Effectiveness of Ultrasound (US) on Adults with Lateral Epicondylitis (LE)

Background: Individuals diagnosed with LE often present with increased pain and decreased functioning in daily activities. LE, commonly referred to as tennis elbow, which results from stress and pain to the lateral epicondyle or extensor carpi radialis brevis (ERCB). This can develop from a single incident, injury or trauma, which results in pain with gripping and lifting (Leadbetter, 2016). Ultrasound (US) utilizes wave production to cause thermal or nonthermal sound waves to stimulate tissue by increasing collagen extensibility and enabling the inflammatory process (Knight & Draper, 2013). Areas being treated by US require different depths; a 1.0 mHz sound head reaches a depth of 3-5 cm and a 3.0 mHZ sound head reaches a depth of 1-2 cm (Ledbetter, 2016)

Transition to Chaos in a Shell Model of Turbulence

We study a shell model for the energy cascade in three dimensional turbulence at varying the coefficients of the non-linear terms in such a way that the fundamental symmetries of Navier-Stokes are conserved. When a control parameter $\epsilon$ related to the strength of backward energy transfer is enough small, the dynamical system has a stable fixed point corresponding to the Kolmogorov scaling. This point becomes unstable at $\epsilon=0.3843...$ where a stable limit cycle appears via a Hopf bifurcation. By using the bi-orthogonal decomposition, the transition to chaos is shown to follow the Ruelle-Takens scenario. For $\epsilon > 0.3953..$ the dynamical evolution is intermittent with a positive Lyapunov exponent. In this regime, there exists a strange attractor which remains close to the Kolmogorov (now unstable) fixed point, and a local scaling invariance which can be described via a intermittent one-dimensional map.Comment: 16 pages, Tex, 20 figures available as hard cop

Analytical calculation of the Peierls-Nabarro pinning barrier for one-dimensional parametric double-well models

Lattice effects on the kink families of two models for one-dimensional nonlinear Klein-Gordon systems with double-well on-site potentials are considered. The analytical expression of the generalized Peierls-Nabarro pinning potential is obtained and confronted with numerical simulations.Comment: RevTex, 10 pages, 4 figure

Avalanches in the Weakly Driven Frenkel-Kontorova Model

A damped chain of particles with harmonic nearest-neighbor interactions in a spatially periodic, piecewise harmonic potential (Frenkel-Kontorova model) is studied numerically. One end of the chain is pulled slowly which acts as a weak driving mechanism. The numerical study was performed in the limit of infinitely weak driving. The model exhibits avalanches starting at the pulled end of the chain. The dynamics of the avalanches and their size and strength distributions are studied in detail. The behavior depends on the value of the damping constant. For moderate values a erratic sequence of avalanches of all sizes occurs. The avalanche distributions are power-laws which is a key feature of self-organized criticality (SOC). It will be shown that the system selects a state where perturbations are just able to propagate through the whole system. For strong damping a regular behavior occurs where a sequence of states reappears periodically but shifted by an integer multiple of the period of the external potential. There is a broad transition regime between regular and irregular behavior, which is characterized by multistability between regular and irregular behavior. The avalanches are build up by sound waves and shock waves. Shock waves can turn their direction of propagation, or they can split into two pulses propagating in opposite directions leading to transient spatio-temporal chaos. PACS numbers: 05.70.Ln,05.50.+q,46.10.+zComment: 33 pages (RevTex), 15 Figures (available on request), appears in Phys. Rev.

Asymptotic stability of breathers in some Hamiltonian networks of weakly coupled oscillators

We consider a Hamiltonian chain of weakly coupled anharmonic oscillators. It is well known that if the coupling is weak enough then the system admits families of periodic solutions exponentially localized in space (breathers). In this paper we prove asymptotic stability in energy space of such solutions. The proof is based on two steps: first we use canonical perturbation theory to put the system in a suitable normal form in a neighborhood of the breather, second we use dispersion in order to prove asymptotic stability. The main limitation of the result rests in the fact that the nonlinear part of the on site potential is required to have a zero of order 8 at the origin. From a technical point of view the theory differs from that developed for Hamiltonian PDEs due to the fact that the breather is not a relative equilibrium of the system

