515 research outputs found
Note on Logarithmic Switchback Terms in Regular and Singular Perturbation Expansions
The occurrence of logarithmic switchback is studied for ordinary differential equations containing a parameter k which is allowed to take any value in a continuum of real numbers and with boundary conditions imposed at x = Δ and x = â. Classical theory tells us that if the equation has a regular singular point at the origin there is a family of solutions which varies continuously with k, and the expansion around the origin has log x terms for a discrete set of values of k. It is shown here how nonlinearity enlarges this set so that it may even be dense in some interval of the real numbers. A log x term in the expansion in x leads to expansion coefficients containing log Δ (switchback) in the perturbation expansion. If for a given value of k logarithmic terms in x and Δ occur they may be obtained by continuity from neighboring values of k. Switchback terms occurred conspicuously in singular-perturbation solutions of problems posed for semi-infinite domain x ℠Δ. This connection is historical rather than logical. In particular we study here switchback terms for a specific example using methods of both singular and regular perturbations
The Penetration of a Finger into a Viscous Fluid in a Channel and Tube
The steady-state shape of a finger penetrating into a region filled with a viscous fluid is examined. The two-dimensional and axisymmetric problems are solved using Stokes equations for low Reynolds number flow. To solve the equations, an assumption for the shape of the finger is made and the normal-stress boundary condition is dropped. The remaining equations are solved numerically by covering the domain with a composite mesh composed of a curvilinear grid which follows the curved interface, and a rectilinear grid parallel to the straight boundaries. The shape of the finger is then altered to satisfy the normal-stress boundary condition by using a nonlinear least squares iteration method. The results are compared with the singular perturbation solution of Bretherton (J. Fluid Mech., 10 (1961), pp. 166â188). When the axisymmetric finger moves through a tube, a fraction of the viscous fluid is left behind on the walls of the tube. The fraction was measured experimentally by Taylor (J. Fluid Mech., 10 (1961), pp. 161â165) as a function of the dimensionless parameter ”U/T. The numerical results are compared with the experimental results of Taylor
Mechanical probing of liquid foam aging
We present experimental results on the Stokes experiment performed in a 3D
dry liquid foam. The system is used as a rheometric tool : from the force
exerted on a 1cm glass bead, plunged at controlled velocity in the foam in a
quasi static regime, local foam properties are probed around the sphere. With
this original and simple technique, we show the possibility of measuring the
foam shear modulus, the gravity drainage rate and the evolution of the bubble
size during coarsening
The influence of nanostructure on the mechanical properties of 3D printed polylactide/nanoclay composites
An obstacle for wider application of 3D printed parts is their inferior mechanical performance compared with those from conventional fabrication. This research aims to overcome this deficiency by developing nanostructured PLA/clay composite filaments that are 3D printable by the FFF technique, investigating the effect of filament composition on mechanical properties, and correlating it with the extent of intercalation of different types of clay. The results showed the addition of 5 wt% organomodified clay to PLA raised the elastic and flexural modulus by 10% and 14% respectively. Einsteinâs composite theory did not hold for the PLA/organoclay composites but the Halpin-Tsai model was successful in interpreting the measured moduli of the organoclays. The model also showed that increasing the clay intercalation was much more effective than raising the total clay content
Prewetting transition on a weakly disordered substrate : evidence for a creeping film dynamics
We present the first microscopic images of the prewetting transition of a
liquid film on a solid surface. Pictures of the local coverage map of a helium
film on a cesium metal surface are taken while the temperature is raised
through the transition. The film edge is found to advance at constant
temperature by successive avalanches in a creep motion with a macroscopic
correlation length. The creep velocity varies strongly in a narrow temperature
range. The retreat motion is obtained only at much lower temperature,
conforming to the strong hysteresis observed for prewetting transition on a
disordered surface. Prewetting transition on such disordered surfaces appears
to give rise to dynamical phenomena similar to what is observed for domain wall
motions in 2D magnets.Comment: 7 pages, 3 figures, to be published in Euro.Phys.Let
Accelerated Stochastic Sampling of Discrete Statistical Systems
We propose a method to reduce the relaxation time towards equilibrium in
stochastic sampling of complex energy landscapes in statistical systems with
discrete degrees of freedom by generalizing the platform previously developed
for continuous systems. The method starts from a master equation, in contrast
to the Fokker-Planck equation for the continuous case. The master equation is
transformed into an imaginary-time Schr\"odinger equation. The Hamiltonian of
the Schr\"odinger equation is modified by adding a projector to its known
ground state. We show how this transformation decreases the relaxation time and
propose a way to use it to accelerate simulated annealing for optimization
problems. We implement our method in a simplified kinetic Monte Carlo scheme
and show an acceleration by an order of magnitude in simulated annealing of the
symmetric traveling salesman problem. Comparisons of simulated annealing are
made with the exchange Monte Carlo algorithm for the three-dimensional Ising
spin glass. Our implementation can be seen as a step toward accelerating the
stochastic sampling of generic systems with complex landscapes and long
equilibration times.Comment: 18 pages, 6 figures, to appear in Phys. Rev.
Packing While Traveling: Mixed Integer Programming for a Class of Nonlinear Knapsack Problems
Packing and vehicle routing problems play an important role in the area of
supply chain management. In this paper, we introduce a non-linear knapsack
problem that occurs when packing items along a fixed route and taking into
account travel time. We investigate constrained and unconstrained versions of
the problem and show that both are NP-hard. In order to solve the problems, we
provide a pre-processing scheme as well as exact and approximate mixed integer
programming (MIP) solutions. Our experimental results show the effectiveness of
the MIP solutions and in particular point out that the approximate MIP approach
often leads to near optimal results within far less computation time than the
exact approach
Genetic Algorithm with Optimal Recombination for the Asymmetric Travelling Salesman Problem
We propose a new genetic algorithm with optimal recombination for the
asymmetric instances of travelling salesman problem. The algorithm incorporates
several new features that contribute to its effectiveness: (i) Optimal
recombination problem is solved within crossover operator. (ii) A new mutation
operator performs a random jump within 3-opt or 4-opt neighborhood. (iii)
Greedy constructive heuristic of W.Zhang and 3-opt local search heuristic are
used to generate the initial population. A computational experiment on TSPLIB
instances shows that the proposed algorithm yields competitive results to other
well-known memetic algorithms for asymmetric travelling salesman problem.Comment: Proc. of The 11th International Conference on Large-Scale Scientific
Computations (LSSC-17), June 5 - 9, 2017, Sozopol, Bulgari
Lin-Kernighan Heuristic Adaptations for the Generalized Traveling Salesman Problem
The Lin-Kernighan heuristic is known to be one of the most successful
heuristics for the Traveling Salesman Problem (TSP). It has also proven its
efficiency in application to some other problems. In this paper we discuss
possible adaptations of TSP heuristics for the Generalized Traveling Salesman
Problem (GTSP) and focus on the case of the Lin-Kernighan algorithm. At first,
we provide an easy-to-understand description of the original Lin-Kernighan
heuristic. Then we propose several adaptations, both trivial and complicated.
Finally, we conduct a fair competition between all the variations of the
Lin-Kernighan adaptation and some other GTSP heuristics. It appears that our
adaptation of the Lin-Kernighan algorithm for the GTSP reproduces the success
of the original heuristic. Different variations of our adaptation outperform
all other heuristics in a wide range of trade-offs between solution quality and
running time, making Lin-Kernighan the state-of-the-art GTSP local search.Comment: 25 page
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