The force distribution function of an oscillator model of polymer stretching at constant velocity

Recent simulations of the stretching of tethered biopolymers at a constant speed v (Ponmurugan and Vemparala, 2011 Phys. Rev. E 84 060101(R)) have suggested that for any time t, the distribution of the fluctuating forces f responsible for chain deformation is governed by a relation of the form P(+ f)/ P(- f) = expgamma f], gamma being a coefficient that is solely a function of v and the temperature T. This result, which is reminiscent of the fluctuation theorems applicable to stochastic trajectories involving thermodynamic variables, is derived in this paper from an analytical calculation based on a generalization of Mazonka and Jarzynski's classic model of dragged particle dynamics Mazonka and Jarzynski, 1999 arXiv:cond-\textbackslashmat/9912121v1]. However, the analytical calculations suggest that the result holds only if t >> 1 and the force fluctuations are driven by white rather than colored noise; they further suggest that the coefficient gamma in the purported theorem varies not as v(0.15)T-(0.7), as indicated by the simulations, but as vT(-1).

Modeling of Ascending/Descending Velocity of Metal Droplet Emulsified in Pb-Salt System

Metal-slag emulsion is an important process to enhance the reaction rate between the two phases; thus, it improves the heat and mass transfer of the process significantly. Various experimental studies have been carried out, and some system specific relations have been proposed by various investigators. A unified, theoretical study is lacking to model this complex phenomenon. Therefore, two simple models based on fundamental laws for metal droplet velocity (both ascending and descending) and bubble velocity, as well as its position at any instant of time, have been proposed. Analytical solutions have been obtained for the developed equations. Analytical solutions have been verified for the droplet velocity, traveling time, and size distribution in slag phase by performing high-temperature experiments in a Pb-salt system and comparing the obtained data with theory. The proposed model has also been verified with published experimental data for various liquid systems with a wide range of physical properties. A good agreement has been found between the analytical solution and the experimental and published data in all cases.

Velocity and rotation measurements in acoustically levitated droplets

The velocity scale inside an acoustically levitated droplet depends on the levitator and liquid properties. Using Particle Imaging Velocimetry (PIV), detailed velocity measurements have been made in a levitated droplet of different diameters and viscosity. The maximum velocity and rotation are normalized using frequency and amplitude of acoustic levitator, and droplet viscosity. The non-dimensional data are fitted for micrometer- and millimeter-sized droplets levitated in different levitators for different viscosity fluids. It is also shown that the rotational speed of nanosilica droplets at an advanced stage of vaporization compares well with that predicted by exponentially fitted parameters. (C) 2012 Elsevier B.V. All rights reserved.

Effect of compressibility on the velocity gradient tensor at free shear flow boundaries

Analyses of the invariants of the velocity gradient ten- sor were performed on flow fields obtained by DNS of compressible plane mixing layers at convective Mach num- bers Mc=0:15 and 1.1. Joint pdfs of the 2nd and 3rd invariants were examined at turbulent/nonturbulent (T/NT) boundaries—defined as surfaces where the local vorticity first exceeds a threshold fraction of the maximum of the mean vorticity. By increasing the threshold from very small lev-els, the boundary points were moved closer into the turbulent region, and the effects on the pdfs of the invariants were ob-served. Generally, T/NT boundaries are in sheet-like regions at both Mach numbers. At the higher Mach number a distinct lobe appears in the joint pdf isolines which has not been ob-served/reported before. A connection to the delayed entrain-ment and reduced growth rate of the higher Mach number flow is proposed.

