Shock structure formation in dusty plasmas

The problem of the evolution of a perturbation in a dusty plasma and its transformation into a nonlinear wave structure is considered. A computational method that allows one to solve the set of nonlinear evolutionary equations describing variable-charge dust grains, Boltzmann electrons, and inertial ions is developed. Exact steady-state solutions corresponding to ion-acoustic shock structures associated with anomalous dissipation originating from dust grain charging are found taking into account the effect of electron and ion charge separation. The role of this effect increases with the speed of the shock. The evolutions of an initial soliton (which is a steady-state wave solution in a plasma containing dust grains with a constant charge) and an initially immobile perturbation with a constant increased ion density are investigated. In a charge-varying dusty plasma, the soliton evolves into a nonsteady shock wave structure that propagates at a constant speed and whose amplitude decreases with time. The initially immobile perturbation with a constant increased ion density evolves into a shock structure similar to a steady-state shock wave. In the latter case, the compression shock wave is accompanied by a rarefaction region (dilatation wave), which finally leads to the destruction of the shock structure. The solution of the problem of the evolution of a perturbation and its transformation into a shock wave in a charge-varying dusty plasma opens up the possibility of describing real phenomena (such as supernova explosions) and laboratory and active space experiments.     

A minimum energy cost hypothesis for human arm trajectories

 Many tasks require the arm to move from its initial position to a specified target position, but leave us free to choose the trajectory between them. This paper presents and tests the hypothesis that trajectories are chosen to minimize metabolic energy costs. Costs are calculated for the range of possible trajectories, for movements between the end points used in previously published experiments. Calculated energy minimizing trajectories for a model with biarticular elbow muscles agree well with observed trajectories for fast movements. Good agreement is also obtained for slow movements if they are assumed to be performed by slower muscles. A model in which all muscles are uniarticular is less successful in predicting observed trajectories. The effects of loads and of reversing the direction of movement are investigated. Received: 11 July 1995 / Accepted in revised form: 7 October 1996     

The dominance boundary method of determining motivational state

A model is outlined in which physiological state affects behaviour through command variables. Theoretically command space can be divided into regions in which different behaviours are dominant. These regions are bounded by switching lines which should be experimentally observable. It is shown that, in the case of the Barbary dove, it is possible by use of a suitable reward schedule (the ‘double interruption’ schedule) to hold all causal factors for feeding and drinking other than physiological deficit constant (or to mask their variation). When this is done either, feeding or drinking occurs according to whether the deficit for food or water is greater. This is equivalent to saying that there exists a straight switching line (estimated by the dominance boundary) in a deficit space with axes food deficit and water deficit, both measured in grams. The position of this line in deficit space does not vary systematically over a period of time, and is not affected either by initial deprivation or by radical alterations in the consequences of feeding and drinking. It is possible to estimate the motivational state of the animal from a knowledge of its position in deficit space and the position of the dominance boundary. Analogous experiments with pigs give less clear-cut results.     

The role of pH fronts in reversible electroporation

We present experimental measurements and theoretical predictions of ion transport in agar gels during reversible electroporation (ECT) for conditions typical to many clinical studies found in the literature, revealing the presence of pH fronts emerging from both electrodes. These results suggest that pH fronts are immediate and substantial. Since they might give rise to tissue necrosis, an unwanted condition in clinical applications of ECT as well as in irreversible electroporation (IRE) and in electrogenetherapy (EGT), it is important to quantify their extent and evolution. Here, a tracking technique is used to follow the space-time evolution of these pH fronts. It is found that they scale in time as , characteristic of a predominantly diffusive process. Comparing ECT pH fronts with those arising in electrotherapy (EChT), another treatment applying constant electric fields whose main goal is tissue necrosis, a striking result is observed: anodic acidification is larger in ECT than in EChT, suggesting that tissue necrosis could also be greater. Ways to minimize these adverse effects in ECT are suggested.     

Transition from slow to ballistic movement: development of triphasic electromyogram patterns.

The purpose of this investigation was to determine how the triphasic electromyogram (EMG) pattern of muscle activation developed from the agonist muscle only pattern as movement time (tmov) decreased. Six adult women produced a series of 30 degrees elbow extension movements in the horizontal plane at speeds ranging from ballistic (less than 400-ms tmov) to very slow (greater than 800-ms tmov). Surface EMG from triceps brachii (agonist) and biceps brachii (antagonist) muscles were recorded, together with elbow angle, on a microcomputer. The results showed that triphasic EMG patterns developed systematically as tmov decreased from 1000 ms to less than 200 ms. In trials with very long tmov, many elbow extension movements were produced by a single continuous activation of the agonist triceps brachii muscle. As tmov decreased however, agonist activation became predominantly burst-like and other components of the triphasic EMG pattern [activation of the antagonist (Ant) and second agonist activation (Ag2)] began to appear. At the fastest movement speeds, triphasic EMG patterns (Ag1-Ant-Ag2, Ag1 being first activation of agonist muscle) were always present. This data indicated that the triphasic pattern of muscle activation was not switched on when a particular tmov was achieved. Rather, each component systematically developed until all were present, as distinctive bursts of activity, in most trials with tmov less than 400 ms.     