Solitons in Triangular and Honeycomb Dynamical Lattices with the Cubic Nonlinearity

We study the existence and stability of localized states in the discrete nonlinear Schr{\"o}dinger equation (DNLS) on two-dimensional non-square lattices. The model includes both the nearest-neighbor and long-range interactions. For the fundamental strongly localized soliton, the results depend on the coordination number, i.e., on the particular type of the lattice. The long-range interactions additionally destabilize the discrete soliton, or make it more stable, if the sign of the interaction is, respectively, the same as or opposite to the sign of the short-range interaction. We also explore more complicated solutions, such as twisted localized modes (TLM's) and solutions carrying multiple topological charge (vortices) that are specific to the triangular and honeycomb lattices. In the cases when such vortices are unstable, direct simulations demonstrate that they turn into zero-vorticity fundamental solitons.Comment: 17 pages, 13 figures, Phys. Rev.

Stability, mobility and power currents in a two-dimensional model for waveguide arrays with nonlinear coupling

A two-dimensional nonlinear Schrodinger lattice with nonlinear coupling, modelling a square array of weakly coupled linear optical waveguides embedded in a nonlinear Kerr material, is studied. We find that despite a vanishing energy difference (Peierls-Nabarro barrier) of fundamental stationary modes the mobility of localized excitations is very poor. This is attributed to a large separation in parameter space of the bifurcation points of the involved stationary modes. At these points the stability of the fundamental modes is changed and an asymmetric intermediate solution appears that connects the points. The control of the power flow across the array when excited with plane waves is also addressed and shown to exhibit great flexibility that may lead to applications for power-coupling devices. In certain parameter regimes, the direction of a stable propagating plane-wave current is shown to be continuously tunable by amplitude variation (with fixed phase gradient). More exotic effects of the nonlinear coupling terms like compact discrete breathers and vortices, and stationary complex modes with non-trivial phase relations are also briefly discussed. Regimes of dynamical linear stability are found for all these types of solutions.Comment: 31 pages, 12 figures, submitted to Physica D (21 September 2006, revised 23 April 2008

Antibiotic resistance in the environment, with particular reference to MRSA

The introduction of β-lactam antibiotics (penicillins and cephalosporins) in the 1940s and 1950s probably represents the most dramatic event in the battle against infection in human medicine. Even before widespread global use of penicillin, resistance was already recorded. E. coli producing a penicillinase was reported in Nature in 1940 (Abraham, 1940) and soon after a similar penicillinase was discovered in Staphylococcus aureus (Kirby, 1944). The appearance of these genes, so quickly after the discovery and before the widespread introduction of penicillin, clearly shows that the resistance genes pre-dated clinical use of the antibiotic itself

Tumor classification: molecular analysis meets Aristotle

BACKGROUND: Traditionally, tumors have been classified by their morphologic appearances. Unfortunately, tumors with similar histologic features often follow different clinical courses or respond differently to chemotherapy. Limitations in the clinical utility of morphology-based tumor classifications have prompted a search for a new tumor classification based on molecular analysis. Gene expression array data and proteomic data from tumor samples will provide complex data that is unobtainable from morphologic examination alone. The growing question facing cancer researchers is, "How can we successfully integrate the molecular, morphologic and clinical characteristics of human cancer to produce a helpful tumor classification?" DISCUSSION: Current efforts to classify cancers based on molecular features ignore lessons learned from millennia of experience in biological classification. A tumor classification must include every type of tumor and must provide a unique place for each tumor within the classification. Groups within a classification inherit the properties of their ancestors and impart properties to their descendants. A classification was prepared grouping tumors according to their histogenetic development. The classification is simple (reducing the complexity of information received from the molecular analysis of tumors), comprehensive (providing a place for every tumor of man), and consistent with recent attempts to characterize tumors by cytogenetic and molecular features. The clinical and research value of this historical approach to tumor classification is discussed. SUMMARY: This manuscript reviews tumor classification and provides a new and comprehensive classification for neoplasia that preserves traditional nomenclature while incorporating information derived from the molecular analysis of tumors. The classification is provided as an open access XML document that can be used by cancer researchers to relate tumor classes with heterogeneous experimental and clinical tumor databases

Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model