Transient state work fluctuation theorem for a classical harmonic oscillator linearly coupled to a harmonic bath

Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is not restricted only to the Ohmic bath, rather it is more general, for a non-Ohmic bath. We also derive expressions of the average work done and the variance of the work done in terms of the two-time correlation function of the fluctuations of the position of the harmonic oscillator. In the case of an Ohmic bath, we use these relations to evaluate the average work done and the variance of the work done analytically and verify the transient state work fluctuation theorem quantitatively. Actually these relations have far-reaching consequences. They can be used to numerically evaluate the average work done and the variance of the work done in the case of a non-Ohmic bath when analytical evaluation is not possible.

An algorithm to detect linearly separable clusters of binary patterns

The clusters of binary patterns can be considered as Boolean functions of the (binary) features. Such a relationship between the linearly separable (LS) Boolean functions and LS clusters of binary patterns is examined. An algorithm is presented to answer the questions of the type: “Is the cluster formed by the subsets of the (binary) data set having certain features AND/NOT having certain other features, LS from the remaining set?” The algorithm uses the sequences of Numbered Binary Form (NBF) notation and some elementary (NPN) transformations of the binary data.

An algorithm to detect linearly separable clusters of binary patterns

The clusters of binary patterns can be considered as Boolean functions of the (binary) features. Such a relationship between the linearly separable (LS) Boolean functions and LS clusters of binary patterns is examined. An algorithm is presented to answer the questions of the type: “Is the cluster formed by the subsets of the (binary) data set having certain features AND/NOT having certain other features, LS from the remaining set?” The algorithm uses the sequences of Numbered Binary Form (NBF) notation and some elementary (NPN) transformations of the binary data.

Bearing Capacity of Clays whose Cohesion Increases Linearly with Depth

Experimental studies (Bishop 1966) show that for saturated normally consolidated clay the cohesion varies linearly with depth. The ultimate bearing capacity in such soil is generally obtained by limit equilibrium and limit analysis methods. Sokolovski's (1960) approach to the method of characteristics is used to find the ultimate bearing capacity of saturated clay whose cohesion is homogeneous and isotropic. In this technical note, the method of characteristics is further developed to determine ultimate bearing capacity of clay whose cohesion varies linearly with depth.

Features in visual search combine linearly

Single features such as line orientation and length are known to guide visual search, but relatively little is known about how multiple features combine in search. To address this question, we investigated how search for targets differing in multiple features ( intensity, length, orientation) from the distracters is related to searches for targets differing in each of the individual features. We tested race models (based on reaction times) and coactivation models ( based on reciprocal of reaction times) for their ability to predict multiple feature searches. Multiple feature searches were best accounted for by a co-activation model in which feature information combined linearly (r = 0.95). This result agrees with the classic finding that these features are separable i.e., subjective dissimilarity ratings sum linearly. We then replicated the classical finding that the length and width of a rectangle are integral features-in other words, they combine nonlinearly in visual search. However, to our surprise, upon including aspect ratio as an additional feature, length and width combined linearly and this model outperformed all other models. Thus, length and width of a rectangle became separable when considered together with aspect ratio. This finding predicts that searches involving shapes with identical aspect ratio should be more difficult than searches where shapes differ in aspect ratio. We confirmed this prediction on a variety of shapes. We conclude that features in visual search co-activate linearly and demonstrate for the first time that aspect ratio is a novel feature that guides visual search.

On the Maximum Number of Linearly Independent Cycles and Paths in a Network

Central to network tomography is the problem of identifiability, the ability to identify internal network characteristics uniquely from end-to-end measurements. This problem is often underconstrained even when internal network characteristics such as link delays are modeled as additive constants. While it is known that the network topology can play a role in determining the extent of identifiability, there is a lack in the fundamental understanding of being able to quantify it for a given network. In this paper, we consider the problem of identifying additive link metrics in an arbitrary undirected network using measurement nodes and establishing paths/cycles between them. For a given placement of measurement nodes, we define and derive the ``link rank'' of the network-the maximum number of linearly independent cycles/paths that may be established between the measurement nodes. We achieve this in linear time. The link rank helps quantify the exact extent of identifiability in a network. We also develop a quadratic time algorithm to compute a set of cycles/paths that achieves the maximum rank.

