Dense shallow granular flows

Simplified equations are derived for a granular flow in the `dense' limit where the volume fraction is close to that for dynamical arrest, and the `shallow' limit where the stream-wise length for flow development (L) is large compared with the cross-stream height (h). The mass and diameter of the particles are set equal to 1 in the analysis without loss of generality. In the dense limit, the equations are simplified by taking advantage of the power-law divergence of the pair distribution function chi proportional to (phi(ad) - phi)(-alpha), and a faster divergence of the derivativ rho(d chi/d rho) similar to (d chi/d phi), where rho and phi are the density and volume fraction, and phi(ad) is the volume fraction for arrested dynamics. When the height h is much larger than the conduction length, the energy equation reduces to an algebraic balance between the rates of production and dissipation of energy, and the stress is proportional to the square of the strain rate (Bagnold law). In the shallow limit, the stress reduces to a simplified Bagnold stress, where all components of the stress are proportional to (partial derivative u(x)/partial derivative y)(2), which is the cross-stream (y) derivative of the stream-wise (x) velocity. In the simplified equations for dense shallow flows, the inertial terms are neglected in the y momentum equation in the shallow limit because the are O(h/L) smaller than the divergence of the stress. The resulting model contains two equations, a mass conservation equations which reduces to a solenoidal condition on the velocity in the incompressible limit, and a stream-wise momentum equation which contains just one parameter B which is a combination of the Bagnold coefficients and their derivatives with respect to volume fraction. The leading-order dense shallow flow equations, as well as the first correction due to density variations, are analysed for two representative flows. The first is the development from a plug flow to a fully developed Bagnold profile for the flow down an inclined plane. The analysis shows that the flow development length is ((rho) over barh(3)/B) , where (rho) over bar is the mean density, and this length is numerically estimated from previous simulation results. The second example is the development of the boundary layer at the base of the flow when a plug flow (with a slip condition at the base) encounters a rough base, in the limit where the momentum boundary layer thickness is small compared with the flow height. Analytical solutions can be found only when the stream-wise velocity far from the surface varies as x(F), where x is the stream-wise distance from the start of the rough base and F is an exponent. The boundary layer thickness increases as (l(2)x)(1/3) for all values of F, where the length scale l = root 2B/(rho) over bar. The analysis reveals important differences between granular flows and the flows of Newtonian fluids. The Reynolds number (ratio of inertial and viscous terms) turns out to depend only on the layer height and Bagnold coefficients, and is independent of the flow velocity, because both the inertial terms in the conservation equations and the divergence of the stress depend on the square of the velocity/velocity gradients. The compressibility number (ratio of the variation in volume fraction and mean volume fraction) is independent of the flow velocity and layer height, and depends only on the volume fraction and Bagnold coefficients.

Precoding-Based Network Alignment Using Transform Approach for Acyclic Networks With Delay

The algebraic formulation for linear network coding in acyclic networks with the links having integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay assumed for the links, the output symbols at the sink nodes, at any given time instant, is a F(p)m-linear combination of the input symbols across different generations, where F(p)m denotes the field over which the network operates (p is prime and m is a positive integer). We use finite-field discrete Fourier transform to convert the output symbols at the sink nodes, at any given time instant, into a F(p)m-linear combination of the input symbols generated during the same generation without making use of memory at the intermediate nodes. We call this as transforming the acyclic network with delay into n-instantaneous networks (n is sufficiently large). We show that under certain conditions, there exists a network code satisfying sink demands in the usual (nontransform) approach if and only if there exists a network code satisfying sink demands in the transform approach. When the zero-interference conditions are not satisfied, we propose three precoding-based network alignment (PBNA) schemes for three-source three-destination multiple unicast network with delays (3-S 3-D MUN-D) termed as PBNA using transform approach and time-invariant local encoding coefficients (LECs), PBNA using time-varying LECs, and PBNA using transform approach and block time-varying LECs. We derive sets of necessary and sufficient conditions under which throughputs close to n' + 1/2n' + 1, n'/2n' + 1, and n'/2n' + 1 are achieved for the three source-destination pairs in a 3-S 3-D MUN-D employing PBNA using transform approach and time-invariant LECs, and PBNA using transform approach and block time-varying LECs, where n' is a positive integer. For PBNA using time-varying LECs, we obtain a sufficient condition under which a throughput demand of n(1)/n, n(2)/n, and n(3)/n can be met for the three source-destination pairs in a 3-S 3-D MUN-D, where n(1), n(2), and n(3) are positive integers less than or equal to the positive integer n. This condition is also necessary when n(1) + n(3) = n(1) + n(2) = n where n(1) >= n(2) >= n(3).

