Critical number of atoms for attractive Bose-Einstein condensates with cylindrically symmetrical traps

The critical number of atoms for Bose-Einstein condensates with cylindrically symmetrical traps were calculated. The time evolution of the condensate was also studied at changing ground state. A conjecture on higher-order nonlinear effects was also discussed to determine its signal and strength. The results show that by exchanging frequencies, the geometry favors the condensation of larger number of particles.

Effect of anharmonicities in the critical number of trapped condensed atoms with an attractive two-body interaction

The quantitative effect in the maximum number of particles and other static observables was determined. A deviation in the harmonic trap potential that is effective only outside the central part of the potential, with the addition of a term that is proportional to a cubic or quartic power of the distance was considered. Results showed that this study could be easily transferred to other trap geometries to estimate anharmonic effects.

Critical numbers of attractive Bose-Einstein condensed atoms in asymmetric traps

A quantitative analysis of the critical number of attractive Bose-Einstein condensed atoms in asymmetric traps was studied. The Gross-Pitaevskii (GP) formalism for an atomic system with arbitrary nonspherically symmetric harmonic trap was also discussed. Characteristic limits were obtained for reductions from three to two and one dimensions from three to two and one dimensions, in perfect cylindrical symmetries as well as in deformed ones.

Critical evaluation of FBD, pq and CPT current decompositions for four-wire circuits

This paper investigates the major similarities and discrepancies of three important current decompositions proposed for the interpretation of unbalanced and/or non linear three-phase four-wire circuits. The considered approaches were the so-called FBD Theory, the pq-Theory and the CPT. Although the methods are based on different concepts, the results obtained under ideal conditions (sinusoidal and balanced signals) are very similar. The main differences appear in the presence of unbalanced and non linear load conditions. It will be demonstrated and discussed how the choice of the voltage referential and the return conductor impedance can influence in the resulting current components, as well as, the way of interpreting a power circuit with return conductor. Under linear unbalanced conditions, both FBD and pq-Theory suggest that the some current components contain a third-order harmonic. Besides, neither pq-Theory nor FBD method are able to provide accurate information for reactive current under unbalanced and distorted conditions, what seems to be done by means of the CPT. © 2009 IEEE.

A Commentary on de Sousa′s towards an Integrative Theory of Consciousness

De Sousa′s comprehensive two-part review of a diversity of contemporary approaches to the study of consciousness is highly welcome. He makes us aware of a proliferation of theoretical and empirical approaches targeting a common theme, but diverging in many ways. He skilfully accomplishes a classification of kinds of approach, identification of the main representatives, their contributions, and respective limitations. However, he does not show how the desired integration could be accomplished. Besides summarising de Sousa′s efficient analytical work, I make critical comments and briefly report my contribution for the integration project.© MSM 2013.

A critical analysis of the ubiquity of linear local-regional richness relationships

Synthesis Despite theoretical criticisms, the ubiquity of linear relationships between local and regional species richness has long been used to justify it as a valid framework to conclude that local communities are not saturated with species. However, we reanalyzed published studies with a new unbiased method and found no prevalence of linear relationships and more than 40% of misclassifications, including textbook examples. We thus conclude that the prevailing argument in favor of associating a valid ecological interpretation to local-regional species richness plots, its ubiquity, is not sustained, and that ecologists could use for instance metacommunity theory to make inference on the strength of local and regional processes. Identifying the relative importance of regional and local processes to local species diversity is a central issue to many questions in basic and applied ecology. One widely-used method is to plot local species richness against its regional richness to infer whether regional or local processes determine local diversity. However, this method increases the tendency to find regional prevalence as suggested by a recent simulation. We reanalyzed studies in the literature with an unbiased method and found no prevalence of either regional or local processes. In addition, almost 40% of the studies and 50% of the ecology textbook examples using the traditional method were misclassified. Our findings reinforce the need of alternative, novel tools identified by for instance metacommunity theory to go beyond the studies of local-regional relationships in the ecological literature that focus on the interdependence of regional and local processes.© 2013 The Authors. Oikos © 2013 Nordic Society Oikos.

Planning “Discrete” Movements Using a Continuous System: Insights from a Dynamic Field Theory of Movement Preparation

The timed-initiation paradigm developed by Ghez and colleagues (1997) has revealed two modes of motor planning: continuous and discrete. Continuous responding occurs when targets are separated by less than 60° of spatial angle, and discrete responding occurs when targets are separated by greater than 60°. Although these two modes are thought to reflect the operation of separable strategic planning systems, a new theory of movement preparation, the Dynamic Field Theory, suggests that two modes emerge flexibly from the same system. Experiment 1 replicated continuous and discrete performance using a task modified to allow for a critical test of the single system view. In Experiment 2, participants were allowed to correct their movements following movement initiation (the standard task does not allow corrections). Results showed continuous planning performance at large and small target separations. These results are consistent with the proposal that the two modes reflect the time-dependent “preshaping” of a single planning system.

