Front propagation in spatially modulated media

A two-dimensional reaction-diffusion front which propagates in a modulated medium is studied. The modulation consists of a spatial variation of the local front velocity in the transverse direction to that of the front propagation. We study analytically and numerically the final steady-state velocity and shape of the front, resulting from a nontrivial interplay between the local curvature effects and the global competition process between different maxima of the control parameter. The transient dynamics of the process is also studied numerically and analytically by means of singular perturbation techniques.

Front propagation in spatially modulated media

A two-dimensional reaction-diffusion front which propagates in a modulated medium is studied. The modulation consists of a spatial variation of the local front velocity in the transverse direction to that of the front propagation. We study analytically and numerically the final steady-state velocity and shape of the front, resulting from a nontrivial interplay between the local curvature effects and the global competition process between different maxima of the control parameter. The transient dynamics of the process is also studied numerically and analytically by means of singular perturbation techniques.

Auditory-somatosensory multisensory interactions are spatially modulated by stimulated body surface and acoustic spectra

Previous research has provided inconsistent results regarding the spatial modulation of auditory-somatosensory interactions. The present study reports three experiments designed to investigate the nature of these interactions in the space close to the head. Human participants made speeded detection responses to unimodal auditory, somatosensory, or simultaneous auditory-somatosensory stimuli. In Experiment 1, electrocutaneous stimuli were presented to either earlobe, while auditory stimuli were presented from the same versus opposite sides, and from one of two distances (20 vs. 70cm) from the participant's head. The results demonstrated a spatial modulation of auditory-somatosensory interactions when auditory stimuli were presented from close to the head. In Experiment 2, electrocutaneous stimuli were delivered to the hands, which were placed either close to or far from the head, while the auditory stimuli were again presented at one of two distances. The results revealed that the spatial modulation observed in Experiment 1 was specific to the particular body part stimulated (head) rather than to the region of space (i.e. around the head) where the stimuli were presented. The results of Experiment 3 demonstrate that sounds that contain high-frequency components are particularly effective in eliciting this auditory-somatosensory spatial effect. Taken together, these findings help to resolve inconsistencies in the previous literature and suggest that auditory-somatosensory multisensory integration is modulated by the stimulated body surface and acoustic spectra of the stimuli presented.

Effective potential of two coupled binary matter wave bright solitons with spatially modulated nonlinearity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Evolutions of matter-wave bright soliton with spatially modulated nonlinearity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Self-trapping of Fermi and Bose gases under spatially modulated repulsive nonlinearity and transverse confinement

We show that self-localized ground states can be created in the spin-balanced gas of fermions with repulsion between the spin components, whose strength grows from the center to periphery, in combination with the harmonic-oscillator (HO) trapping potential acting in one or two transverse directions. We also consider the ground state in the noninteracting Fermi gas under the action of the spatially growing tightness of the one- or two-dimensional (1D or 2D) HO confinement. These settings are considered in the framework of the Thomas-Fermi-von Weizsäcker (TF-vW) density functional. It is found that the vW correction to the simple TF approximation (the gradient term) is nearly negligible in all situations. The properties of the ground state under the action of the 2D and 1D HO confinement with the tightness growing in the transverse directions are investigated too for the Bose-Einstein condensate with the self-repulsive nonlinearity. © 2013 American Physical Society.

Bright solitons in quasi-one-dimensional dipolar condensates with spatially modulated interactions

We introduce a model for the condensate of dipolar atoms or molecules, in which the dipole-dipole interaction (DDI) is periodically modulated in space due to a periodic change of the local orientation of the permanent dipoles, imposed by the corresponding structure of an external field (the necessary field can be created, in particular, by means of magnetic lattices, which are available to the experiment). The system represents a realization of a nonlocal nonlinear lattice, which has a potential to support various spatial modes. By means of numerical methods and variational approximation (VA), we construct bright one-dimensional solitons in this system and study their stability. In most cases, the VA provides good accuracy and correctly predicts the stability by means of the Vakhitov-Kolokolov criterion. It is found that the periodic modulation may destroy some solitons, which exist in the usual setting with unmodulated DDI and can create stable solitons in other cases, not verified in the absence of modulations. Unstable solitons typically transform into persistent localized breathers. The solitons are often mobile, with inelastic collisions between them leading to oscillating localized modes. © 2013 American Physical Society.

Modelling responses to spatially fractionated radiation fields using preclinical image-guided radiotherapy

OBJECTIVES: Radiotherapy is planned to achieve the optimal physical dose distribution to the target tumour volume whilst minimising dose to the surrounding normal tissue. Recent in vitro experimental evidence has demonstrated an important role for intercellular communication in radiobiological responses following non-uniform exposures. This study aimed to model the impact of these effects in the context of techniques involving highly modulated radiation fields or spatially fractionated treatments such as GRID therapy.

METHODS: Using the small animal radiotherapy research platform (SARRP) as a key enabling technology to deliver precision imaged-guided radiotherapy, it is possible to achieve spatially modulated dose distributions that model typical clinical scenarios. In this work, we planned uniform and spatially fractionated dose distributions using multiple isocentres with beam sizes of 0.5 - 5 mm to obtain 50% volume coverage in a subcutaneous murine tumour model, and applied a model of cellular response that incorporates intercellular communication to assess the potential impact of signalling effects with different ranges.

RESULTS: Models of GRID treatment plans which incorporate intercellular signalling showed increased cell killing within the low dose region. This results in an increase in the Equivalent Uniform Dose (EUD) for GRID exposures compared to standard models, with some GRID exposures being predicted to be more effective than uniform delivery of the same physical dose.