Riemann shock tube: 1D normal shocks in air, simulations and experiments

This paper presents numerical simulation of the evolution of one-dimensional normal shocks, their propagation, reflection and interaction in air using a single diaphragm Riemann shock tube and validate them using experimental results. Mathematical model is derived for one-dimensional compressible flow of viscous and conducting medium. Dimensionless form of the mathematical model is used to construct space-time finite element processes based on minimization of the space-time residual functional. The space-time local approximation functions for space-time p-version hierarchical finite elements are considered in higher order GRAPHICS] spaces that permit desired order of global differentiability of local approximations in space and time. The resulting algebraic systems from this approach yield unconditionally positive-definite coefficient matrices, hence ensure unique numerical solution. The evolution is computed for a space-time strip corresponding to a time increment Delta t and then time march to obtain the evolution up to any desired value of time. Numerical studies are designed using recently invented hand-driven shock tube (Reddy tube) parameters, high/low side density and pressure values, high- and low-pressure side shock tube lengths, so that numerically computed results can be compared with actual experimental measurements.

Hardware Accelerator for 3D Method of Moments based Parasitic Extraction

A Field Programmable Gate Array (FPGA) based hardware accelerator for multi-conductor parasitic capacitance extraction, using Method of Moments (MoM), is presented in this paper. Due to the prohibitive cost of solving a dense algebraic system formed by MoM, linear complexity fast solver algorithms have been developed in the past to expedite the matrix-vector product computation in a Krylov sub-space based iterative solver framework. However, as the number of conductors in a system increases leading to a corresponding increase in the number of right-hand-side (RHS) vectors, the computational cost for multiple matrix-vector products present a time bottleneck, especially for ill-conditioned system matrices. In this work, an FPGA based hardware implementation is proposed to parallelize the iterative matrix solution for multiple RHS vectors in a low-rank compression based fast solver scheme. The method is applied to accelerate electrostatic parasitic capacitance extraction of multiple conductors in a Ball Grid Array (BGA) package. Speed-ups up to 13x over equivalent software implementation on an Intel Core i5 processor for dense matrix-vector products and 12x for QR compressed matrix-vector products is achieved using a Virtex-6 XC6VLX240T FPGA on Xilinx's ML605 board.

A nodal domain theorem for integrable billiards in two dimensions

Eigenfunctions of integrable planar billiards are studied - in particular, the number of nodal domains, nu of the eigenfunctions with Dirichlet boundary conditions are considered. The billiards for which the time-independent Schrodinger equation (Helmholtz equation) is separable admit trivial expressions for the number of domains. Here, we discover that for all separable and nonseparable integrable billiards, nu satisfies certain difference equations. This has been possible because the eigenfunctions can be classified in families labelled by the same value of m mod kn, given a particular k, for a set of quantum numbers, m, n. Further, we observe that the patterns in a family are similar and the algebraic representation of the geometrical nodal patterns is found. Instances of this representation are explained in detail to understand the beauty of the patterns. This paper therefore presents a mathematical connection between integrable systems and difference equations. (C) 2014 Elsevier Inc. All rights reserved.

