Trajectory-based interpretation of Young's experiment, the Arago-Fresnel laws and the Poisson-Arago spot for photons and massive particles

We present a trajectory based interpretation for Young's experiment, the Arago-Fresnel laws and the Poisson-Arago spot. This approach is based on the equation of the trajectory associated with the quantum probability current density in the case of massive particles, and the Poynting vector for the electromagnetic field in the case of photons. Both the form and properties of the evaluated photon trajectories are in good agreement with the averaged trajectories of single photons observed recently in Young's experiment by Steinberg's group at the University of Toronto. In the case of the Arago-Fresnel laws for polarized light, the trajectory interpretation presented here differs from those interpretations based on the concept of "which-way" (or "which-slit") information and quantum erasure. More specifically, the observer's information about the slit that photons went through is not relevant to the existence of interference; what is relevant is the form of the electromagnetic energy density and its evolution, which will model consequently the distribution of trajectories and their topology. Finally, we also show that the distributions of end points of a large number of evaluated photon trajectories are in agreement with the distributions measured at the screen behind a circular disc, clearly giving rise to the Poisson-Arago spot.Comment: 8 pages, 5 figure

Evolution of the wave function of an atom hit by a photon in a three-grating interferometer

In 1995, Chapman et al. (1995 Phys. Rev. Lett. 75 2783) showed experimentally that the interference contrast in a three-grating atom interferometer does not vanish under the presence of scattering events with photons, as required by the complementarity principle. In this work we provide an analytical study of this experiment, determining the evolution of the atom wave function along the three-grating Mach-Zehnder interferometer under the assumption that the atom is hit by a photon after passing through the first grating. The consideration of a transverse wave function in momentum representation is essential in this study. As is shown, the number of atoms transmitted through the third grating is given by a simple periodic function of the lateral shift along this grating, both in the absence and in the presence of photon scattering. Moreover, the relative contrast (laser on/laser off) is shown to be a simple analytical function of the ratio d_p/\lambda_i, where d_p is the distance between atomic paths at the scattering locus and \lambda_i the scattered photon wavelength. We argue that this dependence, being in agreement with experimental results, can be regarded to show compatibility of the wave and corpuscle properties of atoms.Comment: 8 pages, 4 figure

Should particle trajectories comply with the transverse momentum distribution?

The momentum distributions associated with both the wave function of a particle behind a grating and the corresponding Bohmian trajectories are investigated and compared. Near the grating, it is observed that the former does not depend on the distance from the grating, while the latter changes with this distance. However, as one moves further apart from the grating, in the far field, both distributions become identical.Comment: 10 pages, 7 figure

Brain Network Connectivity During Language Comprehension: Interacting Linguistic and Perceptual Subsystems.

The dynamic neural processes underlying spoken language comprehension require the real-time integration of general perceptual and specialized linguistic information. We recorded combined electro- and magnetoencephalographic measurements of participants listening to spoken words varying in perceptual and linguistic complexity. Combinatorial linguistic complexity processing was consistently localized to left perisylvian cortices, whereas competition-based perceptual complexity triggered distributed activity over both hemispheres. Functional connectivity showed that linguistically complex words engaged a distributed network of oscillations in the gamma band (20-60 Hz), which only partially overlapped with the network supporting perceptual analysis. Both processes enhanced cross-talk between left temporal regions and bilateral pars orbitalis (BA47). The left-lateralized synchrony between temporal regions and pars opercularis (BA44) was specific to the linguistically complex words, suggesting a specific role of left frontotemporal cross-cortical interactions in morphosyntactic computations. Synchronizations in oscillatory dynamics reveal the transient coupling of functional networks that support specific computational processes in language comprehension.This work was supported by an EPSRC grant to W.M.-W. (EP/F030061/1), an ERC Advanced Grant (Neurolex) to W.M.-W., and by MRC Cognition and Brain Sciences Unit (CBU) funding to W.M.-W. (U.1055.04.002.00001.01). Computing resources were provided by the MRC-CBU. Funding to pay the Open Access publication charges for this article was provided by the Advanced Investigator Grant (Neurolex) to W.D.M.-W.This is the final published version which appears at http://dx.doi.org/10.1093/cercor/bhu28

Formation and Interaction of Membrane Tubes

We show that the formation of membrane tubes (or membrane tethers), which is a crucial step in many biological processes, is highly non-trivial and involves first order shape transitions. The force exerted by an emerging tube is a non-monotonic function of its length. We point out that tubes attract each other, which eventually leads to their coalescence. We also show that detached tubes behave like semiflexible filaments with a rather short persistence length. We suggest that these properties play an important role in the formation and structure of tubular organelles.Comment: 4 pages, 3 figure

