Phase space path integral approach to harmonic oscillator with a time-dependent force constant

The quantum statistical mechanical propagator for a harmonic oscillator with a time-dependent force constant, m omega(2)(t), has been investigated in the past and was found to have only a formal solution in terms of the solutions of certain ordinary differential equations. Such path integrals are frequently encountered in semiclassical path integral evaluations and having exact analytical expressions for such path integrals is of great interest. In a previous work, we had obtained the exact propagator for motion in an arbitrary time-dependent harmonic potential in the overdamped limit of friction using phase space path integrals in the context of Levy flights - a result that can be easily extended to Brownian motion. In this paper, we make a connection between the overdamped Brownian motion and the imaginary time propagator of quantum mechanics and thereby get yet another way to evaluate the latter exactly. We find that explicit analytic solution for the quantum statistical mechanical propagator can be written when the time-dependent force constant has the form omega(2)(t) = lambda(2)(t) - d lambda(t)/dt where lambda(t) is any arbitrary function of t and use it to evaluate path integrals which have not been evaluated previously. We also employ this method to arrive at a formal solution of the propagator for both Levy flights and Brownian subjected to a time-dependent harmonic potential in the underdamped limit of friction. (C) 2015 Elsevier B.V. All rights reserved.

Estimation of nonlinearities from pseudodynamic and dynamic responses of bridge structures using the Delay Vector Variance method

Analysis of the variability in the responses of large structural systems and quantification of their linearity or nonlinearity as a potential non-invasive means of structural system assessment from output-only condition remains a challenging problem. In this study, the Delay Vector Variance (DVV) method is used for full scale testing of both pseudo-dynamic and dynamic responses of two bridges, in order to study the degree of nonlinearity of their measured response signals. The DVV detects the presence of determinism and nonlinearity in a time series and is based upon the examination of local predictability of a signal. The pseudo-dynamic data is obtained from a concrete bridge during repair while the dynamic data is obtained from a steel railway bridge traversed by a train. We show that DVV is promising as a marker in establishing the degree to which a change in the signal nonlinearity reflects the change in the real behaviour of a structure. It is also useful in establishing the sensitivity of instruments or sensors deployed to monitor such changes. (C) 2015 Elsevier B.V. All rights reserved.

Two-Dimensional Noise-Predictive Maximum Likelihood Method for Magnetic Recording Channels

Noise-predictive maximum likelihood (NPML) is a well known signal detection technique used in partial response maximum likelihood (PRML) scheme in 1D magnetic recording channels. The noise samples colored by the partial response (PR) equalizer are predicted/ whitened during the signal detection using a Viterbi detector. In this paper, we propose an extension of the NPML technique for signal detection in 2D ISI channels. The impact of noise prediction during signal detection is studied in PRML scheme for a particular choice of 2D ISI channel and PR targets.

Trace Formulae in Operator Theory

In this article, we survey several kinds of trace formulas that one encounters in the theory of single and multi-variable operators. We give some sketches of the proofs, often based on the principle of finite-dimensional approximations to the objects at hand in the formulas.

Autoregressive cascades on random networks

A network cascade model that captures many real-life correlated node failures in large networks via load redistribution is studied. The considered model is well suited for networks where physical quantities are transmitted, e.g., studying large scale outages in electrical power grids, gridlocks in road networks, and connectivity breakdown in communication networks, etc. For this model, a phase transition is established, i.e., existence of critical thresholds above or below which a small number of node failures lead to a global cascade of network failures or not. Theoretical bounds are obtained for the phase transition on the critical capacity parameter that determines the threshold above and below which cascade appears or disappears, respectively, that are shown to closely follow numerical simulation results. (C) 2015 Elsevier B.V. All rights reserved.

