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.

Coherent states on Hilbert modules

We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over C*-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert C*-modules which have a natural left action from another C*-algebra, say A. The coherent states are well defined in this case and they behave well with respect to the left action by A. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive definite kernel between two C*-algebras, in complete analogy to the Hilbert space situation. Related to this, there is a dilation result for positive operator-valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory. Some possible physical applications are also mentioned.

Symmetry-breaking transitions in equilibrium shapes of coherent precipitates: Effect of elastic anisotropy and inhomogeneity

We examine the symmetry-breaking transitions in equilibrium shapes of coherent precipitates in two-dimensional (2-D) systems under a plane-strain condition with the principal misfit strain components epsilon(xx)*. and epsilon(yy)*. For systems with cubic elastic moduli, we first show all the shape transitions associated with different values of t = epsilon(yy)*/epsilon(xx)*. We also characterize each of these transitions, by studying its dependence on elastic anisotropy and inhomogeneity. For systems with dilatational misfit (t = 1) and those with pure shear misfit (t = -1), the transition is from an equiaxed shape to an elongated shape, resulting in a break in rotational symmetry. For systems with nondilatational misfit (-1 < t < 1; t not equal 0), the transition involves a break in mirror symmetries normal to the x- and y-axes. The transition is continuous in all cases, except when 0 < t < 1. For systems which allow an invariant line (-1 less than or equal to t < 0), the critical size increases with an increase in the particle stiffness. However, for systems which do not allow an invariant line (0 < t less than or equal to 1), the critical size first decreases, reaches a minimum, and then starts increasing with increasing particle stiffness; moreover, the transition is also forbidden when the particle stiffness is greater than a critical value.

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.

Influence of two photon absorption induced free carriers on coherent polariton and phonon generation in ZnTe crystals

Combination of femtosecond Kerr, two photon absorption, and impulsive stimulated Raman scattering (ISRS) experiments have been carried out to investigate the effect of pulse energy and crystal temperature on the generation of coherent polaritons and phonons in 〈110〉 cut ZnTe single crystals of three different resistivities. We demonstrate that the effect of two photon induced free carriers on the creation of both the polaritons and phonons is largest at 4 K where the free carrier lifetime is enhanced. The temperature dependant ISRS on high and low purity ZnTe crystals allows us to unambiguously assign the phonon mode at 3.5 THz to the longitudinal acoustic mode at X-point in the Brillouin zone, LA(X).

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.

Hilbert W*-modules and coherent states

Hilbert C*-module valued coherent states was introduced earlier by Ali, Bhattacharyya and Shyam Roy. We consider the case when the underlying C*-algebra is a W*-algebra. The construction is similar with a substantial gain. The associated reproducing kernel is now algebra valued, rather than taking values in the space of bounded linear operators between two C*-algebras.

Ultrasound modulation of coherent light in a multiple-scattering medium: experimental verification of nonzero average phase carried by light

We demonstrate the phase fluctuation introduced by oscillation of scattering centers in the focal volume of an ultrasound transducer in an optical tomography experiment has a nonzero mean. The conditions to be met for the above are: (i) the frequency of the ultrasound should be in the vicinity of the most dominant natural frequency of vibration of the ultrasound focal volume, (ii) the corresponding acoustic wavelength should be much larger than l(n)*, a modified transport mean-free-path applicable for phase decorrelation and (iii) the focal volume of the ultrasound transducer should not be larger than 4 - 5 times (l(n)*)(3). We demonstrate through simulations that as the ratio of the ultrasound focal volume to (l(n)*)(3) increases, the average of the phase fluctuation decreases and becomes zero when the focal volume becomes greater than around 4(l(n)*)(3); and through simulations and experiments that as the acoustic frequency increases from 100 Hz to 1 MHz, the average phase decreases to zero. Through experiments done in chicken breast we show that the average phase increases from around 110 degrees to 130 degrees when the background medium is changed from water to glycerol, indicating that the average of the phase fluctuation can be used to sense changes in refractive index deep within tissue.

Compressive sensing for music signals: comparison of transforms with coherent dictionaries

Compressive Sensing (CS) is a new sensing paradigm which permits sampling of a signal at its intrinsic information rate which could be much lower than Nyquist rate, while guaranteeing good quality reconstruction for signals sparse in a linear transform domain. We explore the application of CS formulation to music signals. Since music signals comprise of both tonal and transient nature, we examine several transforms such as discrete cosine transform (DCT), discrete wavelet transform (DWT), Fourier basis and also non-orthogonal warped transforms to explore the effectiveness of CS theory and the reconstruction algorithms. We show that for a given sparsity level, DCT, overcomplete, and warped Fourier dictionaries result in better reconstruction, and warped Fourier dictionary gives perceptually better reconstruction. “MUSHRA” test results show that a moderate quality reconstruction is possible with about half the Nyquist sampling.

Identification of coherent synchronous generators in a multi- machine power system using support vector clustering

This paper illustrates the application of a new technique, based on Support Vector Clustering (SVC) for the direct identification of coherent synchronous generators in a large interconnected Multi-Machine Power Systems. The clustering is based on coherency measures, obtained from the time domain responses of the generators following system disturbances. The proposed clustering algorithm could be integrated into a wide-area measurement system that enables fast identification of coherent clusters of generators for the construction of dynamic equivalent models. An application of the proposed method is demonstrated on a practical 15 generators 72-bus system, an equivalent of Indian Southern grid in an attempt to show the effectiveness of this clustering approach. The effects of short circuit fault locations on coherency are also investigated.