Reactive Dye Degradation by AOPs; Development of a Kinetic Model for UV/H2O2 Process

An application of UV/H2O2 process for the treatment of model wastewater containing organic reactive azo dye C.I. Reactive Blue 137 (RB137) was studied. The efficiency of applied process for decolorization and mineralization of RB137 model solution is discussed. The influence of operating process parameters, initial pH and initial concentration of H2O2, as well as initial dye mass concentration on process effectiveness was investigated. Both direct UV photolysis and OH radical attack were assumed as RB137 degradation mechanisms and a detailed kinetic model for dye degradation by UV/H2O2 process was proposed. The predicted system behavior was compared with experimentally obtained results of decolorization and mineralization of RB137 wastewater. A sensitivity analysis for the evaluation of importance of each reaction used in the model development was also included

Grammatical analysis as a distributed neurobiological function.

This is the final version of the article. It first appeared from [publisher] via http://dx.doi.org/10.1002/hbm.22696Language processing engages large-scale functional networks in both hemispheres. Although it is widely accepted that left perisylvian regions have a key role in supporting complex grammatical computations, patient data suggest that some aspects of grammatical processing could be supported bilaterally. We investigated the distribution and the nature of grammatical computations across language processing networks by comparing two types of combinatorial grammatical sequences--inflectionally complex words and minimal phrases--and contrasting them with grammatically simple words. Novel multivariate analyses revealed that they engage a coalition of separable subsystems: inflected forms triggered left-lateralized activation, dissociable into dorsal processes supporting morphophonological parsing and ventral, lexically driven morphosyntactic processes. In contrast, simple phrases activated a consistently bilateral pattern of temporal regions, overlapping with inflectional activations in L middle temporal gyrus. These data confirm the role of the left-lateralized frontotemporal network in supporting complex grammatical computations. Critically, they also point to the capacity of bilateral temporal regions to support simple, linear grammatical computations. This is consistent with a dual neurobiological framework where phylogenetically older bihemispheric systems form part of the network that supports language function in the modern human, and where significant capacities for language comprehension remain intact even following severe left hemisphere damage.Computing resources were provided by the MRC-CBU. Li Su was partly supported by the Cambridge Dementia Biomedical Research Unit

Accumulation of driver and passenger mutations during tumor progression

Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. In the current study, we provide a novel mathematical model that begins to address this challenge. We model tumors as a discrete time branching process that starts with a single driver mutation and proceeds as each new driver mutation leads to a slightly increased rate of clonal expansion. Using the model, we observe tremendous variation in the rate of tumor development - providing an understanding of the heterogeneity in tumor sizes and development times that have been observed by epidemiologists and clinicians. Furthermore, the model provides a simple formula for the number of driver mutations as a function of the total number of mutations in the tumor. Finally, when applied to recent experimental data, the model allows us to calculate, for the first time, the actual selective advantage provided by typical somatic mutations in human tumors in situ. This selective advantage is surprisingly small, 0.005 +- 0.0005, and has major implications for experimental cancer research

Exact solution of a two-type branching process: Clone size distribution in cell division kinetics

We study a two-type branching process which provides excellent description of experimental data on cell dynamics in skin tissue (Clayton et al., 2007). The model involves only a single type of progenitor cell, and does not require support from a self-renewed population of stem cells. The progenitor cells divide and may differentiate into post-mitotic cells. We derive an exact solution of this model in terms of generating functions for the total number of cells, and for the number of cells of different types. We also deduce large time asymptotic behaviors drawing on our exact results, and on an independent diffusion approximation.Comment: 16 page

Stresses in lipid membranes

The stresses in a closed lipid membrane described by the Helfrich hamiltonian, quadratic in the extrinsic curvature, are identified using Noether's theorem. Three equations describe the conservation of the stress tensor: the normal projection is identified as the shape equation describing equilibrium configurations; the tangential projections are consistency conditions on the stresses which capture the fluid character of such membranes. The corresponding torque tensor is also identified. The use of the stress tensor as a basis for perturbation theory is discussed. The conservation laws are cast in terms of the forces and torques on closed curves. As an application, the first integral of the shape equation for axially symmetric configurations is derived by examining the forces which are balanced along circles of constant latitude.Comment: 16 pages, introduction rewritten, other minor changes, new references added, version to appear in Journal of Physics