Exact analytical solution of viscous Korteweg-deVries equation for water waves

The evolution of a solitary wave with very weak nonlinearity which was originally investigated by Miles [4] is revisited. The solution for a one-dimensional gravity wave in a water of uniform depth is considered. This leads to finding the solution to a Korteweg-de Vries (KdV) equation in which the nonlinear term is small. Also considered is the asymptotic solution of the linearized KdV equation both analytically and numerically. As in Miles [4], the asymptotic solution of the KdV equation for both linear and weakly nonlinear case is found using the method of inversescattering theory. Additionally investigated is the analytical solution of viscous-KdV equation which reveals the formation of the Peregrine soliton that decays to the initial sech^2(\xi) soliton and eventually growing back to a narrower and higher amplitude bifurcated Peregrine-type soliton.Comment: 15 page

Asymptotic Multi-Layer Analysis of Wind Over Unsteady Monochromatic Surface Waves

Asymptotic multi-layer analyses and computation of solutions for turbulent flows over steady and unsteady monochromatic surface wave are reviewed, in the limits of low turbulent stresses and small wave amplitude. The structure of the flow is defined in terms of asymptotically-matched thin-layers, namely the surface layer and a critical layer, whether it is elevated or immersed, corresponding to its location above or within the surface layer. The results particularly demonstrate the physical importance of the singular flow features and physical implications of the elevated critical layer in the limit of the unsteadiness tending to zero. These agree with the variational mathematical solution of Miles (1957) for small but finite growth rate, but they are not consistent physically or mathematically with his analysis in the limit of growth rate tending to zero. As this and other studies conclude, in the limit of zero growth rate the effect of the elevated critical layer is eliminated by finite turbulent diffusivity, so that the perturbed flow and the drag force are determined by the asymmetric or sheltering flow in the surface shear layer and its matched interaction with the upper region. But for groups of waves, in which the individual waves grow and decay, there is a net contribution of the elevated critical layer to the wave growth. Critical layers, whether elevated or immersed, affect this asymmetric sheltering mechanism, but in quite a different way to their effect on growing waves. These asymptotic multi-layer methods lead to physical insight and suggest approximate methods for analyzing higher amplitude and more complex flows, such as flow over wave groups.Comment: 20 page

Modified Heider Balance on Sparse Random Networks

The lack of signed random networks in standard balance studies has prompted us to extend the Hamiltonian of the standard balance model. Random networks with tunable parameters are suitable for better understanding the behavior of standard balance as an underlying dynamics. Moreover, the standard balance model in its original form does not allow preserving tensed triads in the network. Therefore, the thermal behavior of the balance model has been investigated on a fully connected signed network recently. It has been shown that the model undergoes an abrupt phase transition with temperature. Considering these two issues together, we examine the thermal behavior of the structural balance model defined on Erd\H{o}s-R\'enyi random networks. We provide a Mean-Field solution for the model. We observe a first-order phase transition with temperature, for both the sparse and densely connected networks. We detect two transition temperatures, $T_{cold}$ and $T_{hot}$, characterizing a hysteresis loop. We find that with increasing the network sparsity, both $T_{cold}$ and $T_{hot}$ decrease. But the slope of decreasing $T_{hot}$ with sparsity is larger than the slope of decreasing $T_{cold}$. Hence, the hysteresis region gets narrower, until, in a certain sparsity, it disappears. We provide a phase diagram in the temperature-tie density plane to observe the meta-stable/coexistence region behavior more accurately. Then we justify our Mean-Field results with a series of Monte-Carlo simulations.Comment: 10 Pages, 5 Figure

Population inversion of a NAHS mixture adsorbed into a cylindrical pore

A cylindrical nanopore immersed in a non-additive hard sphere binary fluid is studied by means of integral equation theories and Monte Carlo simulations. It is found that at low and intermediate values of the bulk total number density the more concentrated bulk species is preferentially absorbed by the pore, as expected. However, further increments of the bulk number density lead to an abrupt population inversion in the confined fluid and an entropy driven prewetting transition at the outside wall of the pore. These phenomena are a function of the pore size, the non-additivity parameter, the bulk number density, and particles relative number fraction. We discuss our results in relation to the phase separation in the bulk.Comment: 7 pages, 8 Figure

Logopenic and nonfluent variants of primary progressive aphasia are differentiated by acoustic measures of speech production

Differentiation of logopenic (lvPPA) and nonfluent/agrammatic (nfvPPA) variants of Primary Progressive Aphasia is important yet remains challenging since it hinges on expert based evaluation of speech and language production. In this study acoustic measures of speech in conjunction with voxel-based morphometry were used to determine the success of the measures as an adjunct to diagnosis and to explore the neural basis of apraxia of speech in nfvPPA. Forty-one patients (21 lvPPA, 20 nfvPPA) were recruited from a consecutive sample with suspected frontotemporal dementia. Patients were diagnosed using the current gold-standard of expert perceptual judgment, based on presence/absence of particular speech features during speaking tasks. Seventeen healthy age-matched adults served as controls. MRI scans were available for 11 control and 37 PPA cases; 23 of the PPA cases underwent amyloid ligand PET imaging. Measures, corresponding to perceptual features of apraxia of speech, were periods of silence during reading and relative vowel duration and intensity in polysyllable word repetition. Discriminant function analyses revealed that a measure of relative vowel duration differentiated nfvPPA cases from both control and lvPPA cases (r2 = 0.47) with 88% agreement with expert judgment of presence of apraxia of speech in nfvPPA cases. VBM analysis showed that relative vowel duration covaried with grey matter intensity in areas critical for speech motor planning and programming: precentral gyrus, supplementary motor area and inferior frontal gyrus bilaterally, only affected in the nfvPPA group. This bilateral involvement of frontal speech networks in nfvPPA potentially affects access to compensatory mechanisms involving right hemisphere homologues. Measures of silences during reading also discriminated the PPA and control groups, but did not increase predictive accuracy. Findings suggest that a measure of relative vowel duration from of a polysyllable word repetition task may be sufficient for detecting most cases of apraxia of speech and distinguishing between nfvPPA and lvPPA

Weak mean flows induced by anisotropic turbulence impinging onto planar and undulating surfaces

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