Oscillating mushrooms: adiabatic theory for a non-ergodic system

Can elliptic islands contribute to sustained energy growth as parameters of a Hamiltonian system slowly vary with time? In this paper we show that a mushroom billiard with a periodically oscillating boundary accelerates the particle inside it exponentially fast. We provide an estimate for the rate of acceleration. Our numerical experiments confirms the theory. We suggest that a similar mechanism applies to general systems with mixed phase space.Comment: final revisio

An analytical study of transport, mixing and chaos in an unsteady vortical flow

We examine the transport properties of a particular two-dimensional, inviscid incompressible flow using dynamical systems techniques. The velocity field is time periodic and consists of the field induced by a vortex pair plus an oscillating strainrate field. In the absence of the strain-rate field the vortex pair moves with a constant velocity and carries with it a constant body of fluid. When the strain-rate field is added the picture changes dramatically; fluid is entrained and detrained from the neighbourhood of the vortices and chaotic particle motion occurs. We investigate the mechanism for this phenomenon and study the transport and mixing of fluid in this flow. Our work consists of both numerical and analytical studies. The analytical studies include the interpretation of the invariant manifolds as the underlying structure which govern the transport. For small values of strain-rate amplitude we use Melnikov's technique to investigate the behaviour of the manifolds as the parameters of the problem change and to prove the existence of a horseshoe map and thus the existence of chaotic particle paths in the flow. Using the Melnikov technique once more we develop an analytical estimate of the flux rate into and out of the vortex neighbourhood. We then develop a technique for determining the residence time distribution for fluid particles near the vortices that is valid for arbitrary strainrate amplitudes. The technique involves an understanding of the geometry of the tangling of the stable and unstable manifolds and results in a dramatic reduction in computational effort required for the determination of the residence time distributions. Additionally, we investigate the total stretch of material elements while they are in the vicinity of the vortex pair, using this quantity as a measure of the effect of the horseshoes on trajectories passing through this region. The numerical work verifies the analytical predictions regarding the structure of the invariant manifolds, the mechanism for entrainment and detrainment and the flux rate

A Study on Physical Factors that may Influence the Spread and Occurrence of Influenza

Influenza is one of respiratory infections causing the highest morbidity and mortality rates. Every day tens of millions of people suffer from virus infection worldwide with varying severity and with a high economic impact. Influenza transmission from person to person occurs in various ways. This study is an attempt to understand airborne transmission in indoor locations by examining the relation between environmental parameters such as temperature and relative humidity with the number of influenza like illness (ILI) cases. It is proposed that the pattern of influenza activity is primarily a function of indoor relative humidity in temperate regions. This conclusion is based on previous virus viability experiments and on our observation of a strong correlation between influenza like illness cases and indoor relative humidity. Historical data reveals that the peak in influenza like illness cases occurs when the indoor relative humidity is around 10-30%. This study also focuses on the aerosol mode of transmission via expelled particles of human cough. Experiments were carried out for concentration measurements at various locations of cough particles in an Environmental Chamber (EC) at a Morgantown NIOSH facility. A simulated cough machine capable of replicating human cough in real time flow and particle size distribution was used for the aerosol injection. A computational fluid dynamics (CFD) model was developed to simulate the human cough in a modeled room. The results of experiments and simulations are compared to assess the suitability and accuracy of CFD simulation for such flow. The last step in this study is to evaluate the potential of inhalation of dispersed cough droplets in room by breathing. Since the primary mechanism of infection transmission is believed to be via inhalation of virus laden droplets, a theoretical study was conducted to define the sphere of influence of human breathing

Stable motions of high energy particles interacting via a repelling potential

The motion of N particles interacting by a smooth repelling potential and confined to a compact d-dimensional region is proved to be, under mild conditions, non-ergodic for all sufficiently large energies. Specifically, choreographic solutions, for which all particles follow approximately the same path close to an elliptic periodic orbit of the single-particle system, are proved to be KAM stable in the high energy limit. Finally, it is proved that the motion of N repelling particles in a rectangular box is non-ergodic at high energies for a generic choice of interacting potential: there exists a KAM-stable periodic motion by which the particles move fast only in one direction, each on its own path, yet in synchrony with all the other parallel moving particles. Thus, we prove that for smooth interaction potentials the Boltzmann ergodic hypothesis fails for a finite number of particles even in the high energy limit at which the smooth system appears to be very close to the Boltzmann hard-sphere gas