Autoregressive cascades on random networks

A network cascade model that captures many real-life correlated node failures in large networks via load redistribution is studied. The considered model is well suited for networks where physical quantities are transmitted, e.g., studying large scale outages in electrical power grids, gridlocks in road networks, and connectivity breakdown in communication networks, etc. For this model, a phase transition is established, i.e., existence of critical thresholds above or below which a small number of node failures lead to a global cascade of network failures or not. Theoretical bounds are obtained for the phase transition on the critical capacity parameter that determines the threshold above and below which cascade appears or disappears, respectively, that are shown to closely follow numerical simulation results. (C) 2015 Elsevier B.V. All rights reserved.

Cost effective campaigning in social networks

Campaigners are increasingly using online social networking platforms for promoting products, ideas and information. A popular method of promoting a product or even an idea is incentivizing individuals to evangelize the idea vigorously by providing them with referral rewards in the form of discounts, cash backs, or social recognition. Due to budget constraints on scarce resources such as money and manpower, it may not be possible to provide incentives for the entire population, and hence incentives need to be allocated judiciously to appropriate individuals for ensuring the highest possible outreach size. We aim to do the same by formulating and solving an optimization problem using percolation theory. In particular, we compute the set of individuals that are provided incentives for minimizing the expected cost while ensuring a given outreach size. We also solve the problem of computing the set of individuals to be incentivized for maximizing the outreach size for given cost budget. The optimization problem turns out to be non trivial; it involves quantities that need to be computed by numerically solving a fixed point equation. Our primary contribution is, that for a fairly general cost structure, we show that the optimization problems can be solved by solving a simple linear program. We believe that our approach of using percolation theory to formulate an optimization problem is the first of its kind. (C) 2016 Elsevier B.V. All rights reserved.

Counting zero kernel pairs over a finite field

Helmke et al. have recently given a formula for the number of reachable pairs of matrices over a finite field. We give a new and elementary proof of the same formula by solving the equivalent problem of determining the number of so called zero kernel pairs over a finite field. We show that the problem is, equivalent to certain other enumeration problems and outline a connection with some recent results of Guo and Yang on the natural density of rectangular unimodular matrices over F-qx]. We also propose a new conjecture on the density of unimodular matrix polynomials. (C) 2016 Elsevier Inc. All rights reserved.

Stimuli and shape responsive `boron-containing' luminescent organic materials

Recent advancements of material science and its applications have been immensely influenced by the modern development of organic luminescent materials. Among all organic luminogens, boron containing compounds have already established their stature as one of the indispensable classes of luminescent dyes. Boron, in its various forms e. g. triarylboranes, borate dyes and boron clusters, has attracted considerable attention owing to its several unique and excellent photophysical features. In very recent times, beyond the realms of solution-state studies, luminescent boron-containing compounds have emerged as a large and versatile class of stimuli responsive materials. Based on several fundamental concepts of chemistry, researchers have come up with an admirable variety of boron-containing materials with AIE (aggregation-induced emission), mechano-responsive luminescence, thermoresponsive-luminescence as well as a number of purely organic phosphorescent materials and other standalone examples. The unique chemical as well as physical properties of boron-containing compounds are largely responsible for the development of such materials. In this review these new findings are brought together.

Biosensor with Total Internal reflection Imaging Ellipsometry

In order to monitor multiple protein reaction processes simultaneously, a biosensor based on imaging ellipsometry operated in the total internal reflection mode is proposed. It could be realised as an automatic analysis for protein interaction processes with real-time label-free method. Its principle and methodology as well as a demonstration for its applications are presented.