Seismic site classification and correlation between standard penetration test N value and shear wave velocity for Lucknow city in Indo-Gangetic basin

Subsurface lithology and seismic site classification of Lucknow urban center located in the central part of the Indo-Gangetic Basin (IGB) are presented based on detailed shallow subsurface investigations and borehole analysis. These are done by carrying out 47 seismic surface wave tests using multichannel analysis of surface waves (MASW) and 23 boreholes drilled up to 30 m with standard penetration test (SPT) N values. Subsurface lithology profiles drawn from the drilled boreholes show low- to medium-compressibility clay and silty to poorly graded sand available till depth of 30 m. In addition, deeper boreholes (depth >150 m) were collected from the Lucknow Jal Nigam (Water Corporation), Government of Uttar Pradesh to understand deeper subsoil stratification. Deeper boreholes in this paper refer to those with depth over 150 m. These reports show the presence of clay mix with sand and Kankar at some locations till a depth of 150 m, followed by layers of sand, clay, and Kankar up to 400 m. Based on the available details, shallow and deeper cross-sections through Lucknow are presented. Shear wave velocity (SWV) and N-SPT values were measured for the study area using MASW and SPT testing. Measured SWV and N-SPT values for the same locations were found to be comparable. These values were used to estimate 30 m average values of N-SPT (N-30) and SWV (V-s(30)) for seismic site classification of the study area as per the National Earthquake Hazards Reduction Program (NEHRP) soil classification system. Based on the NEHRP classification, the entire study area is classified into site class C and D based on V-s(30) and site class D and E based on N-30. The issue of larger amplification during future seismic events is highlighted for a major part of the study area which comes under site class D and E. Also, the mismatch of site classes based on N-30 and V-s(30) raises the question of the suitability of the NEHRP classification system for the study region. Further, 17 sets of SPT and SWV data are used to develop a correlation between N-SPT and SWV. This represents a first attempt of seismic site classification and correlation between N-SPT and SWV in the Indo-Gangetic Basin.

Velocity Fluctuations in Helical Propulsion: How Small Can a Propeller Be

Helical propulsion is at the heart of locomotion strategies utilized by various natural and artificial swimmers. We used experimental observations and a numerical model to study the various fluctuation mechanisms that determine the performance of an externally driven helical propeller as the size of the helix is reduced. From causality analysis, an overwhelming effect of orientational noise at low length scales is observed, which strongly affects the average velocity and direction of motion of a propeller. For length scales smaller than a few micrometers in aqueous media, the operational frequency for the propulsion system would have to increase as the inverse cube of the size, which can be the limiting factor for a helical propeller to achieve locomotion in the desired direction.

Dynamic Site Characterization and Correlation of Shear Wave Velocity with Standard Penetration Test `N' Values for the City of Agartala, Tripura State, India

Seismic site characterization is the basic requirement for seismic microzonation and site response studies of an area. Site characterization helps to gauge the average dynamic properties of soil deposits and thus helps to evaluate the surface level response. This paper presents a seismic site characterization of Agartala city, the capital of Tripura state, in the northeast of India. Seismically, Agartala city is situated in the Bengal Basin zone which is classified as a highly active seismic zone, assigned by Indian seismic code BIS-1893, Indian Standard Criteria for Earthquake Resistant Design of Structures, Part-1 General Provisions and Buildings. According to the Bureau of Indian Standards, New Delhi (2002), it is the highest seismic level (zone-V) in the country. The city is very close to the Sylhet fault (Bangladesh) where two major earthquakes (M (w) > 7) have occurred in the past and affected severely this city and the whole of northeast India. In order to perform site response evaluation, a series of geophysical tests at 27 locations were conducted using the multichannel analysis of surface waves (MASW) technique, which is an advanced method for obtaining shear wave velocity (V (s)) profiles from in situ measurements. Similarly, standard penetration test (SPT-N) bore log data sets have been obtained from the Urban Development Department, Govt. of Tripura. In the collected data sets, out of 50 bore logs, 27 were selected which are close to the MASW test locations and used for further study. Both the data sets (V (s) profiles with depth and SPT-N bore log profiles) have been used to calculate the average shear wave velocity (V (s)30) and average SPT-N values for the upper 30 m depth of the subsurface soil profiles. These were used for site classification of the study area recommended by the National Earthquake Hazard Reduction Program (NEHRP) manual. The average V (s)30 and SPT-N classified the study area as seismic site class D and E categories, indicating that the city is susceptible to site effects and liquefaction. Further, the different data set combinations between V (s) and SPT-N (corrected and uncorrected) values have been used to develop site-specific correlation equations by statistical regression, as `V (s)' is a function of SPT-N value (corrected and uncorrected), considered with or without depth. However, after considering the data set pairs, a probabilistic approach has also been presented to develop a correlation using a quantile-quantile (Q-Q) plot. A comparison has also been made with the well known published correlations (for all soils) available in the literature. The present correlations closely agree with the other equations, but, comparatively, the correlation of shear wave velocity with the variation of depth and uncorrected SPT-N values provides a more suitable predicting model. Also the Q-Q plot agrees with all the other equations. In the absence of in situ measurements, the present correlations could be used to measure V (s) profiles of the study area for site response studies.

