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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Hermitian matrices and cohomology of Kähler varieties

We give some upper bounds on the dimension of the kernel of the cup product map $H^{1}(X,\mathbb{C}) \otimes H^{1}(X,\mathbb{C}) \to H^{2}(X,\mathbb{C})We give some upper bounds on the dimension of the kernel of the cup product map , where X is a compact K?hler variety without Albanese fibrations.     

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.     

Primal separation for 0/1 polytopes

 The 0/1 primal separation problem is: Given an extreme point xˉ of a 0/1 polytope P and some point x ^*, find an inequality which is tight at xˉ, violated by x ^* and valid for P or assert that no such inequality exists. It is known that this separation variant can be reduced to the standard separation problem for P. We show that 0/1 optimization and 0/1 primal separation are polynomial time equivalent. This implies that the problems 0/1 optimization, 0/1 standard separation, 0/1 augmentation, and 0/1 primal separation are polynomial time equivalent. Then we provide polynomial time primal separation procedures for matching, stable set, maximum cut, and maximum bipartite graph problems, giving evidence that these algorithms are conceptually simpler and easier to implement than their corresponding counterparts for standard separation. In particular, for perfect matching we present an algorithm for primal separation that rests only on simple max-flow computations. In contrast, the known standard separation method relies on an explicit minimum odd cut algorithm. Consequently, we obtain a very simple proof that a maximum weight perfect matching of a graph can be computed in polynomial time. Received: August 20, 2001 / Accepted: April 2002 Published online: December 9, 2002 RID="⋆" ID="⋆" This research was developed while the author was on leave at the Istituto di Analisi dei Sistemi ed Informatica, Viale Manzoni 30, 00185 Roma, supported by the project TMR-DONET nr. ERB FMRX-CT98-0202 of the European Union. Mathematics Subject Classification (2000): 90C10, 90C60, 90C57