Effects of refractive index mismatch in optical CT imaging of polymer gel dosimeters

Purpose: Proposing an image reconstruction technique, algebraic reconstruction technique-refraction correction (ART-rc). The proposed method takes care of refractive index mismatches present in gel dosimeter scanner at the boundary, and also corrects for the interior ray refraction. Polymer gel dosimeters with high dose regions have higher refractive index and optical density compared to the background medium, these changes in refractive index at high dose results in interior ray bending. Methods: The inclusion of the effects of refraction is an important step in reconstruction of optical density in gel dosimeters. The proposed ray tracing algorithm models the interior multiple refraction at the inhomogeneities. Jacob's ray tracing algorithm has been modified to calculate the pathlengths of the ray that traverses through the higher dose regions. The algorithm computes the length of the ray in each pixel along its path and is used as the weight matrix. Algebraic reconstruction technique and pixel based reconstruction algorithms are used for solving the reconstruction problem. The proposed method is tested with numerical phantoms for various noise levels. The experimental dosimetric results are also presented. Results: The results show that the proposed scheme ART-rc is able to reconstruct optical density inside the dosimeter better than the results obtained using filtered backprojection and conventional algebraic reconstruction approaches. The quantitative improvement using ART-rc is evaluated using gamma-index. The refraction errors due to regions of different refractive indices are discussed. The effects of modeling of interior refraction in the dose region are presented. Conclusions: The errors propagated due to multiple refraction effects have been modeled and the improvements in reconstruction using proposed model is presented. The refractive index of the dosimeter has a mismatch with the surrounding medium (for dry air or water scanning). The algorithm reconstructs the dose profiles by estimating refractive indices of multiple inhomogeneities having different refractive indices and optical densities embedded in the dosimeter. This is achieved by tracking the path of the ray that traverses through the dosimeter. Extensive simulation studies have been carried out and results are found to be matching that of experimental results. (C) 2015 American Association of Physicists in Medicine.

Efficient Dictionary for Salted Password Analysis

User authentication is essential for accessing computing resources, network resources, email accounts, online portals etc. To authenticate a user, system stores user credentials (user id and password pair) in system. It has been an interested field problem to discover user password from a system and similarly protecting them against any such possible attack. In this work we show that passwords are still vulnerable to hash chain based and efficient dictionary attacks. Human generated passwords use some identifiable patterns. We have analysed a sample of 19 million passwords, of different lengths, available online and studied the distribution of the symbols in the password strings. We show that the distribution of symbols in user passwords is affected by the native language of the user. From symbol distributions we can build smart and efficient dictionaries, which are smaller in size and their coverage of plausible passwords from Key-space is large. These smart dictionaries make dictionary based attacks practical.

Percolation on networks with antagonistic and dependent interactions

Drawing inspiration from real world interacting systems, we study a system consisting of two networks that exhibit antagonistic and dependent interactions. By antagonistic and dependent interactions we mean that a proportion of functional nodes in a network cause failure of nodes in the other, while failure of nodes in the other results in failure of links in the first. In contrast to interdependent networks, which can exhibit first-order phase transitions, we find that the phase transitions in such networks are continuous. Our analysis shows that, compared to an isolated network, the system is more robust against random attacks. Surprisingly, we observe a region in the parameter space where the giant connected components of both networks start oscillating. Furthermore, we find that for Erdos-Renyi and scale-free networks the system oscillates only when the dependence and antagonism between the two networks are very high. We believe that this study can further our understanding of real world interacting systems.

On the curvature ODE associated to the Ricci flow

In the vector space of algebraic curvature operators we study the reaction ODE which is associated to the evolution equation of the Riemann curvature operator along the Ricci flow. More precisely, we give a partial classification of the zeros of this ODE up to suitable normalization and analyze the stability of a special class of zeros of the same. In particular, we show that the ODE is unstable near the curvature operators of the Riemannian product spaces where is an Einstein (locally) symmetric space of compact type and not a spherical space form when .