Elastic Properties Of Sodium Borovanadate Glasses

The elastic properties of sodium borovanadate glasses have been studied over a wide range of composition using ultrasonic measurements. It is found that variation of different elastic moduli is very similar in any given series of composition. The bulk and shear moduli show a monotonic variation with the covalent bond energy densities calculated from the proposed structural model for these glasses. The bulk moduli also vary as a negative power function of the mean atomic volume. The Debye temperature varies linearly with the glass transition temperature. The implications of the observed behavior have been discussed.

Temperature dependent vibrational lifetimes in supercritical fluids near the critical point

Vibrational relaxation measurements on the CO asymmetric stretching mode (similar to 1980 cm(-1)) of tungsten hexacarbonyl (W(CO)(6)) as a function of temperature at constant density in several supercritical solvents in the vicinity of the critical point are presented. In supercritical ethane, at the critical density, there is a region above the critical temperature (Tc) in which the lifetime increases with increasing temperature. When the temperature is raised sufficiently (similar to T-c + 70 degrees C), the lifetime decreases with further increase in temperature. A recent hydrodynamic/thermodynamic theory of vibrational relaxation in supercritical fluids reproduces this behavior semiquantitatively. The temperature dependent data for fixed densities somewhat above and below the critical density is in better agreement with the theory. In fluoroform solvent at the critical density, the vibrational lifetime also initially increases with increasing temperature. However, in supercritical CO2 at the critical density, the temperature dependent vibrational lifetime decreases approximately linearly with temperature beginning almost immediately above T-c. The theory does not reproduce this behavior. A comparison between the absolute lifetimes in the three solvents and the temperature trends is made.

Flow and heat transfer in a stagnation-point flow over a stretching sheet with a magnetic field

The flow and heat transfer problem in the boundary layer induced by a continuous moving surface is important in many manufacturing processes in industry such as the boundary layer along material handling conveyers, the aerodynamic extrusion of plastic sheet, the cooling of an infinite metalic plate in a cooling bath (which may also be electrolyte). Glass blowing, continuous casting and spinning of fibres also involve the flow due to a stretching surface. Sakiadis [1] was the first to study the flow induced by a semi-infinite moving wall in an ambient fluid. On the other hand, Crane [2] first studied the flow over a linearly stretching sheet in an ambient fluid. Subsequently, Crane [3] also investigated the corresponding heat transfer problem. Since then several authors [4-8] have studied various aspects of this problem such as the effects of mass transfer, variable wall temperature, constant heat flux, magnetic field etc. Recently, Andersson [9] has obtained an exact solution of the Navier-Stokes equations for the MHD flow over a linearly stretching sheet in an ambient fluid. Also Chiam [10] has studied the heat transfer with variable thermal conductivity on a stretching sheet when the velocities of the sheet and the free stream are equal.

Wave propagation in multi-walled carbon nanotube

In this paper, wave propagation in multi-walled carbon nanotubes (MWNTs) are studied by modeling them as continuum multiple shell coupled through van der Waals force of interaction. The displacements, namely, axial, radial and circumferential displacements vary along the circumferential direction. The wave propagation are simulated using the wavelet based spectral finite element (WSFE) method. This technique involves Daubechies scaling function approximation in time and spectral element approach. The WSFE Method allows the study of wave properties in both time and frequency domains. This is in contrast to the conventional Fourier transform based analysis which are restricted to frequency domain analysis. Here, first, the wavenumbers and wave speeds of carbon nanotubes (CNTs) are Studied to obtain the characteristics of the waves. These group speeds have been compared with those reported in literature. Next, the natural frequencies of a single-walled carbon nanotube (SWNT) are studied for different values of the radius. The frequencies of the first five modes vary linearly with the radius of the SWNT. Finally, the time domain responses are simulated for SWNT and three-walled carbon nanotubes.