Soft billiards with corners

We develop a framework for dealing with smooth approximations to billiards with corners in the two-dimensional setting. Let a polygonal trajectory in a billiard start and end up at the same billiard's corner point. We prove that smooth Hamiltonian flows which limit to this billiard have a nearby periodic orbit if and only if the polygon angles at the corner are ''acceptable''. The criterion for a corner polygon to be acceptable depends on the smooth potential behavior at the corners, which is expressed in terms of a {scattering function}. We define such an asymptotic scattering function and prove the existence of it, explain how it can be calculated and predict some of its properties. In particular, we show that it is non-monotone for some potentials in some phase space regions. We prove that when the smooth system has a limiting periodic orbit it is hyperbolic provided the scattering function is not extremal there. We then prove that if the scattering function is extremal, the smooth system has elliptic periodic orbits limiting to the corner polygon, and, furthermore, that the return map near these periodic orbits is conjugate to a small perturbation of the Henon map and therefore has elliptic islands. We find from the scaling that the island size is typically algebraic in the smoothing parameter and exponentially small in the number of reflections of the polygon orbit

Symmetry breaking perturbations and strange attractors

The asymmetrically forced, damped Duffing oscillator is introduced as a prototype model for analyzing the homoclinic tangle of symmetric dissipative systems with \textit{symmetry breaking} disturbances. Even a slight fixed asymmetry in the perturbation may cause a substantial change in the asymptotic behavior of the system, e.g. transitions from two sided to one sided strange attractors as the other parameters are varied. Moreover, slight asymmetries may cause substantial asymmetries in the relative size of the basins of attraction of the unforced nearly symmetric attracting regions. These changes seems to be associated with homoclinic bifurcations. Numerical evidence indicates that \textit{strange attractors} appear near curves corresponding to specific secondary homoclinic bifurcations. These curves are found using analytical perturbational tools

Non-ergodicity of the motion in three dimensional steep repelling dispersing potentials

It is demonstrated numerically that smooth three degrees of freedom Hamiltonian systems which are arbitrarily close to three dimensional strictly dispersing billiards (Sinai billiards) have islands of effective stability, and hence are non-ergodic. The mechanism for creating the islands are corners of the billiard domain.Comment: 6 pages, 8 figures, submitted to Chao

An Overview On Web Scraping Techniques And Tools

From the evolution of WWW, the scenario of internet user and data exchange is fastly changes. As common people join the internet and start to use it, lots of new techniques are promoted to boost up the network. At the same time, to enhance computers and network facility new technologies were introduces which results into automatically decreasing in cost of hardware and website�s related costs. Due to all these changes, large number of users are joined and use the internet facilities. Daily use of internet cose in to a tremendous data is available on internet. Business, academician, researchers all are share their advertisements, information on internet so that they can be connected to people fastly and easily. As a result of exchange, share and store data on internet, a new problem is arise that how to handle such data overload and how the user will get or access the best information in least efforts. To solve this issues, researcher spotout new technique called Web Scraping. Web scraping is very imperative technique which is used to generate structured data on the basis of available unstructured data on the web. Scaping generated structured data then stored in central database and analyze in spreadsheets. Traditional copy-and-paste, Text grapping and regular expression matching, HTTP programming, HTML parsing, DOM parsing, Webscraping software, Vertical aggregation platforms, Semantic annotation recognizing and Computer vision web-page analyzers are some of the common techniques used for data scraping. Previously most user uses the common copy-pest technique for gathering and analyzing data on the internet, but it is a tedious technique where lot of data copied by the user and store on computer files. As compared to this technique web scraping software is easiest scraping technique. Now a days, there are lots of software are available in the market for web scraping. Our paper is focused on the overview on the information extraction technique i.e. web scraping, different techniques of web scraping and some of the recent tools used for a web scraping

Thermoelastic analysis of a nonhomogeneous hollow cylinder with internal heat generation

In the present paper, we have determined the heat conduction and thermal stresses of a hollow cylinder with inhomogeneous material properties and internal heat generation. All the material properties except Poisson’s ratio and density are assumed to be given by a simple power law in axial direction. We have obtained the solution of the two dimensional heat conduction equation in the transient state in terms of Bessel’s and trigonometric functions. The influence of inhomogeneity on the thermal and mechanical behavior is examined. Numerical computations are carried out for both homogeneous and nonhomogeneous cylinders and are represented graphically

Thyroid dysfunction in women with polycystic ovarian syndrome: a comparative study

Background: Polycystic ovary syndrome (PCOS) is the most common endocrinopathy in reproductive age women. Some of the PCOS women show presence of hypothyroidism.Methods: This study was conducted at tertiary care centre Indira Gandhi Government Medical College and Hospital (IGGMC), Nagpur, Maharashtra, India. The study group had 50 diagnosed patients of PCOS and 50 age matched normal regular menstruating women were taken as controls.Results: In this study, PCOS patients showed higher mean TSH level than control group (4.024±1.09 and 2.84±0.83 respectively). And more women were diagnosed with overt hypothyroidism in the PCOS group (6%) than in the control group (2%).Conclusions: The findings of the study showed that PCOS is associated with hypothyroidism as compared to normal population