LDPC Code Designs Based on root I Matrices

LDPC codes can be constructed by tiling permutation matrices that belong to the square root of identity type and similar algebraic structures. We investigate into the properties of such codes. We also present code structures that are amenable for efficient encoding.

State Transition Based Embedding in Cepstrum Domain for Audio Copyright Protection

In this paper, we propose a new state transition based embedding (STBE) technique for audio watermarking with high fidelity. Furthermore, we propose a new correlation based encoding (CBE) scheme for binary logo image in order to enhance the payload capacity. The result of CBE is also compared with standard run-length encoding (RLE) compression and Huffman schemes. Most of the watermarking algorithms are based on modulating selected transform domain feature of an audio segment in order to embed given watermark bit. In the proposed STBE method instead of modulating feature of each and every segment to embed data, our aim is to retain the default value of this feature for most of the segments. Thus, a high quality of watermarked audio is maintained. Here, the difference between the mean values (Mdiff) of insignificant complex cepstrum transform (CCT) coefficients of down-sampled subsets is selected as a robust feature for embedding. Mdiff values of the frames are changed only when certain conditions are met. Hence, almost 50% of the times, segments are not changed and still STBE can convey watermark information at receiver side. STBE also exhibits a partial restoration feature by which the watermarked audio can be restored partially after extraction of the watermark at detector side. The psychoacoustic model analysis showed that the noise-masking ratio (NMR) of our system is less than -10dB. As amplitude scaling in time domain does not affect selected insignificant CCT coefficients, strong invariance towards amplitude scaling attacks is also proved theoretically. Experimental results reveal that the proposed watermarking scheme maintains high audio quality and are simultaneously robust to general attacks like MP3 compression, amplitude scaling, additive noise, re-quantization, etc.

Router Attack toward NoC-enabled MPSoC and Monitoring Countermeasures against such Threat

The growing number of applications and processing units in modern Multiprocessor Systems-on-Chips (MPSoCs) come along with reduced time to market. Different IP cores can come from different vendors, and their trust levels are also different, but typically they use Network-on-Chip (NoC) as their communication infrastructure. An MPSoC can have multiple Trusted Execution Environments (TEEs). Apart from performance, power, and area research in the field of MPSoC, robust and secure system design is also gaining importance in the research community. To build a secure system, the designer must know beforehand all kinds of attack possibilities for the respective system (MPSoC). In this paper we survey the possible attack scenarios on present-day MPSoCs and investigate a new attack scenario, i.e., router attack targeted toward NoC architecture. We show the validity of this attack by analyzing different present-day NoC architectures and show that they are all vulnerable to this type of attack. By launching a router attack, an attacker can control the whole chip very easily, which makes it a very serious issue. Both routing tables and routing logic-based routers are vulnerable to such attacks. In this paper, we address attacks on routing tables. We propose different monitoring-based countermeasures against routing table-based router attack in an MPSoC having multiple TEEs. Synthesis results show that proposed countermeasures, viz. Runtime-monitor, Restart-monitor, Intermediate manager, and Auditor, occupy areas that are 26.6, 22, 0.2, and 12.2 % of a routing table-based router area. Apart from these, we propose Ejection address checker and Local monitoring module inside a router that cause 3.4 and 10.6 % increase of a router area, respectively. Simulation results are also given, which shows effectiveness of proposed monitoring-based countermeasures.

