A microscopic model of wave-function dephasing and decoherence in the double-slit experiment

The act of measurement on a quantum state is supposed to "collapse" the state into one of several eigenstates of the operator corresponding to the observable being measured. This measurement process is sometimes described as outside standard quantum-mechanical evolution and not calculable from Schr\"odinger's equation. There are two general approaches to the study of wave-function collapse: one called the "consistent" or "decoherent" histories approach and the other, the "environmental decoherence" approach, which studies the effect of the environment upon the quantum system, to explain wave-function collapse. In the "environmental decoherence" approach, one usually studies a Markovian-approximated Master equation to study the time-evolution of reduced density matrix and obtains the long-term dependence of the off-diagonal elements of this matrix. We do not make a Markovian assumption and study a particularly simple and calculable example. We find, the short-time behavior of a collapsing system, at least the one considered in this paper, is not exponential, which is a new result (the long-term behavior is, of course, still exponential). This allows one to connect the Fermi-golden rule quadratic-in-time behavior of a transition probability to the exponential long-time behavior of a collapsing wave-function

On resolving the refractive index and the wave vector

The identification of the refractive index and wave vector for general (possibly active) linear, isotropic, homogeneous, and non-spatially dispersive media is discussed. Correct conditions for negative refraction necessarily include the global properties of the permittivity and permeability functions $\epsilon=\epsilon(\omega)$ and $\mu=\mu(\omega)$. On the other hand, a necessary and sufficient condition for left-handedness can be identified at a single frequency (\re\epsilon/|\epsilon|+\re\mu/|\mu|<0). At oblique incidence to semi-infinite, active media it is explained that the wave vector generally loses its usual interpretation for real frequencies

A family of irreducible free divisors in P^2

An infinite family of irreducible homogeneous free divisors in $K[x, y, z]$ is constructed. Indeed, we identify sets of monomials $X$ such that the general polynomial supported on $X$ is a free divisor.Comment: comments are welcom

Implementation of JPEG compression and motion estimation on FPGA hardware

A hardware implementation of JPEG allows for real-time compression in data intensivve applications, such as high speed scanning, medical imaging and satellite image transmission. Implementation options include dedicated DSP or media processors, FPGA boards, and ASICs. Factors that affect the choice of platform selection involve cost, speed, memory, size, power consumption, and case of reconfiguration. The proposed hardware solution is based on a Very high speed integrated circuit Hardware Description Language (VHDL) implememtation of the codec with prefered realization using an FPGA board due to speed, cost and flexibility factors; The VHDL language is commonly used to model hardware impletations from a top down perspective. The VHDL code may be simulated to correct mistakes and subsequently synthesized into hardware using a synthesis tool, such as the xilinx ise suite. The same VHDL code may be synthesized into a number of sifferent hardware architetcures based on constraints given. For example speed was the major constraint when synthesizing the pipeline of jpeg encoding and decoding, while chip area and power consumption were primary constraints when synthesizing the on-die memory because of large area. Thus, there is a trade off between area and speed in logic synthesis

Method of preparing fiber reinforced ceramic material

Alternate layers of mats of specially coated SiC fibers and silicon monotapes are hot pressed in two stages to form a fiber reinforced ceramic material. In the first stage a die is heated to about 600 C in a vacuum furnace and maintained at this temperature for about one-half hour to remove fugitive binder. In the second stage the die temperature is raised to about 1000 C and the layers are pressed at between 35 and 138 MPa. The resulting preform is placed in a reactor tube where a nitriding gas is flowed past the preform at 1100 to 1400 C to nitride the same

From Master Plan to Vision Plan: The Changing Role of Plans and Plan making in City development (with reference to Mumbai)

Master plans are the traditional instruments used by urban local governments in India as forward planning tools by anticipating urban development and making provisions for the same in terms of (a) the allocation of land for various uses, (b) the regulation of its development and (c) the provision of civic infrastructure. However, they failed to meet the expectations of the citizens as well as the decision makers for several reasons: their design and approach were far too simplistic in anticipating the citizens’ needs and aspirations; their very long tenure has been a major hindrance to anticipate socio-economic changes over time horizon; further, the restrictive approach taken to their implementation without adequate flexibility to meet the changing needs of hour has been acting against the spirit of urban planning. Essentially, it is because of these inadequacies in the plan design, plan making and plan implementation that there is a need felt now on steering an alternative course for achieving the city development goals. Vision plans, in this context, have emerged as alternative instruments useful for achieving the city development goals over a medium to long term; and they are increasingly becoming popular in the cities across the USA as well as elsewhere. This paper describes the evolution of master plan in the Indian context and analyses its inadequacies first (as found in literature); subsequently, it explains the positive features of emerging alternative approaches like the strategic vision plans. In particular, it illustrates the specific case of the Strategic Vision Plan for Mumbai, jointly prepared by a partnership of private non-profit initiative and for-profit organisation, as to how its design is different and as how it takes in to account of / built upon some of the principles of master planning approach. It therefore lays down, finally, how the urban planning has to change the course, akin to the economic planning focus change from that in central planning [of pre-modern era] to decentralized planning [of post-modern era].Master plans, City development, Vision plan and Planning focus.