory results, give excellent qualitative agreement with the experimentally observed magnetization in systems with itinerant charge carriers, such as Ga_{1-x}Mn_xAs with 0.03 < x < 0.07, whereas our percolation-theory-based calculations agree well with the existing data in strongly insulating materials, such as Ge_{1-x}Mn_x. We comment on the issue of non-mean-field like magnetization curves and on the observed incomplete saturation magnetization values in diluted magnetic semiconductors from our theoretical perspective. In agreement with experimental observations, we find the carrier density to be the crucial parameter determining the magnetization behavior. Our calculated dependence of magnetization on external magnetic field is also in excellent agreement with the existing experimental data.

Turbulent Transport of Suspended Particles and Dispersing Benthic Organisms: the Hitting-distance Problem for the Local Exchange Model

The local exchange model developed by McNair et al. (1997) provides a stochastic diffusion approximation to the random-like motion of fine particles suspended in turbulent water. Based on this model, McNair (2000) derived equations governing the probability distribution and moments of the hitting time, which is the time until a particle hits the bottom for the first time from a given initial elevation. In the present paper, we derive the corresponding equations for the probability distribution and moments of the hitting distance, which is the longitudinal distance a particle has traveled when it hits the bottom for the first time. We study the dependence of the distribution and moments on a particle's initial elevation and on two dimensionless parameters: an inverse Reynolds numberM̂(a measure of the importance of viscous mixing compared to turbulent mixing of water) and the Rouse number ŝ (a measure of the importance of deterministic gravitational sinking compared to stochastic turbulent mixing in governing the vertical motion of a particle). We also compute predicted hitting-distance distributions for two published data sets. The results show that for fine particles suspended in moderately to highly turbulent water, the hitting-distance distribution is strongly skewed to the right, with mode<median<mean. Because of the distribution's thick upper tail, there is a significant probability that a particle's hitting distance will greatly exceed the mean. The results also show that the position of the mode depends strongly on a particle's initial elevation but, compared to the median or mean, is relatively insensitive to ŝ. These results are broadly similar to those obtained by McNair (2000) for the hitting-time distribution, but the distribution and moments of the hitting distance are noticeably more sensitive toM̂than are the corresponding properties of the hitting time. Comparison of predicted hitting-distance distributions with data of Cushing et al. (1993) on settling distances of fine particulate organic matter in natural streams supports the view that such particles commonly fail to settle the first time they hit the stream bed.

Turbulent Transport of Suspended Particles and Dispersing Benthic Organisms: The Hitting-time Distribution for the Local Exchange Model

Fine particles suspended in turbulent water exhibit highly irregular trajectories as they are buffeted by fluid eddies. The Local Exchange Model provides a stochastic diffusion approximation to the randomlike motion of such particles (e.g. dispersing benthic organisms in a stream). McNair et al. (1997, J. theor. Biol.188, 29) used this model to derive equations governing the mean hitting time, which is the expected time until a particle hits bottom for the first time from a given initial elevation. The present paper derives equations governing the probability distribution of the hitting time, then studies the distribution's dependence on a particle's initial elevation and two dimensionless parameters. The results show that for fine particles suspended in moderately to highly turbulent water, the hitting-time distribution is strongly skewed to the right, with mode<median<mean. Because of the distribution's thick upper tail, there is a significant probability that a particle's hitting time will greatly exceed the mean. The results also show that the position of the mode depends strongly on a particle's initial elevation but, compared to the median or mean, is relatively insensitive to the particle's fall velocity.

Turbulent Transport of Suspended Particles and Dispersing Benthic Organisms: How Long to Hit Bottom?

Turbulence plays an important role in the transport of particles in many aquatic systems. In addition to various types of inorganic sediment (silt, sand, etc.), these particles typically include bacteria, algae, invertebrates, and fine organic debris. In this paper, we focus on one aspect of turbulent particle transport; namely, the average time required for a suspended particle to reach the bottom of a waterbody from a specified initial elevation. This is the mean hitting-time problem, and it is important in determining, for example, the effect of turbulence on downstream transport of organic particles, dispersal times and dispersal propagules. We approach this problem by developing a stochastic diffusion model of particle transport called the Local Exchange Model, which is an extension of a model posed by Denny & Shibata (1989) in an earlier study of the same problem. We show how the mean hitting-time of the Local Exchange Model varies with factors such as a particle's fall velocity an the shape of the vertical profile in turbulent mixing. We also show how the mean hitting-time is related to both the vertical profile in current velocity and the vertical profile in concentration of suspended particles, and how these relationships can be exploited in testing the model. Among other things, our results predict that, with the sole exception of neutrally buoyant particles that do not swim downward, there is always a region of the water-column in which turbulence increases rather than decreases the mean hitting-time. We discuss the significance of this and other results for dispersal by benthic organisms.

Spin density functional theory for the spin wave stiffness coefficient in ferromagnets

The spin density functional theory is used to derive a variational principle (lower bound) for the wavevector dependent static transverse ferromagnetic spin susceptibility chi +-(q) for a general exchange-correlation energy functional. This variational principle is a direct consequence of the Hohenberg and Kohn minimum energy theorem for the ground state. The importance of spin rotational invariance is stressed in choosing the trial function so that the variational expression for chi +-(q) has the correct behaviour for small q. Noting the relationship between the spin wave stiffness coefficient D and chi +-(q), a rigorous upper bound for D is derived for general ferromagnetic systems. The relationships between the present general theory for D and recent theories based on the local exchange model are discussed.

Dynamical susceptibilities in ferromagnetic and antiferromagnetic systems

Abstract The methods for calculating the collective excitations and dynamical susceptibilities in various models of itinerant-electron magnetism are reviewed. The local-exchange model and the model-Hamiltonian approach are discussed, and their advantages and disadvantages as applied to ferromagnetic and antiferromagnetic systems are brought out. Results are presented for a new many-band calculation of a generalised susceptibility corresponding to the case of fcc antiferromagnetic manganese.

The local exchange model of itinerant-electron ferromagnetism: Energy bands in nickel and iron

Abstract The local exchange approximation is considered as a model for itinerant-electron ferromagnetism. Formal properties are reviewed. The current status of calculations based on this model is summarized, with emphasis on recent studies of energy bands in iron and nickel.