On the L2 stability of linear multidimensional time varying systems

This paper analyzes the L2 stability of solutions of systems with time-varying coefficients of the form [A + C(t)]x′ = [B + D(t)]x + u, where A, B, C, D are matrices. Following proof of a lemma, the main result is derived, according to which the system is L2 stable if the eigenvalues of the coefficient matrices are related in a simple way. A corollary of the theorem dealing with small periodic perturbations of constant coefficient systems is then proved. The paper concludes with two illustrative examples, both of which deal with the attitude dynamics of a rigid, axisymmetric, spinning satellite in an eccentric orbit, subject to gravity gradient torques.

An improved representation of vehicle incompatibility in frontal NCAP tests using a modified rigid barrier

With the objective of better understanding the significance of New Car Assessment Program (NCAP) tests conducted by the National Highway Traffic Safety Administration (NHTSA), head-on collisions between two identical cars of different sizes and between cars and a pickup truck are studied in the present paper using LS-DYNA models. Available finite element models of a compact car (Dodge Neon), midsize car (Dodge Intrepid), and pickup truck (Chevrolet C1500) are first improved and validated by comparing theanalysis-based vehicle deceleration pulses against corresponding NCAP crash test histories reported by NHTSA. In confirmation of prevalent perception, simulation-bascd results indicate that an NCAP test against a rigid barrier is a good representation of a collision between two similar cars approaching each other at a speed of 56.3 kmph (35 mph) both in terms of peak deceleration and intrusions. However, analyses carried out for collisions between two incompatible vehicles, such as an Intrepid or Neon against a C1500, point to the inability of the NCAP tests in representing the substantially higher intrusions in the front upper regions experienced by the cars, although peak decelerations in cars arc comparable to those observed in NCAP tests. In an attempt to improve the capability of a front NCAP test to better represent real-world crashes between incompatible vehicles, i.e., ones with contrasting ride height and lower body stiffness, two modified rigid barriers are studied. One of these barriers, which is of stepped geometry with a curved front face, leads to significantly improved correlation of intrusions in the upper regions of cars with respect to those yielded in the simulation of collisions between incompatible vehicles, together with the yielding of similar vehicle peak decelerations obtained in NCAP tests.

Rocking response of rectangular rigid blocks under random noise base excitations

The response of a rigid rectangular block resting on a rigid foundation and acted upon simultaneously by a horizontal and a vertical random white-noise excitation is considered. In the equation of motion, the energy dissipation is modeled through a viscous damping term. Under the assumption that the body does not topple, the steady-state joint probability density function of the rotation and the rotational velocity is obtained using the Fokker-Planck equation approach. Closed form solution is obtained for a specific combination of system parameters. A more general but approximate solution to the joint probability density function based on the method of equivalent non-linearization is also presented. Further, the problem of overturning of the block is approached in the framework of the diffusion methods for first passage failure studies. The overturning of the block is deemed incipient when the response trajectories in the phase plane cross the separatrix of the conservative unforced system. Expressions for the moments of first passage time are obtained via a series solution to the governing generalized Pontriagin-Vitt equations. Numerical results illustra- tive of the theoretical solutions are presented and their validity is examined through limited amount of digital simulations.

Quenching across quantum critical points in periodic systems: Dependence of scaling laws on periodicity

We study the quenching dynamics of a many-body system in one dimension described by a Hamiltonian that has spatial periodicity. Specifically, we consider a spin-1/2 chain with equal xx and yy couplings and subject to a periodically varying magnetic field in the (z) over cap direction or, equivalently, a tight-binding model of spinless fermions with a periodic local chemical potential, having period 2q, where q is a positive integer. For a linear quench of the strength of the magnetic field (or chemical potential) at a rate 1/tau across a quantum critical point, we find that the density of defects thereby produced scales as 1/tau(q/(q+1)), deviating from the 1/root tau scaling that is ubiquitous in a range of systems. We analyze this behavior by mapping the low-energy physics of the system to a set of fermionic two-level systems labeled by the lattice momentum k undergoing a nonlinear quench as well as by performing numerical simulations. We also show that if the magnetic field is a superposition of different periods, the power law depends only on the smallest period for very large values of tau, although it may exhibit a crossover at intermediate values of tau. Finally, for the case where a zz coupling is also present in the spin chain, or equivalently, where interactions are present in the fermionic system, we argue that the power associated with the scaling law depends on a combination of q and the interaction strength.