Wallner lines, crack velocity and mechanisms of crack nucleation and growth in a brittle bulk metallic glass

Mode I fracture experiments were conducted on brittle bulk metallic glass (BMG) samples and the fracture surface features were analyzed in detail to understand the underlying physical processes. Wollner lines, which result from the interaction between the propagating crack front and shear waves emanating from a secondary source, were observed on the fracture surface and geometric analysis of them indicates that the maximum crack velocity is similar to 800 m s(-1), which corresponds to similar to 0.32 times the shear wave speed. Fractography reveals that the sharp crack nucleation at the notch tip occurs at the mid-section of the specimens with the observation of flat and half-penny-shaped cracks. On this basis, we conclude that the crack initiation in brittle BMGs is stress-controlled and occurs through hydrostatic stress-assisted cavity nucleation ahead of the notch tip. High magnification scanning electron and atomic force microscopies of the dynamic crack growth regions reveal highly organized, nanoscale periodic patterns with a spacing of similar to 79 nm. Juxtaposition of the crack velocity with this spacing suggests that the crack takes similar to 10(-10) s for peak-to-peak propagation. This, and the estimated adiabatic temperature rise ahead of the propagating crack tip that suggests local softening, is utilized to critically discuss possible causes for the nanocorrugation formation. Taylor's fluid meniscus instability is unequivocally ruled out. Then, two other possible mechanisms, viz. (a) crack tip blunting and resharpening through nanovoid nucleation and growth ahead of the crack tip and eventual coalescence, and (b) dynamic oscillation of the crack in a thin slab of softened zone ahead of the crack-tip, are critically discussed. (C) 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Maximum group velocity in a one-dimensional model with a sinusoidally varying staggered potential

We use Floquet theory to study the maximum value of the stroboscopic group velocity in a one-dimensional tight-binding model subjected to an on-site staggered potential varying sinusoidally in time. The results obtained by numerically diagonalizing the Floquet operator are analyzed using a variety of analytical schemes. In the low-frequency limit we use adiabatic theory, while in the high-frequency limit the Magnus expansion of the Floquet Hamiltonian turns out to be appropriate. When the magnitude of the staggered potential is much greater or much less than the hopping, we use degenerate Floquet perturbation theory; we find that dynamical localization occurs in the former case when the maximum group velocity vanishes. Finally, starting from an ``engineered'' initial state where the particles (taken to be hard-core bosons) are localized in one part of the chain, we demonstrate that the existence of a maximum stroboscopic group velocity manifests in a light-cone-like spreading of the particles in real space.

Fusing the Navigation Information of Dual Foot-Mounted Zero-Velocity-Update-Aided Inertial Navigation Systems

A range constraint method viz. centroid method is proposed to fuse the navigation information of dual (right and left) foot-mounted Zero-velocity-UPdaTe (ZUPT)-aided Inertial Navigation Systems (INSs). Here, the range constraint means that the distance of separation between the position estimates of right and left foot ZUPT-aided INSs cannot be greater than a quantity known as foot-to-foot maximum separation. We present the experimental results which illustrate the applicability of the proposed method. The results show that the proposed method significantly enhances the accuracy of the navigation solution when compared to using two uncoupled foot-mounted ZUPT-aided INSs. Also, we compare the performance of the proposed method with the existing data fusion methods.

