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 = ε and x = ∞. 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 ε (switchback) in the perturbation expansion. If for a given value of k logarithmic terms in x and ε 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 ≥ ε. 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. 166–188). When the axisymmetric finger moves through a tube, a fraction $m$ of the viscous fluid is left behind on the walls of the tube. The fraction $m$ was measured experimentally by Taylor (J. Fluid Mech., 10 (1961), pp. 161–165) as a function of the dimensionless parameter µU/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. Einstein’s 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

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.

Renormalization for Discrete Optimization

The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our method uses renormalization and recursion, and these processes are embedded in a genetic algorithm. The system is self-consistently optimized on all scales, leading to a high probability of finding the ground state configuration. To demonstrate the generality of such an approach, we perform tests on traveling salesman and spin glass problems. The results show that our ``genetic renormalization algorithm'' is extremely powerful.Comment: 4 pages, no figur

Rapid volumetric brain changes after acute psychosocial stress

Stress is an important trigger for brain plasticity: Acute stress can rapidly affect brain activity and functional connectivity, and chronic or pathological stress has been associated with structural brain changes. Measures of structural magnetic resonance imaging (MRI) can be modified by short-term motor learning or visual stimulation, suggesting that they also capture rapid brain changes. Here, we investigated volumetric brain changes (together with changes in T1 relaxation rate and cerebral blood flow) after acute stress in humans as well as their relation to psychophysiological stress measures.Sixty-seven healthy men (25.8±2.7 years) completed a standardized psychosocial laboratory stressor (Trier Social Stress Test) or a control version while blood, saliva, heart rate, and psychometrics were sampled. Structural MRI (T1 mapping / MP2RAGE sequence) at 3T was acquired 45 min before and 90 min after intervention onset. Grey matter volume (GMV) changes were analysed using voxel-based morphometry. Associations with endocrine, autonomic, and subjective stress measures were tested with linear models.We found significant group-by-time interactions in several brain clusters including anterior/mid-cingulate cortices and bilateral insula: GMV was increased in the stress group relative to the control group, in which several clusters showed a GMV decrease. We found a significant group-by-time interaction for cerebral blood flow, and a main effect of time for T1 values (longitudinal relaxation time). In addition, GMV changes were significantly associated with state anxiety and heart rate variability changes.Such rapid GMV changes assessed with VBM may be induced by local tissue adaptations to changes in energy demand following neural activity. Our findings suggest that endogenous brain changes are counteracted by acute psychosocial stress, which emphasizes the importance of considering homeodynamic processes and generally highlights the influence of stress on the brain

Optimal Scheduling Using Branch and Bound with SPIN 4.0

The use of model checkers to solve discrete optimisation problems is appealing. A model checker can first be used to verify that the model of the problem is correct. Subsequently, the same model can be used to find an optimal solution for the problem. This paper describes how to apply the new PROMELA primitives of SPIN 4.0 to search effectively for the optimal solution. We show how Branch-and-Bound techniques can be added to the LTL property that is used to find the solution. The LTL property is dynamically changed during the verification. We also show how the syntactical reordering of statements and/or processes in the PROMELA model can improve the search even further. The techniques are illustrated using two running examples: the Travelling Salesman Problem and a job-shop scheduling problem

Positivity in younger and in older age: Associations with future time perspective and socioemotional functioning

Aging has been associated with a motivational shift to positive over negative information (i.e., positivity effect), which is often explained by a limited future time perspective (FTP) within the framework of socioemotional selectivity theory (SST). However, whether a limited FTP functions similarly in younger and older adults, and whether inter-individual differences in socioemotional functioning are similarly associated with preference for positive information (i.e., positivity) is still not clear. We investigated younger (20–35 years, N = 73) and older (60–75 years, N = 56) adults’ gaze preferences on pairs of happy, angry, sad, and neutral faces using an eye-tracking system. We additionally assessed several parameters potentially underlying inter-individual differences in emotion processing such as FTP, stress, cognitive functioning, social support, emotion regulation, and well-being. While we found no age-related differences in positivity when the entire trial duration was considered, older adults showed longer fixations on the more positive face in later stages of processing (i.e., positivity shifts). This allocation of resources toward more positive stimuli might serve an emotion regulatory purpose and seems consistent with the SST. However, our findings suggest that age moderates the relationship between FTP and positivity shifts, such that the relationship between FTP and positivity preferences was negative in older, and positive in younger adults, potentially stemming from an age-related differential meaning of the FTP construct across age. Furthermore, our exploratory analyses showed that along with the age and FTP interaction, lower levels of worry also played a significant role in positivity shifts. We conclude that positivity effects cannot be solely explained by aging, or the associated reduced FTP per se, but is rather determined by a complex interplay of psychosocial and emotional features