On the bifurcation in a “modulated” logistic map

We comment on a paper by Luang [On the bifurcation in a ''modulated'' logistic map, Physics Letters A 194(1994) 57]. The numerical evidence given in that paper, for a peculiar type of bifurcation, is shown to be incorrect. The causes of such anomalous results are explained. An accurate bifurcation diagram for the map is also given.

Instability map for cold and warm working of as-cast 304 stainless steel

The deformation characteristics of as-cast 304 stainless steel under compression in the temperature range 20-600 degrees C and strain rate range 0.001-100 s(-1) have been studied with a view to characterizing the flow instabilities occurring in the microstructure. Ar strain rates of less than 0.05 s(-1), as-cast 304 stainless steel exhibits flow localization in the temperature range 20-600 degrees C, whereas dynamic strain ageing occurs at intermediate temperatures and below 5 s(-1). At room temperatures and strain rates of less than 0.05 s(-1), martensite formation is observed. To avoid the above microstructural instabilities warm working should be carried out at strain rates greater than 10 s(-1) in the temperature range 400-600 degrees C and cold working could be done in the range of about 0.05-0.8 s(-1). The continuum criterion developed on the basis of the principles of maximum rate of entropy production and separability of the dissipation function, predicts accurately all of the above instability features. (C) 1997 Elsevier Science S.A.

Processing map for the hot working of near-alpha titanium alloy 685

Using a dynamic materials model, processing and instability maps have been developed for near-alpha titanium alloy 685 in the temperature range 775-1025 degrees C and strain-rate range of 0.001-10 s(-1) to optimise its hot workability. The alloy's beta-transus temperature lies at about 1020 degrees C. The material undergoes superplasticity with a peak efficiency of 80% at 975 degrees C and 0.001 s(-1), which are the optimum parameters for alpha-beta working. The occurrence of superplasticity is attributed to two-phase microduplex structure, higher strain-rate sensitivity, low flow stress and sigmoidal variation between log flow stress and log strain rate. The material also exhibits how localisation due to adiabatic shear-band formation up to its beta-transus temperature with strain rates greater than 0.02 s(-1) and thus cracking along these regions. (C) 1997 Published by Elsevier Science S.A.

Coherence of the real symmetric Hardy algebra

Let D denote the open unit disk in C centered at 0. Let H-R(infinity) denote the set of all bounded and holomorphic functions defined in D that also satisfy f(z) = <(f <(z)over bar>)over bar> for all z is an element of D. It is shown that H-R(infinity) is a coherent ring.

The algebra and geometry of SU(3) matrices

We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular group SU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real Linear vector space, are developed in an SU(3) covariant manner. The f and d symbols of SU(3) lead to two ways of 'multiplying' two vectors to produce a third, and several useful geometric and algebraic identities are derived. The axis-angle parametrization of SU(3) is developed as a generalization of that for SU(2), and the specifically new features are brought out. Application to the dynamics of three-level systems is outlined.

Estimation of elasticity map of soft biological tissue mimicking phantom using laser speckle contrast analysis

Scattering of coherent light from scattering particles causes phase shift to the scattered light. The interference of unscattered and scattered light causes the formation of speckles. When the scattering particles, under the influence of an ultrasound (US) pressure wave, vibrate, the phase shift fluctuates, thereby causing fluctuation in speckle intensity. We use the laser speckle contrast analysis (LSCA) to reconstruct a map of the elastic property (Young's modulus) of soft tissue-mimicking phantom. The displacement of the scatters is inversely related to the Young's modulus of the medium. The elastic properties of soft biological tissues vary, many fold with malignancy. The experimental results show that laser speckle contrast (LSC) is very sensitive to the pathological changes in a soft tissue medium. The experiments are carried out on a phantom with two cylindrical inclusions of sizes 6 mm in diameter, separated by 8 mm between them. Three samples are made. One inclusion has Young's modulus E of 40 kPa. The second inclusion has either a Young's modulus E of 20 kPa, or scattering coefficient of mu'(s), = 3.00 mm(-1) or absorption coefficient of mu(a) = 0.03 mm(-1). The optical absorption (mu(a)), reduced scattering (mu'(s)) coefficient, and the Young's modulus of the background are mu(a) = 0.01 mm(-1), mu'(s) = 1.00 mm(-1) and 12kPa, respectively. The experiments are carried out on all three phantoms. On a phantom with two inclusions of Young's modulus of 20 and 40 kPa, the measured relative speckle image contrasts are 36.55% and 63.72%, respectively. Experiments are repeated on phantoms with inclusions of mu(a) = 0.03 mm-1, E = 40 kPa and mu'(s) = 3.00 mm(-1). The results show that it is possible to detect inclusions with contrasts in optical absorption, optical scattering, and Young's modulus. Studies of the variation of laser speckle contrast with ultrasound driving force for various values of mu(a), mu'(s), and Young's modulus of the tissue mimicking medium are also carried out. (C) 2011 American Institute of Physics. doi:10.1063/1.3592352]