Voltage-sensor movements describe slow inactivation of voltage-gated sodium channels I: Wild-type skeletal muscle NaV1.4

The number of voltage-gated sodium (Na_V) channels available to generate action potentials in muscles and nerves is adjusted over seconds to minutes by prior electrical activity, a process called slow inactivation (SI). The basis for SI is uncertain. Na_V channels have four domains (DI–DIV), each with a voltage sensor that moves in response to depolarizing stimulation over milliseconds to activate the channels. Here, SI of the skeletal muscle channel Na_V1.4 is induced by repetitive stimulation and is studied by recording of sodium currents, gating currents, and changes in the fluorescence of probes on each voltage sensor to assess their movements. The magnitude, voltage dependence, and time course of the onset and recovery of SI are observed to correlate with voltage-sensor movements 10,000-fold slower than those associated with activation. The behavior of each voltage sensor is unique. Development of SI over 1–160 s correlates best with slow immobilization of the sensors in DI and DII; DIII tracks the onset of SI with less fidelity. Showing linkage to the sodium conduction pathway, pore block by tetrodotoxin affects both SI and immobilization of all the sensors, with DI and DII significantly suppressed. Recovery from SI correlates best with slow restoration of mobility of the sensor in DIII. The findings suggest that voltage-sensor movements determine SI and thereby mediate Na_V channel availability.     

Dynamic stability of individuals with transtibial amputation walking in destabilizing environments

Lower limb amputation substantially disrupts motor and proprioceptive function. People with lower limb amputation experience considerable impairments in walking ability, including increased fall risk. Understanding the biomechanical aspects of the gait of these patients is crucial in improving their gait function and their quality of life. In the present study, 9 persons with unilateral transtibial amputation and 13 able-bodied controls walked on a large treadmill in a Computer Assisted Rehabilitation Environment (CAREN). While walking, subjects were either not perturbed, or were perturbed either by continuous mediolateral platform movements or by continuous mediolateral movements of the visual scene. Means and standard deviations of both step lengths and step widths increased significantly during both perturbation conditions (all p<0.001) for both groups. Measures of variability, local and orbital dynamic stability of trunk movements likewise exhibited large and highly significant increases during both perturbation conditions (all p<0.001) for both groups. Patients with amputation exhibited greater step width variability (p=0.01) and greater trunk movement variability (p=0.04) during platform perturbations, but did not exhibit greater local or orbital instability than healthy controls for either perturbation conditions. Our findings suggest that, in the absence of other co-morbidities, patients with unilateral transtibial amputation appear to retain sufficient sensory and motor function to maintain overall upper body stability during walking, even when substantially challenged. Additionally, these patients did not appear to rely more heavily on visual feedback to maintain trunk stability during these walking tasks.     

Does time since introduction influence enemy release of an invasive weed?

Release from natural enemies is considered to potentially play an important role in the initial establishment and success of introduced plants. With time, the species richness of herbivores using non-native plants may increase [species-time relationship (STR)]. We investigated whether enemy release may be limited to the early stages of invasion. Substituting space for time, we sampled invertebrates and measured leaf damage on the invasive species Senecio madagascariensis Poir. at multiple sites, north and south of the introduction site. Invertebrate communities were collected from plants in the field, and reared from collected plant tissue. We also sampled invertebrates and damage on the native congener Senecio pinnatifolius var. pinnatifolius A. Rich. This species served as a control to account for environmental factors that may vary along the latitudinal gradient and as a comparison for evaluating the enemy release hypothesis (ERH). In contrast to predictions of the ERH, greater damage and herbivore abundances and richness were found on the introduced species S. madagascariensis than on the native S. pinnatifolius. Supporting the STR, total invertebrates (including herbivores) decreased in abundance, richness and Shannon diversity from the point of introduction to the invasion fronts of S. madagascariensis. Leaf damage showed the opposite trend, with highest damage levels at the invasion fronts. Reared herbivore loads (as opposed to external collections) were greater on the invader at the point of introduction than on sites further from this region. These results suggest there is a complex relationship between the invader and invertebrate community response over time. S. madagascariensis may be undergoing rapid changes at its invasion fronts in response to environmental and herbivore pressure.     

