Rotation of a nanoparticle cloud in an inductively coupled plasma induced by weak static magnetic fields

Hydrocarbon nanoparticles with diameters between 10 and 30 nanometres are created in a low pressure plasma combining capacitive and inductive power coupling. The particles are generated in the capacitive phase of the experiment and stay confined in the plasma in the inductive phase. The presence of these embedded particles induces a rotation of a particle-free region (void) around the symmetry axis of the reactor. The phenomenon is analysed using optical emission spectroscopy both line integrated and spatially resolved via an intensified charge coupled device camera. From these data, electron temperatures and densities are deduced. We find that the rotation of the void is driven by a tangential component of the ion drag force induced by an external static magnetic field. Two modes are observed: a fast rotation of the void in the direction opposite to that of the tangential component and a slow rotation in the same direction. The rotation speed decreases linearly with the size of the particles. In the fast mode the dependence on the applied magnetic field is weak and consequently the rotation speed can serve as a monitor to detect particle sizes in low temperature plasmas.

On weak and strong Peano theorems

We say that the Peano theorem holds for a topological vector space $E$ if, for any continuous mapping $f : {\Bbb R}\times E \to E$ and any $(t(0), x(0))$ is an element of ${\Bbb R}\times E$, the Cauchy problem $\dot x(t) = f(t,x(t))$, $x(t(0)) = x(0)$, has a solution in some neighborhood of $t(0)$. We say that the weak version of Peano theorem holds for $E$ if, for any continuous map $f : {\Bbb R}\times E \to E$, the equation $\dot x(t) = f (t, x(t))$ has a solution on some interval. We construct an example (answering a question posed by S. G. Lobanov) of a Hausdorff locally convex topological vector space E for which the weak version of Peano theorem holds and the Peano theorem fails to hold. We also construct a Hausdorff locally convex topological vector space E for which the Peano theorem holds and any barrel in E is neither compact nor sequentially compact.

Three constructive examples of separable pre-Hilbert spaces nonisomorphic to their closed hyperplanes

An example of a sigma -compact infinite-dimensional pre-Hilbert space H is constructed such that any continuous linear operator T: H --> H is of the form T = lambdaI + F for some lambda is an element of R and for a finite-dimensional continuous linear operator F. A class of simple examples of pre-Hilbert spaces nonisomorphic to their closed hyperplanes is given. A sigma -compact pre-Hilbert space H isomorphic to H x R x R and nonisomorphic to H x R is also constructed.

An infinite-dimensional separable pre-Hilbert space non-homeomorphic to any of its closed hyperplanes

An example is constructed of an infinite-dimensional separable pre-Hilbert space non-homeomorphic to any of its closed hyperplanes.

Fighting for shells: how private information about resource value changes hermit crab pre-fight displays and escalated fight behaviour

Pre-fight displays typically provide honest, but sometimes dishonest, information about resource holding potential and may be influenced by assessment of resource value and hence motivation to acquire the resource. These assessments of potential costs and benefits are also predicted to influence escalated fight behaviour. This is examined in shell exchange contests of hermit crabs in which we establish an information asymmetry about a particularly poor quality shell. The poor shell was created by gluing sand to the interior whereas control shells lacked sand and the low value of the poor shell could not be accurately assessed by the opponent. Crabs in the poor shell showed changes in the use of pre-fight displays, apparently to increase the chances of swapping shells. When the fights escalated, crabs in poor shells fought harder if they took the role of attacker but gave up quickly if in the defender role. These tactics appear to be adaptive but do not result in a major shift in the roles taken or outcome. We thus link resource assessment with pre-fight displays, the roles taken, tactics used during escalation and the outcome of these contests.

