Abstract:
The surface of a thin liquid film with nonconstant curvature is unstable, as the Laplace pressure drives a flow mediated by viscosity. We present the results of experiments on one of the simplest variable curvature surfaces: a stepped polymer film. Height profiles are measured as a function of time for a variety of molecular weights. The evolution of the profiles is shown to be self-similar. This self-similarity offers a precise measurement of the capillary velocity by comparison with numerical solutions of the thin film equation. We also derive a master expression for the time dependence of the excess free energy as a function of the material properties and film geometry. The experiment and theory are in excellent agreement and indicate the effectiveness of stepped polymer films to elucidate nanoscale rheological properties.

Abstract:
In this study, using the feasible direction method to determine the optimum slope and step height of a stepped spillway while the flow dissipated energy is maximized. Then the obtained optimized slope and step height were used and a wooden physical model of the Maxwill Dam with 1:25 scale has been built. Overall, eighteen experiments were carried run with several flow rates. The flow depths at up and down of the model were measured to calculate the dissipated energy of flow. Results show that the flow kinetic energy decreases by increasing the flow rate. The optimized slope and step height were applied to equation 8 to calculate the maximum flow dissipated energy. Comparing results of two physical and numerical models show a good agreement, which conform the goodness of optimized model.

Abstract:
The run-out of high speed granular masses or avalanches along mountain streams, till their arrest, is analytically modeled. The power balance of a sliding granular mass along two planar sliding surfaces is written by taking into account the mass volume, the slopes of the surfaces, the fluid pressure and the energy dissipation. Dissipation is due to collisions and displacements, both localized within a layer at the base of the mass. The run-out, the transition from the first to the second sliding surface and the final run-up of the mass are described by Ordinary Differential Equations (ODEs), solved in closed form (particular cases) or by means of numerical procedures (general case). The proposed solutions allow to predict the run-up length and the speed evolution of the sliding mass as a function of the involved geometrical, physical and mechanical parameters as well as of the simplified rheological laws assumed to express the energy dissipation effects. The corresponding solutions obtained according to the Mohr-Coulomb or Voellmy resistance laws onto the sliding surfaces are recovered as particular cases. The run-out length of a documented case is finally back analysed through the proposed model.

Abstract:
Transformation of waves on sandy beaches, their breaking, set-up and run-up are the main factors contributing to fluctuations in the water table and groundwater flow. In this paper, the run-up mechanisms have been studied using analytical models. In contrast to the standard models, the waves approaching the shoreline are assumed to be dispersive and the equivalence of the non-linear and linear solutions for the extreme characteristics of wave run-up, such as the height of maximum run-up and the velocity of run-up, are used. A linear system of equations for the run-up of breaking waves is developed. This system is based on the application of the mild-slope equation in the deeper area, where waves are dispersive, while the linear equations of shallow water are applied close to the shoreline, where the water depth is a linear function of distance. The dissipation factor in the shallow water equation has been formulated using its resemblance to the mild-slope equation for a non-permeable sea bottom. Application of the method is illustrated for various bottom profiles and wave characteristics, and theoretical results compared well with experimental data. These solutions of the run-up phenomena will assist future studies on wave-induced beach groundwater flow.

Abstract:
Time evolution of the expectation values of various dynamical operators of the harmonic oscillator with dissipation is analitically obtained within the framework of the Lindblad theory for open quantum systems. We deduce the density matrix of the damped harmonic oscillator from the solution of the Fokker-Planck equation for the coherent state representation, obtained from the master equation for the density operator. The Fokker-Planck equation for the Wigner distribution function, subject to either the Gaussian type or the $\delta$-function type of initial conditions, is also solved by using the Wang-Uhlenbeck method. The obtained Wigner functions are two-dimensional Gaussians with different widths.