CONCLUSIONS: This study demonstrates the potential impact of radiation induced signalling on tumour cell response for spatially fractionated therapies and identifies key experiments to validate this model and quantify these effects in vivo.

ADVANCES IN KNOWLEDGE: This study highlights the unique opportunities now possible using advanced preclinical techniques to develop a foundation for biophysical optimisation in radiotherapy treatment planning.

Localization of collisionally inhomogeneous condensates in a bichromatic optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Distribuição ecológica e dinâmica populacional do camarão barriga branca Nematopalaemon schmitti (Holthuis, 1950) (Caridea, Palaemonidae) na região de Macaé-RJ, Brasil

Pós-graduação em Ciências Biológicas (Zoologia) - IBB

Estabilidade de vórtices em condensados de Bose-Einstein

Neste trabalho de mestrado é estudada a estabilidade de vórtices em condensados de Bose-Einstein com interação atrativa entre os átomos através da solução numérica da equação de Gross-Pitaevskii. Inicialmente são reproduzidos resultados da literatura, nos quais são estudados vórtices em condensados bidimensionais atrativos com potencial interatômico homogêneo em todo o condensado. A estabilidade de tais sistemas é inferida através da solução numérica das equações de Bogoliubov-de Gennes e da evolução temporal dos vórtices. Demonstra-se que esses vórtices são estáveis, até um certo número crítico de átomos, apenas para valores de vorticidade S=1. Em seguida foi proposto um modelo no qual a interação entre os átomos é espacialmente modulada. Neste caso é possível demonstrar que vórtices com valores de vorticidade de até S=6, pelo menos, são estáveis. Finalmente é estudada a estabilidade de vórtices em condensados tridimensionais atrativos, novamente com potencial interatômico homogêneo em todo o condensado. Assim como no caso bidimensional mostra-se que tais vórtices são estáveis para valores de vorticidade de S=1. Espera-se em breve estudar a estabilidade de vórtices em condesados tridimensionais com potencial de interação espacialmente modulado.

Neuronal convergence in early contrast vision: binocular summation is followed by response nonlinearity and area summation

We assessed summation of contrast across eyes and area at detection threshold ( C t). Stimuli were sine-wave gratings (2.5 c/deg) spatially modulated by cosine- and anticosine-phase raised plaids (0.5 c/deg components oriented at ±45°). When presented dichoptically the signal regions were interdigitated across eyes but produced a smooth continuous grating following their linear binocular sum. The average summation ratio ( C t1/([ C t1+2]) for this stimulus pair was 1.64 (4.3 dB). This was only slightly less than the binocular summation found for the same patch type presented to both eyes, and the area summation found for the two different patch types presented to the same eye. We considered 192 model architectures containing each of the following four elements in all possible orders: (i) linear summation or a MAX operator across eyes, (ii) linear summation or a MAX operator across area, (iii) linear or accelerating contrast transduction, and (iv) additive Gaussian, stochastic noise. Formal equivalences reduced this to 62 different models. The most successful four-element model was: linear summation across eyes followed by nonlinear contrast transduction, linear summation across area, and late noise. Model performance was enhanced when additional nonlinearities were placed before binocular summation and after area summation. The implications for models of probability summation and uncertainty are discussed.

Excitation and damping of a self-modulated laser wakefield

Spatially, temporally, and angularly resolved collinear collective Thomson scattering was used to diagnose the excitation and damping of a relativistic-phase-velocity self-modulated laser wakefield. The excitation of the electron plasma wave was observed to be driven by Raman-type instabilities. The damping is believed to originate from both electron beam loading and modulational instability. The collective Thomson scattering of a probe pulse from the ion acoustic waves, resulting from modulational instability, allows us to measure the temporal evolution of the plasma temperature. The latter was found to be consistent with the damping of the electron plasma wave.

Kink stability, propagation, and length-scale competition in the periodically modulated sine-gordon equation

We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on this and related nonlinear problems in four directions. First, we present the results of a numerical simulation program that are not compatible with the existence of a radiative threshold predicted by earlier calculations. Second, we carry out a perturbative calculation that helps interpret those previous predictions, enabling us to understand in depth our numerical results. Third, we apply the collective coordinate formalism to this system and demonstrate numerically that it reproduces accurately the observed kink dynamics. Fourth, we report on the occurrence of length-scale competition in this system and show how it can be understood by means of linear stability analysis. Finally, we conclude by summarizing the general physical framework that arises from our study.

Fourth-root summation of contrast over area:no end in sight when spatially inhomogeneous sensitivity is compensated by a witch's hat

Measurements of area summation for luminance-modulated stimuli are typically confounded by variations in sensitivity across the retina. Recently we conducted a detailed analysis of sensitivity across the visual field (Baldwin et al, 2012) and found it to be well-described by a bilinear “witch’s hat” function: sensitivity declines rapidly over the first 8 cycles or so, more gently thereafter. Here we multiplied luminance-modulated stimuli (4 c/deg gratings and “Swiss cheeses”) by the inverse of the witch’s hat function to compensate for the inhomogeneity. This revealed summation functions that were straight lines (on double log axes) with a slope of -1/4 extending to ≥33 cycles, demonstrating fourth-root summation of contrast over a wider area than has previously been reported for the central retina. Fourth-root summation is typically attributed to probability summation, but recent studies have rejected that interpretation in favour of a noisy energy model that performs local square-law transduction of the signal, adds noise at each location of the target and then sums over signal area. Modelling shows our results to be consistent with a wide field application of such a contrast integrator. We reject a probability summation model, a quadratic model and a matched template model of our results under the assumptions of signal detection theory. We also reject the high threshold theory of contrast detection under the assumption of probability summation over area.