The effect of simultaneous contractions of ipsilateral muscles on changes in corticospinal excitability induced by paired associative stimulation (PAS)

Consideration was given to means of increasing the reliability and muscle specificity of paired associative stimulation (PAS) by utilising the phenomenon of crossed-facilitation. Eight participants completed three separate sessions: isometric flexor contractions of the left wrist at 20% of maximum voluntary contraction (MVC) simultaneously with PAS (20s intervals; 14 min duration) delivered at the right median nerve and left primary motor cortex (MI); isometric contractions at 20% of MVC: and PAS only ( 14 min). Eight further participants completed two sessions of longer duration PAS (28 min): either alone or in conjunction with flexion contractions of the left wrist. Thirty motor potentials (MEPs) were evoked in the right flexor (rFCR) and extensor (rECR) carpi radialis muscles by magnetic stimulation of left M1 Prior to the interventions, immediately post-intervention, and 10 min post-intervention. Both 14 and 28 min of combined PAS and (left wrist flexion) contractions resulted in reliable increases in rFCR MEP amplitude, which were not present in rECR. In the PAS only conditions, 14 min of stimulation gave rise to unreliable increases in MEP amplitudes in rFCR and rECR, whereas 28 min of PAS induced small (unreliable) changes only for rFCR. These results support the conclusion that changes in the excitability of the corticospinal pathway induced by PAS interact with those associated with contraction of the muscles ipsilateral to the site of cortical stimulation. Furthermore, focal contractions applied by the opposite limb increase the extent and muscle specificity of the induced changes in excitability associated with PAS. (C) 2008 Elsevier Ireland Ltd. All rights reserved.

Muscle-specific variations in use-dependent crossed-facilitation of corticospinal pathways mediated by transcranial direct current (DC) stimulation

The tendency for contractions of muscles in the upper limb to give rise to increases in the excitability of corticospinal projections to the homologous muscles of the opposite limb is well known. Although the suppression of this tendency is integral to tasks of daily living, its exploitation may prove to be critical in the rehabilitation of acquired hemiplegias. Transcranial direct current (DC) stimulation induces changes in cortical excitability that outlast the period of application. We present evidence that changes in the reactivity of the corticospinal pathway induced by DC stimulation of the motor cortex interact systematically with those brought about by contraction of the muscles of the ipsilateral limb. During the application of flexion torques (up to 50% of maximum) applied at the left wrist, motor evoked potentials (MEPs) were evoked in the quiescent muscles of the right arm by magnetic stimulation of the left motor cortex (M1). The MEPs were obtained prior to and following 10 min of anodal, cathodal or sham DC stimulation of left M1. Cathodal stimulation counteracted increases in the crossed-facilitation of projections to the (right) wrist flexors that otherwise occurred as a result of repeated flexion contractions at the left wrist. In addition, cathodal stimulation markedly decreased the excitability of corticospinal projections to the wrist extensors of the right limb. Thus changes in corticospinal excitability induced by DC stimulation can be shaped (i.e. differentiated by muscle group) by focal contractions of muscles in the limb ipsilateral to the site of stimulation. (C) 2008 Elsevier Ireland Ltd. All rights reserved.

Reliability of the input-output properties of the cortico-spinal pathway obtained from transcranial magnetic and electrical stimulation

The purpose of this experiment was to assess the test-retest reliability of input-output parameters of the cortico-spinal pathway derived from transcranial magnetic (TMS) and electrical (TES) stimulation at rest and during muscle contraction. Motor evoked potentials (MEPs) were recorded from the first dorsal interosseous muscle of eight individuals on three separate days. The intensity of TMS at rest was varied from 5% below threshold to the maximal output of the stimulator. During trials in which the muscle was active, TMS and TES intensities were selected that elicited MEPs of between 150 and 300 X at rest. MEPs were evoked while the participants exerted torques up to 50% of their maximum capacity. The relationship between MEP size and stimulus intensity at rest was sigmoidal (R-2 = 0.97). Intra-class correlation coefficients (ICC) ranged between 0.47 and 0.81 for the parameters of the sigmoid function. For the active trials, the slope and intercept of regression equations of MEP size on level of background contraction were obtained more reliably for TES (ICC = 0.63 and 0.78, respectively) than for TMS (ICC = 0.50 and 0.53, respectively), These results suggest that input-output parameters of the cortico-spinal pathway may be reliably obtained via transcranial stimulation during longitudinal investigations of cortico-spinal plasticity. (C) 2001 Elsevier Science B.V. All rights reserved.