On the eigenvalues of the spatial sign covariance matrix in more than two dimensions

Acknowledgments Alexander Dürre was supported in part by the Collaborative Research Grant 823 of the German Research Foundation. David E. Tyler was supported in part by the National Science Foundation grant DMS-1407751. A visit of Daniel Vogel to David E. Tyler was supported by a travel grant from the Scottish Universities Physics Alliance. The authors are grateful to the editors and referees for their constructive comments.

ON TWO-DIMENSIONAL QUASITOPOLOGICAL FIELD THEORIES

We study a class of lattice field theories in two dimensions that includes gauge theories. We show that in these theories it is possible to implement a broader notion of local symmetry, based on semisimple Hopf algebras. A character expansion is developed for the quasitopological field theories, and partition functions are calculated with this tool. Expected values of generalized Wilson loops are defined and studied with the character expansion.

Two-dimensional balanced sampling plans excluding contiguous units

A balanced sampling plan excluding contiguous units (or BSEC for short) was first introduced by Hedayat, Rao and Stufken in 1988. These designs can be used for survey sampling when the units are arranged in one-dimensional ordering and the contiguous units in this ordering provide similar information. In this paper, we generalize the concept of a BSEC to the two-dimensional situation and give constructions of two-dimensional BSECs with block size 3. The existence problem is completely solved in the case where lambda = 1.

The relationship of adult attachment dimensions to depression and agoraphobia

We examined the unique relations between the five dimensions of the Attachment Style Questionnaire (ASQ; Feeney, Noller, & Hanrahan, 1994) and depression and agoraphobic behavior (i.e., avoidance of situations where high anxiety is experienced). In addition, we examined mediation models in an attempt to clarify the link between adult attachment and these two dimensions of psychopathology. In testing these models, we administered the ASQ, General Self-Efficacy Scale, Agoraphobic Catastrophic Cognitions Questionnaire, Beck Depression Inventory, and the Mobility Inventory for Agoraphobia (a measure of the degree to which situations are avoided that are typically anxiety provoking for people with agoraphobia) to 122 participants (44 with agoraphobia, 25 with a current major depressive disorder, and 53 with no current psychopathology). The results showed that the insecure attachment dimensions of need for approval, preoccupation with relationships, and relationships as secondary were uniquely associated with depression and that general self-efficacy partly mediated the relationship between need for approval and depression. In contrast, only preoccupation with relationships was uniquely associated with agoraphobic behavior, and catastrophic cognitions about bodily sensations partly mediated this association.

Fronts from two-dimensional dispersal kernels: Beyond the nonoverlapping-generations model

Most integrodifference models of biological invasions are based on the nonoverlapping-generations approximation. However, the effect of multiple reproduction events overlapping generations on the front speed can be very important especially for species with a long life spam . Only in one-dimensional space has this approximation been relaxed previously, although almost all biological invasions take place in two dimensions. Here we present a model that takes into account the overlapping generations effect or, more generally, the stage structure of the population , and we analyze the main differences with the corresponding nonoverlappinggenerations results

Fronts from complex two-dimensional dispersal kernels: theory and application to Reid's paradox

Bimodal dispersal probability distributions with characteristic distances differing by several orders of magnitude have been derived and favorably compared to observations by Nathan [Nature (London) 418, 409 (2002)]. For such bimodal kernels, we show that two-dimensional molecular dynamics computer simulations are unable to yield accurate front speeds. Analytically, the usual continuous-space random walks (CSRWs) are applied to two dimensions. We also introduce discrete-space random walks and use them to check the CSRW results (because of the inefficiency of the numerical simulations). The physical results reported are shown to predict front speeds high enough to possibly explain Reid's paradox of rapid tree migration. We also show that, for a time-ordered evolution equation, fronts are always slower in two dimensions than in one dimension and that this difference is important both for unimodal and for bimodal kernels

Fronts from complex two-dimensional dispersal kernels: theory and application to Reid's paradox

Bimodal dispersal probability distributions with characteristic distances differing by several orders of magnitude have been derived and favorably compared to observations by Nathan [Nature (London) 418, 409 (2002)]. For such bimodal kernels, we show that two-dimensional molecular dynamics computer simulations are unable to yield accurate front speeds. Analytically, the usual continuous-space random walks (CSRWs) are applied to two dimensions. We also introduce discrete-space random walks and use them to check the CSRW results (because of the inefficiency of the numerical simulations). The physical results reported are shown to predict front speeds high enough to possibly explain Reid's paradox of rapid tree migration. We also show that, for a time-ordered evolution equation, fronts are always slower in two dimensions than in one dimension and that this difference is important both for unimodal and for bimodal kernels

Psychophysiological responses to appraisal dimensions in a computer game

A computer game was used to study psychophysiological reactions to emotion-relevant events. Two dimensions proposed by Scherer (1984a, 1984b) in his appraisal theory, the intrinsic pleasantness and goal conduciveness of game events, were studied in a factorial design. The relative level at which a player performed at the moment of an event was also taken into account. A total of 33 participants played the game while cardiac activity, skin conductance, skin temperature, and muscle activity as well as emotion self-reports were assessed. The self-reports indicate that game events altered levels of pride, joy, anger, and surprise. Goal conduciveness had little effect on muscle activity but was associated with significant autonomic effects, including changes to interbeat interval, pulse transit time, skin conductance, and finger temperature. The manipulation of intrinsic pleasantness had little impact on physiological responses. The results show the utility of attempting to manipulate emotion-constituent appraisals and measure their peripheral physiological signatures.

