Full-field interferometry using infinity corrected optics

In this paper the construction of full-field (imaging) interferometers using infinity corrected optics commonly used in microscopy is discussed, with an emphasis on self-mixing interferometry configurations where the imaged light field is mixed with itself rather than a reference wave. Such configurations are used in speckle shearing interferometry, flow visualisation and quantitative flow measurement. The critical considerations for constructing path-length imbalanced full-field interferometers for these and similar applications are discussed, expressions are derived for key calculations and interferograms from example interferometers are presented. These include the concept of balancing the infinity-spaces of the two arms via the use of a glass block to minimise the optical path difference variation across the interferogram and ensure adequate sampling of the fringes on the detector. Further, the use of tilted glass blocks in single-pass and double-pass arrangements is detailed for the generation and control of spatial carrier fringes without extensive realignment of the interferometer, and for phase shifting

Channel characterization for 1D molecular communication with two absorbing receivers

This letter develops a one-dimensional (1D) diffusion-based molecular communication system to analyze channel responses between a single transmitter (TX) and two fully-absorbing receivers (RXs). Incorporating molecular degradation in the environment, rigorous analytical formulas for i) the fraction of molecules absorbed, ii) the corresponding hitting rate, and iii) the asymptotic fraction of absorbed molecules as time approaches infinity at each RX are derived when an impulse of molecules are released at the TX. By using particle-based simulations, the derived analytical expressions are validated. Simulations also present the distance ranges of two RXs that do not impact molecular absorption of each other, and demonstrate that the mutual influence of two active RXs reduces with the increase in the degradation rate

On sets of terms with a given intersection type

We are interested in how much of the structure of a strongly normalizable lambda term is captured by its intersection types and how much all the terms of a given type have in common. In this note we consider the theory BCD (Barendregt, Coppo, and Dezani) of intersection types without the top element. We show: for each strongly normalizable lambda term M, with beta-eta normal form N, there exists an intersection type A such that, in BCD, N is the unique beta-eta normal term of type A. A similar result holds for finite sets of strongly normalizable terms for each intersection type A if the set of all closed terms M such that, in BCD, M has type A, is infinite then, when closed under beta-eta conversion, this set forms an adaquate numeral system for untyped lambda calculus. A number of related results are also proved

One-parameter extension of the Doi-Peliti formalism and relation with orthogonal polynomials

An extension of the Doi-Peliti formalism for stochastic chemical kinetics is proposed. Using the extension, path-integral expressions consistent with previous studies are obtained. In addition, the extended formalism is naturally connected to orthogonal polynomials. We show that two different orthogonal polynomials, i.e., Charlier polynomials and Hermite polynomials, can be used to express the Doi-Peliti formalism explicitly.Comment: 10 page

Towards a Nonequilibrium Quantum Field Theory Approach to Electroweak Baryogenesis

We propose a general method to compute $CP$-violating observables from extensions of the standard model in the context of electroweak baryogenesis. It is alternative to the one recently developed by Huet and Nelson and relies on a nonequilibrium quantum field theory approach. The method is valid for all shapes and sizes of the bubble wall expanding in the thermal bath during a first-order electroweak phase transition. The quantum physics of $CP$-violation and its suppression coming from the incoherent nature of thermal processes are also made explicit.Comment: 19 pages, 1 figure available upon e-mail reques

Implementation of Time-Delay Interferometry for LISA

We discuss the baseline optical configuration for the Laser Interferometer Space Antenna (LISA) mission, in which the lasers are not free-running, but rather one of them is used as the main frequency reference generator (the {\it master}) and the remaining five as {\it slaves}, these being phase-locked to the master (the {\it master-slave configuration}). Under the condition that the frequency fluctuations due to the optical transponders can be made negligible with respect to the secondary LISA noise sources (mainly proof-mass and shot noises), we show that the entire space of interferometric combinations LISA can generate when operated with six independent lasers (the {\it one-way method}) can also be constructed with the {\it master-slave} system design. The corresponding hardware trade-off analysis for these two optical designs is presented, which indicates that the two sets of systems needed for implementing the {\it one-way method}, and the {\it master-slave configuration}, are essentially identical. Either operational mode could therefore be implemented without major implications on the hardware configuration. We then.......Comment: 39 pages, 6 figures, 2 table

Rich Counter-Examples for Temporal-Epistemic Logic Model Checking

Model checking verifies that a model of a system satisfies a given property, and otherwise produces a counter-example explaining the violation. The verified properties are formally expressed in temporal logics. Some temporal logics, such as CTL, are branching: they allow to express facts about the whole computation tree of the model, rather than on each single linear computation. This branching aspect is even more critical when dealing with multi-modal logics, i.e. logics expressing facts about systems with several transition relations. A prominent example is CTLK, a logic that reasons about temporal and epistemic properties of multi-agent systems. In general, model checkers produce linear counter-examples for failed properties, composed of a single computation path of the model. But some branching properties are only poorly and partially explained by a linear counter-example. This paper proposes richer counter-example structures called tree-like annotated counter-examples (TLACEs), for properties in Action-Restricted CTL (ARCTL), an extension of CTL quantifying paths restricted in terms of actions labeling transitions of the model. These counter-examples have a branching structure that supports more complete description of property violations. Elements of these counter-examples are annotated with parts of the property to give a better understanding of their structure. Visualization and browsing of these richer counter-examples become a critical issue, as the number of branches and states can grow exponentially for deeply-nested properties. This paper formally defines the structure of TLACEs, characterizes adequate counter-examples w.r.t. models and failed properties, and gives a generation algorithm for ARCTL properties. It also illustrates the approach with examples in CTLK, using a reduction of CTLK to ARCTL. The proposed approach has been implemented, first by extending the NuSMV model checker to generate and export branching counter-examples, secondly by providing an interactive graphical interface to visualize and browse them.Comment: In Proceedings IWIGP 2012, arXiv:1202.422