Dynamics, rheology and critical properties of colloidal fluid mixtures

Liquids under the influence of external fields exhibit a wide range of intriguing phenomena that can be markedly different from the behaviour of a quiescent system. This work considers two different systems — a glassforming Yukawa system and a colloid-polymer mixture — by Molecular Dynamics (MD) computer simulations coupled to dissipative particle dynamics. The former consists of a 50-50 binary mixture of differently-sized, like-charged colloids interacting via a screened Coulomb (Yukawa) potential. Near the glass transition the influence of an external shear field is studied. In particular, the transition from elastic response to plastic flow is of interest. At first, this model is characterised in equilibrium. Upon decreasing temperature it exhibits the typical dynamics of glassforming liquids, i.e. the structural relaxation time τα grows strongly in a rather small temperature range. This is discussed with respect to the mode-coupling theory of the glass transition (MCT). For the simulation of bulk systems under shear, Lees-Edwards boundary conditions are applied. At constant shear rates γ˙ ≫ 1/τα the relevant time scale is given by 1/γ˙ and the system shows shear thinning behaviour. In order to understand the pronounced differences between a quiescent system and a system under shear, the response to a suddenly commencing or terminating shear flow is studied. After the switch-on of the shear field the shear stress shows an overshoot, marking the transition from elastic to plastic deformation, which is connected to a super-diffusive increase of the mean squared displacement. Since the average static structure only depends on the value of the shear stress, it does not discriminate between those two regimes. The distribution of local stresses, in contrast, becomes broader as soon as the system starts flowing. After a switch-off of the shear field, these additional fluctuations are responsible for the fast decay of stresses, which occurs on a time scale 1/γ˙ . The stress decay after a switch-off in the elastic regime, on the other hand, happens on the much larger time scale of structural relaxation τα. While stresses decrease to zero after a switch-off for temperatures above the glass transition, they decay to a finite value for lower temperatures. The obtained results are important for advancing new theoretical approaches in the framework of mode-coupling theory. Furthermore, they suggest new experimental investigations on colloidal systems. The colloid-polymer mixture is studied in the context of the behaviour near the critical point of phase separation. For the MD simulations a new effective model with soft interaction potentials is introduced and its phase diagram is presented. Here, mainly the equilibrium properties of this model are characterised. While the self-diffusion constants of colloids and polymers do not change strongly when the critical point is approached, critical slowing down of interdiffusion is observed. The order parameter fluctuations can be determined through the long-wavelength limit of static structure factors. For this strongly asymmetric mixture it is shown how the relevant structure factor can be extracted by a diagonalisation of a matrix that contains the partial static structure factors. By presenting first results of this model under shear it is demonstrated that it is suitable for non-equilibrium simulations as well.

Spectral theory of differential operators on finite metric graphs and on bounded domains

Die vorliegende Arbeit widmet sich der Spektraltheorie von Differentialoperatoren auf metrischen Graphen und von indefiniten Differentialoperatoren auf beschränkten Gebieten. Sie besteht aus zwei Teilen. Im Ersten werden endliche, nicht notwendigerweise kompakte, metrische Graphen und die Hilberträume von quadratintegrierbaren Funktionen auf diesen betrachtet. Alle quasi-m-akkretiven Laplaceoperatoren auf solchen Graphen werden charakterisiert, und Abschätzungen an die negativen Eigenwerte selbstadjungierter Laplaceoperatoren werden hergeleitet. Weiterhin wird die Wohlgestelltheit eines gemischten Diffusions- und Transportproblems auf kompakten Graphen durch die Anwendung von Halbgruppenmethoden untersucht. Eine Verallgemeinerung des indefiniten Operators $-tfrac{d}{dx}sgn(x)tfrac{d}{dx}$ von Intervallen auf metrische Graphen wird eingeführt. Die Spektral- und Streutheorie der selbstadjungierten Realisierungen wird detailliert besprochen. Im zweiten Teil der Arbeit werden Operatoren untersucht, die mit indefiniten Formen der Art $langlegrad v, A(cdot)grad urangle$ mit $u,vin H_0^1(Omega)subset L^2(Omega)$ und $OmegasubsetR^d$ beschränkt, assoziiert sind. Das Eigenwertverhalten entspricht in Dimension $d=1$ einer verallgemeinerten Weylschen Asymptotik und für $dgeq 2$ werden Abschätzungen an die Eigenwerte bewiesen. Die Frage, wann indefinite Formmethoden für Dimensionen $dgeq 2$ anwendbar sind, bleibt offen und wird diskutiert.

Jan Fook: Social Work: Critical Theory and Practice & Karen Healy: Social Work Practices: Contemporary Perspectives on Change

In his recent book on the contemporary politics of social work, Powell (2001) nominates Jan Fook and Karen Healy as two Australian authors who have made significant contributions to the radical or critical social work tradition. I have chosen to review them together, as each, in different ways, attempts to achieve the same purpose. That is, they attempt to provide a convincing account for adopting a critical approach to practice in the contemporary conditions of the 21st century and, in doing so, re-invigorate the radical tradition of social work practice. My first comment, important for the readership of this international journal, is that both books easily 'travel' beyond the Australian context.

Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

Deterrence and Incapacitation: Towards a Unified Theory of Criminal Punishment

Economic models of crime have focused primarily on the goal of deterrence; the goal of incapacitation has received much less attention. This paper adapts the standard deterrence model to incorporate incapacitation. When prison only is used, incapacitation can result in a longer or a shorter optimal prison term compared to the deterrence-only model. It is longer if there is underdeterrence, and shorter if there is overdeterrence. In contrast, when a fine is available and it is not constrained by the offender's wealth, the optimal prison term is zero. Since the fine achieves first-best deterrence, only efficient crimes are committed and hence, there is no gain from incapacitation.

Theory of a Flowchart Approach to Industrial Cluster Policy

A flowchart approach to industrial cluster policy emphasizes the importance ofthe ordering of policy measures. The flow of policy implementation is to establish an industrial zone, to invite an anchor company, and to promote its related companies to invest in the industrial zone. This article delineated "a flowchart approach to industrial cluster policy" by proposing sufficient conditions for forming industrial clusters typical in the manufacturing industry in Asia to enhance regional economic growth. The typical industrial cluster policy was theorized by defining an industrial zone as "quasi-public goods", and it was shown that the policy enhances economic growth under a production function of "increasing returns to scale" of an anchor company. Critical amounts of the production of "scale economies" that are used by the related companies to decide whether or not to invest in clusters were also shown.