An efficient numerical scheme for the two-dimensional shallow water equations using arithmetic averaging

A finite difference scheme based on flux difference splitting is presented for the solution of the two-dimensional shallow water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gas dynamics is defined, and a scheme, based on numerical characteristic decomposition is presented for obtaining approximate solutions to the linearised problem, and incorporates the technique of operator splitting. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver, where the computational expense can be prohibitive. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids nonphysical, spurious oscillations. An extension to the two-dimensional equations with source terms is included. The scheme is applied to the one-dimensional problems of a breaking dam and reflection of a bore, and in each case the approximate solution is compared to the exact solution of ideal fluid flow. The scheme is also applied to a problem of stationary bore generation in a channel of variable cross-section. Finally, the scheme is applied to two other dam-break problems, this time in two dimensions with one having cylindrical symmetry. Each approximate solution compares well with those given by other authors.

A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation

We present a variable time step, fully adaptive in space, hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions. The method is based on the hybrid level set/front-tracking approach proposed in [H. D. Ceniceros and A. M. Roma, J. Comput. Phys., 205, 391400, 2005]. Geometric, interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance (level set) function, which is evaluated fast and to machine precision, is used as a fluid indicator. The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in [S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, J. Comput. Phys., 203, 493-516, 2005] whose success for greatly reducing parasitic currents has been demonstrated. The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude. To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic, adaptive mesh refinements. This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step, linearly implicit time integration scheme. We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications: the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability, an example of bubble ascending dynamics, and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.

Numerical solution of the two-dimensional Gross-Pitaevskii equation for trapped interacting atoms

We present a numerical scheme for solving the time-independent nonlinear Gross-Pitaevskii equation in two dimensions describing the Bose-Einstein condensate of trapped interacting neutral atoms at zero temperature. The trap potential is taken to be of the harmonic-oscillator type and the interaction both attractive and repulsive. The Gross-Pitaevskii equation is numerically integrated consistent with the correct boundary conditions at the origin and in the asymptotic region. Rapid convergence is obtained in all cases studied. In the attractive case there is a limit Co the maximum number of atoms in the condensate. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

Dimensional reduction of a binary Bose-Einstein condensate in mixed dimensions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

MODEL INDEPENDENCE OF SCATTERING OF 3 IDENTICAL BOSONS IN 2 DIMENSIONS

Within the framework of scattering integral equations in momentum space, we present numerical results of scattering of three identical bosons at low energies in two dimensions for short-range separable potentials. An analysis of the present numerical results reveals the three-particle scattering observables to be independent of potential shape provided the low-energy two-particle binding energy and scattering length are held fixed throughout the investigation. We think that the present conclusion of model independence will be valid for any potential, local or nonlocal, whose range is much smaller than the size of the two-particle bound state.

Quadratic effective action for QED in D=2,3 dimensions

We calculate the effective action for quantum electrodynamics (QED) in D=2,3 dimensions at the quadratic approximation in the gauge fields. We analyze the analytic structure of the corresponding nonlocal boson propagators nonperturbatively in k/m. In two dimensions for any nonzero fermion mass, we end up with one massless pole for the gauge boson. We also calculate in D=2 the effective potential between two static charges separated by a distance L and find it to be a linearly increasing function of L in agreement with the bosonized theory (massive sine-Gordon model). In three dimensions we find nonperturbatively in k/m one massive pole in the effective bosonic action leading to screening. Fitting the numerical results we derive a simple expression for the functional dependence of the boson mass upon the dimensionless parameter e2/m. ©2000 The American Physical Society.

The importance of vertical and horizontal dimensions of the sediment matrix in structuring nematodes across spatial scales

Intensive surveys have been conducted to unravel spatial patterns of benthic infauna communities. Although it has been recognized that benthic organisms are spatially structured along the horizontal and vertical dimensions of the sediment, little is known on how these two dimensions interact with each other. In this study we investigated the interdependence between the vertical and horizontal dimensions in structuring marine nematodes assemblages. We tested whether the similarity in nematode species composition along the horizontal dimension was dependent on the vertical layer of the sediment. To test this hypothesis, three-cm interval sediment samples (15 cm depth) were taken independently from two bedforms in three estuaries. Results indicated that assemblages living in the top layers are more abundant, species rich and less variable, in terms of species presence/absence and relative abundances, than assemblages living in the deeper layers. Results showed that redox potential explained the greatest amount (12%) of variability in species composition, more than depth or particle size. The fauna inhabiting the more oxygenated layers were more homogeneous across the horizontal scales than those from the reduced layers. In contrast to previous studies, which suggested that reduced layers are characterized by a specific set of tolerant species, the present study showed that species assemblages in the deeper layers are more causal (characterized mainly by vagrant species). The proposed mechanism is that at the superficial oxygenated layers, species have higher chances of being resuspended and displaced over longer distances by passive transport, while at the deeper anoxic layers they are restricted to active dispersal from the above and nearby sediments. Such restriction in the dispersal potential together with the unfavorable environmental conditions leads to randomness in the presence of species resulting in the high variability between assemblages along the horizontal dimension.