Identification of stiffness, dissipation and input parameters of randomly excited non-linear systems: Capability of restricted potential models (RPM)

A dynamic identification technique in the time domain for time invariant systems under random external forces is presented. This technique is based on the use of the class of restricted potential models (RPM), which are characterized by a non-linear stiffness and a special form of damping, that is a product of the input power spectral density (PSD) matrix and the velocity gradient of a non-linear function of the total mechanical energy. By applying stochastic differential calculus and by specific analytical manipulations, some algebraic equations, depending on the response statistics and on the mechanic parameters that characterize RPM, are obtained. These equations can be used for the dynamic identification of the above mechanic parameters once the response statistics of the system to be identified are evaluated. The proposed technique allows one to identify single-degree-of-freedom or multi-degrees-of-freedom systems in the case of unmeasurable input. Further, the probabilistic characteristics of the external forces can be completely estimated in terms of PSD matrix.     

Shock and traveling wave phenomena on an externally damped, non-linear string

We examine the propagation of shocks and traveling wave phenomena on a one-dimensional string that is executing finite-amplitude, transverse vibrations in a resisting medium. As part of our study, we develop an approach that allows us to describe, albeit approximately, the evolution and propagation of a shock front using analytical methods. In addition, exact traveling wave solutions, one of which involves the Lambert W-function, of the string's equation of motion are determined and analyzed. Lastly, a possible new form of the solution to the linearized problem is presented and extensions and other applications of the present work are briefly discussed.     

Shocks and slip systems: Predictions from a mesoscale theory of continuum dislocation dynamics

Exploring a recently developed mesoscale continuum theory of dislocation dynamics, we derive three predictions about plasticity and grain boundary formation in crystals. (1) There is a residual stress jump across grain boundaries and plasticity-induced cell walls as they form, which self-consistently acts to attract neighboring dislocations; residual stress in this theory appears as a remnant of the driving force behind wall formation under both polygonization and plastic deformation. We derive the predicted asymptotic late-time dynamics of the grain-boundary formation process. (2) During grain boundary formation at high temperatures, there is a predicted cusp in the elastic energy density. (3) In early stages of plasticity, when only one type of dislocation is active (single-slip), cell walls do not form in the theory; instead we predict the formation of a hitherto unrecognized jump singularity in the dislocation density.     

Distance rendering and perception of nearby virtual sound sources with a near-field filter model

Headphone rendering of nearby virtual sound sources represents to date an open issue in 3-D audio, due to a number of technical challenges and temporal requirements involved in the measurement of individual Head-Related Transfer Functions (HRTFs). In order to tackle this problem, we propose a filter model of near-field effects based on the Distance Variation Function (Kan et al., 2009). Thanks to its simple structure and low order, the model can be applied to any far-field virtual auditory display to yield a realistic and computationally efficient near-field compensation of spectral and binaural effects. The model is subjectively evaluated in two psychophysical experiments where the relative distance of pairs of virtually rendered sound sources is judged. Results show that even though sound intensity overshadows subtler near-field effects when it is available as a cue for distance, the model is capable of offering relative distance information of near lateral virtual sources when intensity cues are removed. Furthermore, performances of the model in relative distance rendering are compared to those of alternative near-field rendering methods available in the literature.     

Free boundary problem concerning pricing convertible bond

In this paper, we consider some behaviors of the optimal conversion boundaries (i.e. free boundaries) of American‐style convertible bond with finite horizon in some case. The bond's holder may convert it into the stock of its issued firm at any time before maturity, and the firm may call it at any time before maturity. Its pricing model is a parabolic variational inequality, in which the fundamental variables are time and the stock price of the bond's issuer. We achieve some properties of the free boundary, besides the existence and uniqueness of the solution of the variational inequality, such as: the monotonicity, the boundedness, smoothness and its starting point. Moreover, we analyze the relationship between the free boundary and the parameters in the problem, as well as, obtain the critical condition where the free boundary is a constant independent of time. Copyright © 2011 John Wiley & Sons, Ltd.     

On Rockafellar’s theorem using proximal point algorithm involving -maximal monotonicity framework

On the basis of the general framework of H-maximal monotonicity (also referred to as H-monotonicity in the literature), a generalization to Rockafellar’s theorem in the context of solving a general inclusion problem involving a set-valued maximal monotone operator using the proximal point algorithm in a Hilbert space setting is explored. As a matter of fact, this class of inclusion problems reduces to a class of variational inequalities as well as to a class of complementarity problems. This proximal point algorithm turns out to be of interest in the sense that it plays a significant role in certain computational methods of multipliers in nonlinear programming. The notion of H-maximal monotonicity generalizes the general theory of set-valued maximal monotone mappings to a new level. Furthermore, some results on general firm nonexpansiveness and resolvent mapping corresponding to H-monotonicity are also given.     

Solvability of the -Laplacian with nonlocal boundary conditions

Rather mild sufficient conditions are provided for the existence of positive solutions of a boundary value problem of the form

which unify several cases discussed in the literature. In order to formulate these conditions one needs to know only properties of the homeomorphism and have information about the level of growth of the response operator F. No metric information concerning the linear operators L₀,L₁ in the boundary conditions is used, except that they are positive and continuous and such that L_j(1)<1 j{0,1}.