Tempo and mode of sequence evolution in mitochondrial DNA of HawaiianDrosophila

Summary Sequence comparisons were made for up to 667 bp of DNA cloned from 14 kinds of HawaiianDrosophila and five other dipteran species. These sequences include parts of the genes for NADH dehydrogenase (subunits 1, 2, and 5) and rRNA (from the large ribosomal subunit). Because the times of divergence among these species are known approximately, the sequence comparisons give insight into the evolutionary dynamics of this molecule. Transitions account for nearly all of the differences between sequences that have diverged by less than 2%; for these sequences the mean rate of divergence appears to be about 2%/Myr. In comparisons involving greater divergence times and greater sequence divergence, relatively more of the sequence differences are due to transversions. Specifically, the fraction of these differences that are counted as transversions rises from an initial value of less than 0.1 to a plateau value of nearly 0.6. The time required to reach half of the plateau value, about 10 Myr, is similar to that for mammalian mtDNA. The mtDNAs of flies and mammals are also alike in the shape of the curve relating the percentage of positions at which there are differences in protein-coding regions to the time of divergence. For both groups of animals, the curve has a steep initial slope ascribable to fast accumulation of synonymous substitutions and a shallow final slope resulting from the slow accumulation of substitutions causing amino acid replacements. However, the percentage of all sites that can experience a high rate of substitution appears to be only about 8% for fly mtDNA compared to about 20% for mammalian mtDNA. The low percentage of hypervariable sites may be a consequence of a functional constraint associated with the low content of guanine and cytosine in fly mtDNA.     

Neutral Genetic Patterns for Expanding Populations with Nonoverlapping Generations

We investigate the inside dynamics of solutions to integrodifference equations to understand the genetic consequences of a population with nonoverlapping generations undergoing range expansion. To obtain the inside dynamics, we decompose the solution into neutral genetic components. The inside dynamics are given by the spatiotemporal evolution of the neutral genetic components. We consider thin-tailed dispersal kernels and a variety of per capita growth rate functions to classify the traveling wave solutions as either pushed or pulled fronts. We find that pulled fronts are synonymous with the founder effect in population genetics. Adding overcompensation to the dynamics of these fronts has no impact on genetic diversity in the expanding population. However, growth functions with a strong Allee effect cause the traveling wave solution to be a pushed front preserving the genetic variation in the population. In this case, the contribution of each neutral fraction can be computed by a simple formula dependent on the initial distribution of the neutral fractions, the traveling wave solution, and the asymptotic spreading speed.     

Distractor Interference during a Choice Limb Reaching Task

According to action-centered models of attention, the patterns of distractor interference that emerge in selective reaching tasks are related to the time and effort required to resolve a race for activation between competing target and non-target response producing processes. Previous studies have only used unimanual aiming tasks and, as such, only examined the effects of competition that occurs within a limb. The results of studies using unimanual aiming movements often reveal an “ipsilateral effect” - distractors on the same side of space as the effector cause greater interference than distractors on the opposite side of space. The cost of the competition when response selection is between the limbs has yet to be addressed. Participants in the present study executed reaching movements to 1 of 4 (2 left, 2 right) possible target locations with and without a distractor. Participants made ipsilateral reaches (left hand to left targets, right hand to right targets). In contrast to studies using unimanual aiming movements, a “contralateral effect” was observed; distractors affording responses for the other hand (in contralateral space) caused more interference than distractors affording responses for the same hand. The findings from the present research demonstrate that when certain portions of response planning must be resolved prior to response initiation, distractors that code for that dimension cause the greatest interference.     

Slow intermixing of cells during Xenopus embryogenesis contributes to the consistency of the blastomere fate map

The relatively consistent fates of the blastomeres of the frog embryo could result from (i) predetermination of the blastomeres or (ii) reproducible morphogenetic cell movements. In some species, the mixing of the cells during development provides a test between these alternative hypotheses. If blastomeres are predetermined, then random intermixing of the descendants with neighboring cells could not alter their fate. To follow cell mixing during Xenopus development, fluorescent dextran lineage tracers were microinjected into identified blastomeres at the 16-cell stage. The labelled descendants of the injected blastomeres were followed over several stages of embryogenesis. After gastrulation, the labelled descendants formed relatively coherent groups in characteristic regions of the embryo. By larval stages, most of the labelled descendants were still located in characteristic regions. However, coherence was less pronounced and individual descendants were located in many regions of the embryo. Hence, cell mixing is a slow, but progressive, process throughout Xenopus development. This is in sharp contrast to the extensive mixing that occurs during the early development of other vertebrates, such as zebrafish and mice. The slow cell mixing in Xenopus development suggests a simple mechanism for the consistent fates of cleavage-stage blastomeres. The stereotyped cell movements of embryogenesis redistribute the largely coherent descendants to characteristic locations in the embryo. The small amount of mixing that does occur would result in variable locations of a small proportion of the descendants; this could contribute to the observed variability of the blastomere fate map. Because cell mixing during Xenopus development is insufficient to challenge possible lineage restrictions, additional experiments must be performed to establish when and if lineage restrictions occur.     

