Entropy and irreversibility for a single isolated two level system: New individual quantum states and new nonlinear equation of motion

We propose a new nonlinear equation of motion for a single isolated two-level quantum system. The resulting generalized two-level quantum dynamical theory entails a new alternative resolution of the long-standing dilemma on the nature of entropy and irreversibility. Even for a single isolated degree of freedom, in addition to the individual mechanical states for which all the results of conventional quantum mechanics remain valid, our theory implies the existence of new nonmechanical individual quantum states. These states have nonzero individual entropy and, by virtue of a constant-energy, internal redistribution mechanism, relax irreversibly toward stable equilibrium. We discuss the possibility of an experimental verification of these conclusions by means of a high-resolution, essentially single-particle, magnetic-resonance experiment.     

Smart panel with active damping units. Implementation of decentralized control

This paper contains the second part of a study on a smart panel with five decentralized velocity feedback control units using proof mass electrodynamic actuators [Gonzalez Diaz et al., J. Acoust. Soc. Am. 124, 886 (2008)]. The implementation of five decentralized control loops is analyzed, both theoretically and experimentally. The stability properties of the five decentralized control units have been assessed with the generalized Nyquist criterion by plotting the loci of the eigenvalues of the fully populated matrix of frequency response functions between the five error signals and five input signals to the amplifiers driving the actuators. The control performance properties have been assessed in terms of the spatially averaged response of the panel measured with a scanning laser vibrometer and the total sound power radiated measured in an anechoic room. The two analyses have shown that reductions of up to 10 dB in both vibration response and sound radiation are measured at low audio frequencies, below about 250 Hz.     

Supersonic cluster beam fabrication of metal–ionogel nanocomposites for soft robotics

Soft robotics is an emerging field targeting at the development of robotic bodies and architectures characterized by flexibility, adaptability, and motility typical of that of biological systems. The use of electroactive ionic polymer–metal nanocomposites able to reversibly deform in response to low-intensity electric fields constitutes a promising solution for the implementation of actuators into soft robots. Currently, the use of this class of nanocomposites is hampered by several drawbacks, mainly related to the mismatch between the mechanical properties of the polymer and the metallic electrodes compromising their stability and resilience upon cyclic deformation.Here, we report and discuss on the use of supersonic cluster beam implantation (SCBI) as an effective strategy for the fabrication of soft electroactive ionic polymeric nanocomposite actuators. SCBI relies on the use of supersonically accelerated beams of neutral metal nanoparticles that can be aerodynamically collimated and directed onto a polymeric target to generate thin nanostructured metal layers physically interpenetrating with the polymer.Soft electroactive actuators based on engineered ionogel and ionogel-based hybrid nanocomposites provided with monolithically integrated cluster-assembled gold electrodes will be discussed. These systems can undergo long-term bending deformation in a low-voltage regime, due to the nanostructured electrode resilience. The use of cluster-assembled nanostructured electrodes opens new opportunities for the high-throughput manufacturing of soft ionic actuators with excellent mechanical resiliency, high-performance actuation, and high durability.     

Biomolecular Release Stimulated by Electrochemical Signals at a Very Small Potential Applied

DNA release electrochemically stimulated by applying ?10 mV on the modified electrode was studied. The release process was based on the local (interfacial) pH change produced upon H₂O₂ reduction electrocatalyzed by the immobilized microperoxidase‐11. SiO₂ nanoparticles attached to the electrode surface and functionalized with trigonelline and boronic acid species changed their electrical charge from positive to negative upon the interfacial pH change, thus allowing electrostatic adsorption of negatively charged DNA on the positive interface and then its repulsion/release from the negative interface. The loaded/released DNA molecules were labeled with a fluorescent dye to allow easy detection of the released DNA molecules. The important feature of the developed system is the controlled DNA release upon applying very small electrical potential on the modified electrode.     

Bayesian Nonparametric Estimation for Reinforced Markov Renewal Processes

Starting from the definitions and the properties of reinforced renewal processes and reinforced Markov renewal processes, we characterize, via exchangeability and de Finetti’s representation theorem, a prior that consists of a family of Dirichlet distributions on the space of Markov transition matrices and beta-Stacy processes on distribution functions. Then, we show that this family is conjugate and give some estimate results.

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Two-Wavelet Localization Operators on $$ L^p(\mathbb{R}^n) $$ for the Weyl-Heisenberg Group

We give results on the boundedness and compactness of localization operators with two admissible wavelets on for the Weyl-Heisenberg group.     

Existence theory for nonclassical entropy solutions of scalar conservation laws

We establish a general existence theory for the Cauchy problem associated with a scalar conservation law in one-space dimension. The flux-function is assumed to be nonconvex and we consider nonclassical entropy solutions selected by a kinetic relation. To solve the Cauchy problem, we construct a sequence of approximate solutions using a wave-front tracking scheme. The main difficulty is deriving a uniform estimate on the total variation of the approximate solutions. This is achieved here by introducing a generalized total variation functional, which is decreasing in time and, additionally, reduces to the standard total variation functional when the solutions contain only classical shocks. This functional seems sufficiently robust to be useful for systems as well.Received: June 3, 2002; revised: November 12, 2002     

A variational method for the calculation of spin-rovibronic energy levels of triatomic molecules with three interacting electronic states

A general method is presented for the evaluation of the spin rovibronic energy levels of triatomic molecules with up to three interacting potential energy surfaces. The full theory is outlined in detail, both for singlet and for doublet electronic states and the method is then applied to the benchmark example of C₂H. High quality multireference configuration interaction calculations have been carried out to generate the 3-dimensional near-equilibrium adiabatic potential energy surfaces of the three lowest 1²A'(X²Σ⁺), 2²A'(A²Π), 1²A''(A²Π) electronic states of C₂H, and the pair of interacting states of A 0 symmetry have then been diabatized. Results are presented for J up to 7/2 and compared with gas-phase high resolution experimental results for energies up to 5600 cm¹.     

Dirac index classes and the noncommutative spectral flow

We present a detailed proof of the existence-theorem for noncommutative spectral sections (see the noncommutative spectral flow, unpublished preprint, 1997). We apply this result to various index-theoretic situations, extending to the noncommutative context results of Booss–Wojciechowski, Melrose–Piazza and Dai–Zhang. In particular, we prove a variational formula, in K_*(C_r^*(Γ)), for the index classes associated to 1-parameter family of Dirac operators on a Γ-covering with boundary; this formula involves a noncommutative spectral flow for the boundary family. Next, we establish an additivity result, in K_*(C_r^*(Γ)), for the index class defined by a Dirac-type operator associated to a closed manifold M and a map r:M→BΓ when we assume that M is the union along a hypersurface F of two manifolds with boundary M=M_{+ F} M₋. Finally, we prove a defect formula for the signature-index classes of two cut-and-paste equivalent pairs (M₁,r₁:M₁→BΓ) and (M₂,r₂:M₂→BΓ), where

M₁=M_{+ (F,φ1)} M₋, M₂=M_{+ (F,φ2)} M₋

and φ_jDiff(F). The formula involves the noncommutative spectral flow of a suitable 1-parameter family of twisted signature operators on F. We give applications to the problem of cut-and-paste invariance of Novikov's higher signatures on closed oriented manifolds.