Inclusion of body doping in compact models for fully-depleted common double gate MOSFET adapted to gate-oxide thickness asymmetry

Since it is difficult to find the analytical solution of the governing Poisson equation for double gate MOSFETs with the body doping term included, the majority of the compact models are developed for undoped-body devices for which the analytical solution is available. Proposed is a simple technique to included a body doping term in such surface potential based common double gate MOSFET models also by taking into account any differences between the gate oxide thickness. The proposed technique is validated against TCAD simulation and found to be accurate as long as the channel is fully depleted.

Metal cholate hydrogels: versatile supramolecular systems for nanoparticle embedded soft hybrid materials

This work describes the formation of hydrogels from sodium cholate solution in the presence of a variety of metal ions (Ca2+, Cu2+, Co2+, Zn2+, Cd2+, Hg2+ and Ag+). Morphological studies of the xerogels by electron microscopy reveal the presence of helical nanofibres. The rigid helical framework in the calcium cholate hydrogel was utilised to synthesize hybrid materials (AuNPs and AgNPs). Doping of transition metal salts into the calcium cholate hydrogel brings out the possibility of synthesising metal sulphide nano-architectures keeping the hydrogel network intact. These novel gel-nanoparticle hybrid materials have encouraging application potentials.

Wheeler-Feynman absorber revisited: a useful technique to calculate decay rates and lifetimes in small scale optical systems

The Wheeler-Feynman (WF) absorber theory of radiation though no more of interest in explaining self interaction of an electron, can be very useful in today's research in small scale optical systems. The significance of the WF absorber is the use of time-symmetrical solution of Maxwell's equations as opposed to only the retarded solution. The radiative coupling of emitters to nano wires in the near field and change in their lifetimes due to small mode volume enclosures have been elucidated with the retarded solutions before. These solutions have also been shown to agree with quantum electrodynamics, thus allowing for classical electromagnetic approaches in such problems. It is here assumed that the radiative coupling of the emitter with a body is in proportion to its contribution to the classical force of radiative reaction as derived in the WF absorber theory. Representing such nano structures as a partial WF absorber acting on the emitter makes the computations considerably easier than conventional electromagnetic solutions for full boundary conditions.

Energy Loss in the Impact of Elastic Spheres on a Rigid Half-Space in Presence of Adhesion

Adhesion can cause energy losses in asperities or particles coming into dynamic contact resulting in frictional dissipation, even if the deformation occurring is purely elastic. Such losses are of special significance in impact of nanoparticles and friction between surfaces under low contact pressure to hardness ratio. The objective of this work is to study the effect of adhesion during the normal impact of elastic spheres on a rigid half-space, with an emphasis on understanding the mechanism of energy loss. We use finite element method for modeling the impact phenomenon, with the adhesion due to van der Waals force and the short-range repulsion included as body forces distributed over the volume of the sphere. This approach, in contrast with commonly used surface force approximation, helps to model the interactions in a more precise way. We find that the energy loss in impact of elastic spheres is negligible unless there are adhesion-induced instabilities. Significant energy loss through elastic stress waves occurs due to jump-to-contact and jump-out-of-contact instabilities and can even result in capture of the elastic sphere on the half-space.

Emergency Handling in MICS based Body Area Network

Body Area Network, a new wireless networking paradigm, promises to revolutionize the healthcare applications. A number of tiny sensor nodes are strategically placed in and around the human body to obtain physiological information. The sensor nodes are connected to a coordinator or a data collector to form a Body Area Network. The tiny devices may sense physiological parameters of emergency in nature (e.g. abnormality in heart bit rate, increase of glucose level above the threshold etc.) that needs immediate attention of a physician. Due to ultra low power requirement of wireless body area network, most of the time, the coordinator and devices are expected to be in the dormant mode, categorically when network is not operational. This leads to an open question, how to handle and meet the QoS requirement of emergency data when network is not operational? Emergency handling becomes more challenging at the MAC layer, if the channel access related information is unknown to the device with emergency message. The aforementioned scenarios are very likely scenarios in a MICS (Medical Implant Communication Service, 402-405 MHz) based healthcare systems. This paper proposes a mechanism for timely and reliable transfer of emergency data in a MICS based Body Area Network. We validate our protocol design with simulation in a C++ framework. Our simulation results show that more than 99 p ercentage of the time emergency messages are reached at the coordinator with a delay of 400ms.