Cryptic genetic variation can make “irreducible complexity” a common mode of adaptation in sexual populations

The existence of complex (multiple‐step) genetic adaptations that are “irreducible” (i.e., all partial combinations are less fit than the original genotype) is one of the longest standing problems in evolutionary biology. In standard genetics parlance, these adaptations require the crossing of a wide adaptive valley of deleterious intermediate stages. Here, we demonstrate, using a simple model, that evolution can cross wide valleys to produce “irreducibly complex” adaptations by making use of previously cryptic mutations. When revealed by an evolutionary capacitor, previously cryptic mutants have higher initial frequencies than do new mutations, bringing them closer to a valley‐crossing saddle in allele frequency space. Moreover, simple combinatorics implies an enormous number of candidate combinations exist within available cryptic genetic variation. We model the dynamics of crossing of a wide adaptive valley after a capacitance event using both numerical simulations and analytical approximations. Although individual valley crossing events become less likely as valleys widen, by taking the combinatorics of genotype space into account, we see that revealing cryptic variation can cause the frequent evolution of complex adaptations.     

Sub-Optimal Allocation of Time in Sequential Movements

The allocation of limited resources such as time or energy is a core problem that organisms face when planning complex actions. Most previous research concerning planning of movement has focused on the planning of single, isolated movements. Here we investigated the allocation of time in a pointing task where human subjects attempted to touch two targets in a specified order to earn monetary rewards. Subjects were required to complete both movements within a limited time but could freely allocate the available time between the movements. The time constraint presents an allocation problem to the subjects: the more time spent on one movement, the less time is available for the other. In different conditions we assigned different rewards to the two tokens. How the subject allocated time between movements affected their expected gain on each trial. We also varied the angle between the first and second movements and the length of the second movement. Based on our results, we developed and tested a model of speed-accuracy tradeoff for sequential movements. Using this model we could predict the time allocation that would maximize the expected gain of each subject in each experimental condition. We compared human performance with predicted optimal performance. We found that all subjects allocated time sub-optimally, spending more time than they should on the first movement even when the reward of the second target was five times larger than the first. We conclude that the movement planning system fails to maximize expected reward in planning sequences of as few as two movements and discuss possible interpretations drawn from economic theory.     

Sine-Gordon Equation in (1+2) and (1+3) dimensions: Existence and Classification of Traveling-Wave Solutions

The (1+1)-dimensional Sine-Gordon equation passes integrability tests commonly applied to nonlinear evolution equations. Its kink solutions (one-dimensional fronts) are obtained by a Hirota algorithm. In higher space-dimensions, the equation does not pass these tests. Although it has been derived over the years for quite a few physical systems that have nothing to do with Special Relativity, the Sine-Gordon equation emerges as a non-linear relativistic wave equation. This opens the way for exploiting the tools of the Theory of Special Relativity. Using no more than the relativistic kinematics of tachyonic momentum vectors, from which the solutions are constructed through the Hirota algorithm, the existence and classification of N-moving-front solutions of the (1+2)- and (1+3)-dimensional equations for all N ≥ 1 are presented. In (1+2) dimensions, each multi-front solution propagates rigidly at one velocity. The solutions are divided into two subsets: Solutions whose velocities are lower than a limiting speed, c = 1, or are greater than or equal to c. To connect with concepts of the Theory of Special Relativity, c will be called “the speed of light.” In (1+3)-dimensions, multi-front solutions are characterized by spatial structure and by velocity composition. The spatial structure is either planar (rotated (1+2)-dimensional solutions), or genuinely three-dimensional – branes. Planar solutions, propagate rigidly at one velocity, which is lower than, equal to, or higher than c. Branes must contain clusters of fronts whose speed exceeds c = 1. Some branes are “hybrids”: different clusters of fronts propagate at different velocities. Some velocities may be lower than c but some must be equal to, or exceed, c. Finally, the speed of light cannot be approached from within the subset of slower-than-light solutions in both (1+2) and (1+3) dimensions.