Texture strengthening in warm-rolled cadmium-1% silver alloy

The variation in the tensile properties at 77 K and 300 K in warm-rolled (300 K) Cd-1% Ag alloy with deformation has been studied in longitudinal as well as transverse specimens. The low-temperature yield strength increases with warm rolling without much loss in ductility. The strength at 300 K, however, decreases with heavy warm deformation. From microstructural studies and X-ray investigations, it was observed that changes in grain size and texture occur during warm rolling. Both these changes are found to be important in deciding the tensile properties. The longitudinal and transverse strengths at 77 K vary linearly with l-frac12, where l is the average grain diameter, and thus they obey the Hall-Petch relation. The Hall-Petch slope, k, is lower in specimens with favourable lcub1013rcub texture while the intercept σo is higher when the lcub0002rcub texture is less favourable.

Energetics of the condensed ternary fuel-oxidizer systems

the heats of reaction of an oxygen-balanced ternary fuel-oxidizer system have been shown to be linearly related to the total oxidizing valences (P0) of the composition. Because calculation of P0 is simple, the method is found to help in evaluating the energetics of such systems. The accuracy of the method when applied to various ternary systems has been discussed.

Indentation strength of a piezoelectric ceramic: Experiments and simulations

The spherical indentation strength of a lead zirconate titanate (PZT) piezoelectric ceramic was investigated under poled and unpoled conditions and with different electrical boundary conditions (arising through the use of insulating or conducting indenters). Experimental results show that the indentation strength of the poled PZT is higher than that of the unpoled PZT. The strength of a poled PZT under a conducting indenter is higher than that under an insulating indenter. Poling direction (with respect to the direction of indentation loading) did not significantly affect the strength of material. Complementary finite element analysis (FEA) of spherical indentation of an elastic, linearly coupled piezoelectric half-space is conducted for rationalizing the experimental observations. Simulations show marked dependency of the contact stress on the boundary conditions. In particular, contact stress redistribution in the Coupled problem leads to a change in the fracture initiation, from Hertzian cracking in the unpoled material to Subsurface damage initiation in poled PZT. These observations help explain the experimental ranking of strength the PZT in different material conditions or under different boundary conditions.

Bearing capacity factor N-c under phi=0 condition for piles in clays

Bearing capacity factor N-c for axially loaded piles in clays whose cohesion increases linearly with depth has been estimated numerically under undrained (phi=0) condition. The Study follows the lower bound limit analysis in conjunction With finite elements and linear programming. A new formulation is proposed for solving an axisymmetric geotechnical stability problem. The variation of N-c with embedment ratio is obtained for several rates of the increase of soil cohesion with depth; a special case is also examined when the pile base was placed on the stiff clay stratum overlaid by a soft clay layer. It was noticed that the magnitude of N-c reaches almost a constant value for embedment ratio greater than unity. The roughness of the pile base and shaft affects marginally the magnitudes of N-c. The results obtained from the present study are found to compare quite well with the different numerical solutions reported in the literature.

Syntactic Approach to ECG Rhythm Analysis

A diagnostic system for ECG rhythm monitoring based on syntactic approaches to pattern recognition is presented here. The method proposed exploits the difference in shape and structure between arrhythmic and normal ECG patterns to generate distinctly different descriptions in terms of a chosen set of primitives. A given frame of signal is first approximated piecewise linearly into a set of line segments which are completely specified in terms of their length and slope values. The slope values are quantized into seven distinct levels and a unit-length line segment with a slope value in each of these levels is coded as a slope symbol. Seven such slope symbols constitute the set of primitives. The given signal is represented as a string of such symbols based on the length and angle of the line segments approximating the signal. Context-free languages are used for describing the classes of abnormal and normal ECG patterns considered here. Analysis of actual ECG data shows efficiency comparable with that of existing methods and a saving in processing time.