Abstract:
This study examined the validity and reliability of a sequential "Run-Bike-Run" test (RBR) in age-group triathletes. Eight Olympic distance (OD) specialists (age 30.0 ± 2.0 years, mass 75.6 ± 1.6 kg, run VO2max 63.8 ± 1.9 ml·kg-1·min-1, cycle VO2peak 56.7 ± 5.1 ml·kg-1·min-1) performed four trials over 10 days. Trial 1 (TRVO2max) was an incremental treadmill running test. Trials 2 and 3 (RBR1 and RBR2) involved: 1) a 7-min run at 15 km·h-1 (R1) plus a 1-min transition to 2) cycling to fatigue (2 W·kg-1 body mass then 30 W each 3 min); 3) 10-min cycling at 3 W·kg-1 (Bsubmax); another 1-min transition and 4) a second 7-min run at 15 km·h-1 (R2). Trial 4 (TT) was a 30-min cycle - 20-min run time trial. No significant differences in absolute oxygen uptake (VO2), heart rate (HR), or blood lactate concentration ([BLA]) were evidenced between RBR1 and RBR2. For all measured physiological variables, the limits of agreement were similar, and the mean differences were physiologically unimportant, between trials. Low levels of test-retest error (i.e. ICC <0.8, CV<10%) were observed for most (logged) measurements. However [BLA] post R1 (ICC 0.87, CV 25.1%), [BLA] post Bsubmax (ICC 0.99, CV 16.31) and [BLA] post R2 (ICC 0.51, CV 22.9%) were least reliable. These error ranges may help coaches detect real changes in training status over time. Moreover, RBR test variables can be used to predict discipline specific and overall TT performance. Cycle VO2peak, cycle peak power output, and the change between R1 and R2 (deltaR1R2) in [BLA] were most highly related to overall TT distance (r = 0.89, p < 0. 01; r = 0.94, p < 0.02; r = 0.86, p < 0.05, respectively). The percentage of TR VO2max at 15 km·h-1, and deltaR1R2 HR, were also related to run TT distance (r = -0.83 and 0.86, both p < 0.05)

Abstract:
We present results for collective diffusion of adatoms on a stepped substrate with a submonolayer coverage. We study the combined effect of the additional binding at step edge, the Schwoebel barrier, the enhanced diffusion along step edges, and the finite coverage on diffusion as a function of step density. In particular, we examine the crossover from step--dominated diffusion at high step density to terrace-dominated behavior at low step density in a lattice-gas model using analytical Green's function techniques and Monte Carlo simulations. The influence of steps on diffusion is shown to be more pronounced than previously anticipated.

Abstract:
Time evolution of the expectation values of various dynamical operators of the harmonic oscillator with dissipation is analitically obtained within the framework of the Lindblad's theory for open quantum systems. We deduce the density matrix of the damped harmonic oscillator from the solution of the Fokker-Planck equation for the coherent state representation, obtained from the master equation for the density operator. The Fokker-Planck equation for the Wigner distribution function is also solved by using the Wang-Uhlenbeck method of transforming it into a linearized partial differential equation for the Wigner function, subject to either the Gaussian type or the $\delta$-function type of initial conditions. The Wigner functions which we obtain are two-dimensional Gaussians with different widths.

Abstract:
We study the orbital evolution of hot Jupiters due to the excitation and damping of tidally driven $g$-modes within solar-type host stars. Linearly resonant $g$-modes (the dynamical tide) are driven to such large amplitudes in the stellar core that they excite a sea of other $g$-modes through weakly nonlinear interactions. By solving the dynamics of large networks of nonlinearly coupled modes, we show that the nonlinear dissipation rate of the dynamical tide is several orders of magnitude larger than the linear dissipation rate. As a result, we find that the orbits of planets with mass $M_p > 0.5M_J$ and period $P < 2\textrm{ days}$ decay on timescales that are small compared to the main-sequence lifetime of their solar-type hosts. This corresponds to stellar tidal quality factors $Q_\ast^\prime \simeq 10^5-10^6$ for this range of $M_p$ and $P$. Our results imply that there are $\simeq10$ currently known exoplanetary systems, including WASP-19b and HAT-P-36-b, with orbital decay timescales shorter than a Gyr. Rapid, tide induced orbital decay may explain the observed paucity of planets with $M_p > M_J$ and $P< 2\textrm{ days}$ around solar-type hosts and could generate detectable transit-timing variations in the near future.

Abstract:
A general formalism for obtaining the Lagrangian and Hamiltonian for a one dimensional dissipative system is developed. The formalism is illustrated by applying it to the case of a relativistic particle with linear dissipation. The relativistic wave equation is solved for a free particle with linear dissipation.