Fluctuations, Phase Separation and Wetting Films near Liquid-Gas Critical Point

Gravity on Earth limits the study of the properties of pure fluids near critical point because they become stratified under their own weight. Near the critical point, all thermodynamic properties either diverge or converge and the heating and cooling cause instabilities of the convective flow as a consequence of the expansibility divergence. In order to study boiling, fluctuation and phase separation processes near the critical point of pure fluids without the influence of the Earth\u27s gravity, a number of experiments were performed in the weightlessness of Mir space station. The experimental setup called ALICE II instrument was designed to suppress sedimentation and buoyancy-driven flow. Another set of experiments were carried out on Earth using a carefully density matched system of deuterated methanolcycloxexane to observe critical fluctuations directly. The set of experiments performed on board of Mir space station studied boiling and wetting film dynamics during evaporation near the critical point of two pure fluids (sulfur hexafluoride and carbon dioxide) using a defocused grid method. The specially designed cell containing the pure fluid was heated and, as a result, a low contrast line appeared on the wetting film that corresponded to a sharp change in the thickness of the film. A large mechanical response was observed in response to the cell heating and we present quantitative results about the receding contact lines. It is found that the vapor recoil force is responsible for the receding contact line. Local density fluctuations were observed by illuminating a cylindrical cell filled with the pure fluid near its liquid- gas critical point and recorded using a microscope and a video recorder. Microscopic fluctuations were analyzed both in sulfur hexafluoride and in a binary mixture of methanol cyclohexane. Using image processing techniques, we were able to estimate the properties of the fluid from the recorded images showing fluctuations of the transmitted and scattered light. We found that the histogram of an image can be fitted to a Gaussian relationship and by determining its width we were able to estimate the position of the critical point. The characteristic length of the fluctuations corresponding to the maximum of the radial average of the power spectrum was also estimated. The power law growth for the early stage of the phase separation was determined for two different temperature quenches in pure fluid and these results are in agreement with other experimental results and computational simulations

Solutions without singularities in gauge theory of gravitation

A de-Sitter gauge theory of the gravitational field is developed using a spherical symmetric Minkowski space-time as base manifold. The gravitational field is described by gauge potentials and the mathematical structure of the underlying space-time is not affected by physical events. The field equations are written and their solutions without singularities are obtained by imposing some constraints on the invariants of the model. An example of such a solution is given and its dependence on the cosmological constant is studied. A comparison with results obtained in General Relativity theory is also presented. Keywords: gauge theory, gravitation, singularity, computer algebraComment: 9 pages, no figure

A Multi-Dimensional Width-Bounded Geometric Separator and its Applications to Protein Folding

We used a divide-and-conquer algorithm to recursively solve the two-dimensional problem of protein folding of an HP sequence with the maximum number of H-H contacts. We derived both lower and upper bounds for the algorithmic complexity by using the newly introduced concept of multi-directional width-bounded geometric separator. We proved that for a grid graph G with n grid points P, there exists a balanced separator A subseteq P$ such that A has less than or equal to 1.02074 sqrt{n} points, and G-A has two disconnected subgraphs with less than or equal to {2over 3}n nodes on each subgraph. We also derive a 0.7555sqrt {n} lower bound for our balanced separator. Based on our multidirectional width-bounded geometric separator, we found that there is an O(n^{5.563sqrt{n}}) time algorithm for the 2D protein folding problem in the HP model. We also extended the upper bound results to rectangular and triangular lattices

Bounds for Haralick features in synthetic images with sinusoidal gradients

Introduction: The gray-level co-occurrence matrix (GLCM) reduces the dimension of an image to a square matrix determined by the number of gray-level intensities present in that image. Since GLCM only measures the co-occurrence frequency of pairs of gray levels at a given distance from each other, it also stores information regarding the gradients of gray-level intensities in the original image.Methods: The GLCM is a second-order statical method of encoding image information and dimensionality reduction. Image features are scalars that reduce GLCM dimensionality and allow fast texture classification. We used Haralick features to extract information regarding image gradients based on the GLCM.Results: We demonstrate that a gradient of k gray levels per pixel in an image generates GLCM entries on the kth parallel line to the main diagonal. We find that, for synthetic sinusoidal periodic gradients with different wavelengths, the number of gray levels due to intensity quantization follows a power law that also transpires in some Haralick features. We estimate bounds for four of the most often used Haralick features: energy, contrast, correlation, and entropy. We find good agreement between our analytically predicted values of Haralick features and the numerical results from synthetic images of sinusoidal periodic gradients.Discussion: This study opens the possibility of deriving bounds for Haralick features for targeted textures and provides a better selection mechanism for optimal features in texture analysis applications

Modeling Pharmacological Clock and Memory Patterns of Interval Timing in a Striatal Beat-Frequency Model with Realistic, Noisy Neurons

In most species, the capability of perceiving and using the passage of time in the seconds-to-minutes range (interval timing) is not only accurate but also scalar: errors in time estimation are linearly related to the estimated duration. The ubiquity of scalar timing extends over behavioral, lesion, and pharmacological manipulations. For example, in mammals, dopaminergic drugs induce an immediate, scalar change in the perceived time (clock pattern), whereas cholinergic drugs induce a gradual, scalar change in perceived time (memory pattern). How do these properties emerge from unreliable, noisy neurons firing in the milliseconds range? Neurobiological information relative to the brain circuits involved in interval timing provide support for an striatal beat frequency (SBF) model, in which time is coded by the coincidental activation of striatal spiny neurons by cortical neural oscillators. While biologically plausible, the impracticality of perfect oscillators, or their lack thereof, questions this mechanism in a brain with noisy neurons. We explored the computational mechanisms required for the clock and memory patterns in an SBF model with biophysically realistic and noisy Morris–Lecar neurons (SBF–ML). Under the assumption that dopaminergic drugs modulate the firing frequency of cortical oscillators, and that cholinergic drugs modulate the memory representation of the criterion time, we show that our SBF–ML model can reproduce the pharmacological clock and memory patterns observed in the literature. Numerical results also indicate that parameter variability (noise) – which is ubiquitous in the form of small fluctuations in the intrinsic frequencies of neural oscillators within and between trials, and in the errors in recording/retrieving stored information related to criterion time – seems to be critical for the time-scale invariance of the clock and memory patterns