Recursive relations are derived for nonlinear optical response functions of a two-level chromophore with stochastic frequency fluctuations described by a continuous-time random walk. Stationary ensembles are constructed and signatures of anomalous relaxation in the photon echo signal are discussed for a two state jump modulation with a power law waiting time density function psi(t) approximatel...

We study single-electron quantum dots on helium surface created by electrodes submerged into the helium. The intradot potential is electrostatically controlled. We find the electron energy spectrum and identify relaxation mechanisms. Strong in-plane confinement significantly slows down electron relaxation. Energy relaxation is due primarily to coupling to phonons in helium. Dephasing is determi...

We study the convex hull of a set arising as a relaxation of difficult convex mixed integer quadratic programs (MIQP). We characterize the extreme points of our set and the extreme points of its continuous relaxation. We derive four quadratic cutting surfaces that improve the strength of the continuous relaxation. Each of the cutting surfaces is second-order-cone representable. Via a shooting e...

Ultrafast infrared transient absorption measurements of the complete hydroxyl OD stretching mode spectrum of HOD in water, from 100 fs to tens of picoseconds, observe hydrogen bond breaking and monitor the equilibration of the hydrogen bond network in water. In addition, the vibrational lifetime, the time constant for hydrogen bond breaking, and the rate of orientational relaxation are determin...

In this work, we present a Lagrangean relaxation of the hull-reformulation of discrete-continuous optimization problems formulated as linear generalized disjunctive programs (GDP). The proposed Lagrangean relaxation has three important properties. The first property is that it can be applied to any linear GDP. The second property is that the solution to its continuous relaxation always yields 0...

Knowledge of the relaxation spectrum is important because (I) it provides an intrinsic characterization of the mechanical properties for linearly viscoelastic materials and (.%‘) it offers a rational way to derive the coefficients for a Prony or Dirichlet series representation of the relaxation modulus of importance to some engineering analyses. A numerical solution based on Simpson quadrature ...

For description of the visco-elastic behavior of soft biological tissues, Fung proposed a visco-elastic model formulated in terms of a relaxation function and corresponding relaxation spectrum. For the corresponding creep function, Fung proposed an expression which needs correction to obtain a consistent formulation. This creep function and the corresponding creep spectrum are derived in this n...