Mapping of local electronic properties in nanostructured CMR thin films by Scanning Tunneling Microscopy (STM) and Local Conductance Map (LCMAP)

We have investigated the local electronic properties and the spatially resolved magnetoresistance of a nanostructured film of a colossal magnetoresistive (CMR) material by local conductance mapping (LCMAP) using a variable temperature Scanning Tunneling Microscope (STM) operating in a magnetic field. The nanostructured thin films (thickness ≈500nm) of the CMR material La0.67Sr0.33MnO3 (LSMO) on quartz substrates were prepared using chemical solution deposition (CSD) process. The CSD grown films were imaged by both STM and atomic force microscopy (AFM). Due to the presence of a large number of grain boundaries (GB's), these films show low field magnetoresistance (LFMR) which increases at lower temperatures. The measurement of spatially resolved electronic properties reveal the extent of variation of the density of states (DOS) at and close to the Fermi level (EF) across the grain boundaries and its role in the electrical resistance of the GB. Measurement of the local conductance maps (LCMAP) as a function of magnetic field as well as temperature reveals that the LFMR occurs at the GB. While it was known that LFMR in CMR films originates from the GB, this is the first investigation that maps the local electronic properties at a GB in a magnetic field and traces the origin of LFMR at the GB.

Influence of homogenization on the processing map for hot working of as-cast Mg-2Zn-1Mn alloy

Processing maps have been developed for hot deformation of Mg-2Zn-1Mn alloy in as-cast condition and after homogenization with a view to evaluate the influence of homogenization. Hot compression data in the temperature range 300-500degreesC and strain rate range 0.001-100 s(-1) were used for generating the processing map. In the map for the as-cast alloy the domain of dynamic recrystallization occurring, at 450degreesC and 0.1 s(-1) has merged with another domain occurring at 500degreesC and 0.001 s(-1) representing grain boundary cracking. The latter domain is eliminated by homogenization and the dynamic recrystallization domain expanded with a higher peak efficiency occurring at 500 degreesC and 0.05 s(-1). The flow localization occurring at strain rates higher than 5 s(-1) is unaffected by homogenization.

Accelerating Numerical Linear Algebra Kernels on a Scalable Run Time Reconfigurable Platform

Numerical Linear Algebra (NLA) kernels are at the heart of all computational problems. These kernels require hardware acceleration for increased throughput. NLA Solvers for dense and sparse matrices differ in the way the matrices are stored and operated upon although they exhibit similar computational properties. While ASIC solutions for NLA Solvers can deliver high performance, they are not scalable, and hence are not commercially viable. In this paper, we show how NLA kernels can be accelerated on REDEFINE, a scalable runtime reconfigurable hardware platform. Compared to a software implementation, Direct Solver (Modified Faddeev's algorithm) on REDEFINE shows a 29X improvement on an average and Iterative Solver (Conjugate Gradient algorithm) shows a 15-20% improvement. We further show that solution on REDEFINE is scalable over larger problem sizes without any notable degradation in performance.