工程地质力学及其应用中的若干问题

工程地质力学是以工程为目的研究地质体变形破坏规律的科学。地质体具有非连续、非均匀、流-固耦合以及未知的初始状态的特性，工程地质力学的关键科学问题包括如何判断地质体的当前状态、描述地质体的力学特性以及分析地质体由连续到非连续的演化过程。工程地质力学研究应当以地学为基础、力学为手段、工程为目的，迫切需要解决的工程问题包括探测地质体的几何和力学特性，给出地质体稳定性的分析方法、地质工程设计依据以及地质灾害的预测预报方法。无论是模型实验还是模拟实验的结果能否回答工程问题取决于对地质条件的认知程度，但是，实验研究可以作为验证数值模拟结果的有力工具；地质调查和现场测量是工程地质力学必不可少的组成部分，地质体的力学分类体现了地学的基础作用，可实现地质环境描述定量化。针对工程需求建立力学模型可主要考虑含结构面岩体、土石混合体以及地质中裂隙流和岩土体的相互作用；实验室岩块实验的试样尺寸应作为地质体多尺度计算模型中的基本尺度。工程地质力学的主要研究内容应当包括给出关键的力学测量参数、研究获得这些参数的方法及相关的仪器：在提出和完善力学模型的同时，应更加注重新的计算方法的验证以及工程应用研究。

Stainless steel sandwich

The Cambridge University's Gordon Laboratory, in collaboration with Fibertech and the Defence Science and Technology Laboratory in the UK, has developed a novel melt spun fiber bore called 'Fibrecore', fabricated entirely from stainless steel with thin faceplates. Fibrecore is typically manufactured by 5mm-long and 70μm thick stainless steel fibers, produced by a melt overflow process. Its entirely metallic construction allows spot welding and tungsten inert gas welding without difficulty. Fibrecore exhibits different energy absorption mechanisms such as core cushioning, core-faceplate delamination, and plastic faceplate deformation, often in a concertina-like fashion. Its low-cost, high structural efficiency and good energy absorption characteristics make it attractive for a range of commercial and military applications. Such applications being evaluated include vehicle body panels, exhaust system noise reduction, low cost filters, and lightweight physical protection. In addition to these characteristics, Fibrecore exhibits properties such as corrosion protection, vibrational damping, and thermal insulation, which also extend its applications.

Addition of ferromagnetic CoFe2O4 to YBCO thin films for enhanced flux pinning

An attempt has been made to prepare a YBa2Cu3O 7-δ (YBCO) thin film doped with ferromagnetic CoFe 2O4. Transmission electron microscopy of the resultant samples shows, however, that Y(Fe, Co)O3 forms as a nanoparticulate dispersion throughout the film in preference to CoFe2O4, leaving the YBCO yttrium deficient. As a consequence, the superconducting properties of the sample are poor, with a self-field critical current density of just 0.25 MA cm-2. Magnetic measurements indicate however that the Y(Fe, Co)O3 content, together with any other residual phases, is also ferromagnetic, and some interesting features are present in the in-field critical current behaviour, including a reduced dependence on applied field and a strong c-axis peak in the angular dependence. The work points the way towards future attempts utilising YFeO3 as an effective ferromagnetic pinning additive for YBCO. © 2009 Elsevier B.V. All rights reserved.

Fabrication and properties of TBCCO films via air-atomising spray deposition of thallium-free precursors

The high-field properties of polycrystalline superconducting TlBaCaCuO films fabricated by the incorporation of thallium vapour into air-atomised BaCaCuO precursors are described. Thick films with Tc values in the range 106-111 K have been prepared on polycrystalline yttria-stabilised zirconia substrates. The surface morphology, crystal structure and composition of the films are related to their high-field transport and magnetisation properties. Typical 10 mm × 9 mm films show Jc values > 1×104 A/cm2 at 77 K (0 T). The best film has a Jc=1.3×104 A/cm2 (Ic=3.6 A) at 77 K (0 T). Films prepared on 26 mm×9 mm substrates show typical large-area Jc values > 0.5×104 A/cm2 (77 K, 0 T). A square planar specimen of dimensions 4.3 mm ×4.3 mm exhibited magnetisation Jc values=1.2×105 A/cm2 at 4.2 K (0.1 T), 9.3×104 A/cm2 at 10 K (0.1 T), 3.3×104 A/ cm2 at 4 K (8 T), and 1.6×104 A/cm2 at 10 K (8 T). © 1994.