A Time-based Low Voltage Body Temperature Monitoring Unit

A neonatal temperature monitoring system operating in subthreshold regime that utilizes time mode signal processing is presented. Resistance deviations in a thermistor due to temperature variations are converted to delay variations that are subsequently quantized by a Delay measurement unit (DMU). The DMU does away with the need for any analog circuitry and is synthesizable entirely from digital logic. An FPGA implementation of the system demonstrates the viability of employing time mode signal processing, and measured results show that temperature resolution better than 0.1 degrees C can be achieved using this approach.

Multiobjective Optimization of Piezoelectric Bimorph Actuator with Rigid Extension

Production of high tip deflection in a piezoelectric bimorph laminar actuator by applying high voltage is limited by many physical constraints. Therefore, piezoelectric bimorph actuator with a rigid extension of non-piezoelectric material at its tip is used to increase the tip deflection of such an actuator. Research on this type of piezoelectric bending actuator is either limited to first order constitutive relations, which do not include non-linear behavior of piezoelectric element at high electric field, or limited to curve fitting techniques. Therefore, this paper considers high electric field, and analytically models tapered piezoelectric bimorph actuator with a rigid extension of non-piezoelectric material at its tip. The stiffness, capacitance, effective tip deflection, block force, output strain energy, output energy density, input electrical energy and energy efficiency of the actuator are calculated analytically. The paper also discusses the multi-objective optimization of this type of actuator subjected to the mechanical and electrical constraints.

Many-Body Localization in the Presence of a Single-Particle Mobility Edge

In one dimension, noninteracting particles can undergo a localization-delocalization transition in a quasiperiodic potential. Recent studies have suggested that this transition transforms into a many-body localization (MBL) transition upon the introduction of interactions. It has also been shown that mobility edges can appear in the single particle spectrum for certain types of quasiperiodic potentials. Here, we investigate the effect of interactions in two models with such mobility edges. Employing the technique of exact diagonalization for finite-sized systems, we calculate the level spacing distribution, time evolution of entanglement entropy, optical conductivity, and return probability to detect MBL. We find that MBL does indeed occur in one of the two models we study, but the entanglement appears to grow faster than logarithmically with time unlike in other MBL systems.

Length scales in glass-forming liquids and related systems: a review

The central problem in the study of glass-forming liquids and other glassy systems is the understanding of the complex structural relaxation and rapid growth of relaxation times seen on approaching the glass transition. A central conceptual question is whether one can identify one or more growing length scale(s) associated with this behavior. Given the diversity of molecular glass-formers and a vast body of experimental, computational and theoretical work addressing glassy behavior, a number of ideas and observations pertaining to growing length scales have been presented over the past few decades, but there is as yet no consensus view on this question. In this review, we will summarize the salient results and the state of our understanding of length scales associated with dynamical slow down. After a review of slow dynamics and the glass transition, pertinent theories of the glass transition will be summarized and a survey of ideas relating to length scales in glassy systems will be presented. A number of studies have focused on the emergence of preferred packing arrangements and discussed their role in glassy dynamics. More recently, a central object of attention has been the study of spatially correlated, heterogeneous dynamics and the associated length scale, studied in computer simulations and theoretical analysis such as inhomogeneous mode coupling theory. A number of static length scales have been proposed and studied recently, such as the mosaic length scale discussed in the random first-order transition theory and the related point-to-set correlation length. We will discuss these, elaborating on key results, along with a critical appraisal of the state of the art. Finally we will discuss length scales in driven soft matter, granular fluids and amorphous solids, and give a brief description of length scales in aging systems. Possible relations of these length scales with those in glass-forming liquids will be discussed.