Distributed Function Computation over Fields and Rings via Linear Compression of Sources

The setting considered in this paper is one of distributed function computation. More specifically, there is a collection of N sources possessing correlated information and a destination that would like to acquire a specific linear combination of the N sources. We address both the case when the common alphabet of the sources is a finite field and the case when it is a finite, commutative principal ideal ring with identity. The goal is to minimize the total amount of information needed to be transmitted by the N sources while enabling reliable recovery at the destination of the linear combination sought. One means of achieving this goal is for each of the sources to compress all the information it possesses and transmit this to the receiver. The Slepian-Wolf theorem of information theory governs the minimum rate at which each source must transmit while enabling all data to be reliably recovered at the receiver. However, recovering all the data at the destination is often wasteful of resources since the destination is only interested in computing a specific linear combination. An alternative explored here is one in which each source is compressed using a common linear mapping and then transmitted to the destination which then proceeds to use linearity to directly recover the needed linear combination. The article is part review and presents in part, new results. The portion of the paper that deals with finite fields is previously known material, while that dealing with rings is mostly new.Attempting to find the best linear map that will enable function computation forces us to consider the linear compression of source. While in the finite field case, it is known that a source can be linearly compressed down to its entropy, it turns out that the same does not hold in the case of rings. An explanation for this curious interplay between algebra and information theory is also provided in this paper.

Seismic hazard map of Coimbatore using subsurface fault rupture

This study presents the future seismic hazard map of Coimbatore city, India, by considering rupture phenomenon. Seismotectonic map for Coimbatore has been generated using past earthquakes and seismic sources within 300 km radius around the city. The region experienced a largest earthquake of moment magnitude 6.3 in 1900. Available earthquakes are divided into two categories: one includes events having moment magnitude of 5.0 and above, i.e., damaging earthquakes in the region and the other includes the remaining, i.e., minor earthquakes. Subsurface rupture character of the region has been established by considering the damaging earthquakes and total length of seismic source. Magnitudes of each source are estimated by assuming the subsurface rupture length in terms of percentage of total length of sources and matched with reported earthquake. Estimated magnitudes match well with the reported earthquakes for a RLD of 5.2% of the total length of source. Zone of influence circles is also marked in the seismotectonic map by considering subsurface rupture length of fault associated with these earthquakes. As earthquakes relive strain energy that builds up on faults, it is assumed that all the earthquakes close to damaging earthquake have released the entire strain energy and it would take some time for the rebuilding of strain energy to cause a similar earthquake in the same location/fault. Area free from influence circles has potential for future earthquake, if there is seismogenic source and minor earthquake in the last 20 years. Based on this rupture phenomenon, eight probable locations have been identified and these locations might have the potential for the future earthquakes. Characteristic earthquake moment magnitude (M-w) of 6.4 is estimated for the seismic study area considering seismic sources close to probable zones and 15% increased regional rupture character. The city is divided into several grid points at spacing of 0.01 degrees and the peak ground acceleration (PGA) due to each probable earthquake is calculated at every grid point in city by using the regional attenuation model. The maximum of all these eight PGAs is taken for each grid point and the final PGA map is arrived. This map is compared to the PGA map developed based on the conventional deterministic seismic hazard analysis (DSHA) approach. The probable future rupture earthquakes gave less PGA than that of DSHA approach. The occurrence of any earthquake may be expected in near future in these eight zones, as these eight places have been experiencing minor earthquakes and are located in well-defined seismogenic sources.

Noniterative inversion strategy for photoacoustic tomography: recovery of absorbed energy map from boundary pressure measurements

The inverse problem in photoacoustic tomography (PAT) seeks to obtain the absorbed energy map from the boundary pressure measurements for which computationally intensive iterative algorithms exist. The computational challenge is heightened when the reconstruction is done using boundary data split into its frequency spectrum to improve source localization and conditioning of the inverse problem. The key idea of this work is to modify the update equation wherein the Jacobian and the perturbation in data are summed over all wave numbers, k, and inverted only once to recover the absorbed energy map. This leads to a considerable reduction in the overall computation time. The results obtained using simulated data, demonstrates the efficiency of the proposed scheme without compromising the accuracy of reconstruction.