Position-dependent velocity of an effective temperature point for the estimation of the thermal diffusivity of solids

A new approach is proposed to estimate the thermal diffusivity of optically transparent solids at ambient temperature based on the velocity of an effective temperature point (ETP), and by using a two-beam interferometer the proposed concept is corroborated. 1D unsteady heat flow via step-temperature excitation is interpreted as a `micro-scale rectilinear translatory motion' of an ETP. The velocity dependent function is extracted by revisiting the Fourier heat diffusion equation. The relationship between the velocity of the ETP with thermal diffusivity is modeled using a standard solution. Under optimized thermal excitation, the product of the `velocity of the ETP' and the distance is a new constitutive equation for the thermal diffusivity of the solid. The experimental approach involves the establishment of a 1D unsteady heat flow inside the sample through step-temperature excitation. In the moving isothermal surfaces, the ETP is identified using a two-beam interferometer. The arrival-time of the ETP to reach a fixed distance away from heat source is measured, and its velocity is calculated. The velocity of the ETP and a given distance is sufficient to estimate the thermal diffusivity of a solid. The proposed method is experimentally verified for BK7 glass samples and the measured results are found to match closely with the reported value.

Multiphase technique improves mud-pulse velocity calculations

Measurement while drilling (MWD) has become a popular survey technology to monitor directional data, drilling data, formation evaluation data and safety data in the world. And closed loop drilling shows promise in recent years. Obviously, the method of tr

Detection and Characterization of Long-Pulse Low-Velocity Impact Damage in Plastic Bonded Explosives

Damage not only degrades the mechanical properties of explosives, but also influences the shock sensitivity, combustion and even detonation behavior of explosives. The study of impact damage is crucial in the vulnerability evaluation of explosives. A long-pulse low-velocity gas gun with a gas buffer was developed and used to induce impact damage in a hot pressed plastic bonded explosive. Various methods were used to detect and characterize the impact damage of the explosive. The microstructure was examined by use of polarized light microscopy. Fractal analysis of the micrographs was conducted by use of box counting method. The correlation between the fractal dimensions and microstructures was analyzed. Ultrasonic testing was conducted using a pulse through-transmission method to obtain the ultrasonic velocity and ultrasonic attenuation. Spectra analyses were carried out for recorded ultrasonic signals using fast Fourier transform. The correlations between the impact damage and ultrasonic parameters including ultrasonic velocities and attenuation coefficients were also analyzed. To quantitatively assess the impact induced explosive crystal fractures, particle size distribution analyses of explosive crystals were conducted by using a thorough etching technique, in which the explosives samples were soaked in a solution for enough time that the binder was totally removed. Impact induces a large extent of explosive crystal fractures and a large number of microcracks. The ultrasonic velocity decreases and attenuation coefficients increase with the presence of impact damage. Both ultrasonic parameters and fractal dimension can be used to quantitatively assess the impact damage of plastic bonded explosives.

DPIV and Interferometry Technique for Velocity Field and Concentration Fields Measurement in Crystal Growth

The property of crystal depends seriously on the solution concentration distribution near the growth surface of a crystal. However, the concentration distributions are affected by the diffusion and convection of the solution. In the present experiment, the two methods of optical measurement are used to obtained velocity field and concentration field of NaClO₃ solution. The convection patterns in sodium chlorate (NaClO₃) crystal growth are measured by Digital Particle image Velocimetry (DPIV) technology. The 2-dimentional velocity distributions in the solution of NaClO3 are obtained from experiments. And concentration field are obtained by a Mach-Zehnder interferometer with a phase shift servo system. Interference patterns were recorded directly by a computer via a CCD camera. The evolution of velocity field and concentration field from dissolution to crystallization are visualized clearly. The structures of velocity fields were compared with that of concentration field.