A hybrid method for stochastic response analysis of a vibrating structure

Response analysis of a linear structure with uncertainties in both structural parameters and external excitation is considered here. When such an analysis is carried out using the spectral stochastic finite element method (SSFEM), often the computational cost tends to be prohibitive due to the rapid growth of the number of spectral bases with the number of random variables and the order of expansion. For instance, if the excitation contains a random frequency, or if it is a general random process, then a good approximation of these excitations using polynomial chaos expansion (PCE) involves a large number of terms, which leads to very high cost. To address this issue of high computational cost, a hybrid method is proposed in this work. In this method, first the random eigenvalue problem is solved using the weak formulation of SSFEM, which involves solving a system of deterministic nonlinear algebraic equations to estimate the PCE coefficients of the random eigenvalues and eigenvectors. Then the response is estimated using a Monte Carlo (MC) simulation, where the modal bases are sampled from the PCE of the random eigenvectors estimated in the previous step, followed by a numerical time integration. It is observed through numerical studies that this proposed method successfully reduces the computational burden compared with either a pure SSFEM of a pure MC simulation and more accurate than a perturbation method. The computational gain improves as the problem size in terms of degrees of freedom grows. It also improves as the timespan of interest reduces.

Ray tracing based path-length calculations for polarized light tomographic imaging

A ray tracing based path length calculation is investigated for polarized light transport in a pixel space. Tomographic imaging using polarized light transport is promising for applications in optical projection tomography of small animal imaging and turbid media with low scattering. Polarized light transport through a medium can have complex effects due to interactions such as optical rotation of linearly polarized light, birefringence, diattenuation and interior refraction. Here we investigate the effects of refraction of polarized light in a non-scattering medium. This step is used to obtain the initial absorption estimate. This estimate can be used as prior in Monte Carlo (MC) program that simulates the transport of polarized light through a scattering medium to assist in faster convergence of the final estimate. The reflectance for p-polarized (parallel) and s-polarized (perpendicular) are different and hence there is a difference in the intensities that reach the detector end. The algorithm computes the length of the ray in each pixel along the refracted path and this is used to build the weight matrix. This weight matrix with corrected ray path length and the resultant intensity reaching the detector for each ray is used in the algebraic reconstruction (ART) method. The proposed method is tested with numerical phantoms for various noise levels. The refraction errors due to regions of different refractive index are discussed, the difference in intensities with polarization is considered. The improvements in reconstruction using the correction so applied is presented. This is achieved by tracking the path of the ray as well as the intensity of the ray as it traverses through the medium.

Fully 3D refraction correction dosimetry system

The irradiation of selective regions in a polymer gel dosimeter results in an increase in optical density and refractive index (RI) at those regions. An optical tomography-based dosimeter depends on rayline path through the dosimeter to estimate and reconstruct the dose distribution. The refraction of light passing through a dose region results in artefacts in the reconstructed images. These refraction errors are dependant on the scanning geometry and collection optics. We developed a fully 3D image reconstruction algorithm, algebraic reconstruction technique-refraction correction (ART-rc) that corrects for the refractive index mismatches present in a gel dosimeter scanner not only at the boundary, but also for any rayline refraction due to multiple dose regions inside the dosimeter. In this study, simulation and experimental studies have been carried out to reconstruct a 3D dose volume using 2D CCD measurements taken for various views. The study also focuses on the effectiveness of using different refractive-index matching media surrounding the gel dosimeter. Since the optical density is assumed to be low for a dosimeter, the filtered backprojection is routinely used for reconstruction. We carry out the reconstructions using conventional algebraic reconstruction (ART) and refractive index corrected ART (ART-rc) algorithms. The reconstructions based on FDK algorithm for cone-beam tomography has also been carried out for comparison. Line scanners and point detectors, are used to obtain reconstructions plane by plane. The rays passing through dose region with a RI mismatch does not reach the detector in the same plane depending on the angle of incidence and RI. In the fully 3D scanning setup using 2D array detectors, light rays that undergo refraction are still collected and hence can still be accounted for in the reconstruction algorithm. It is found that, for the central region of the dosimeter, the usable radius using ART-rc algorithm with water as RI matched medium is 71.8%, an increase of 6.4% compared to that achieved using conventional ART algorithm. Smaller diameter dosimeters are scanned with dry air scanning by using a wide-angle lens that collects refracted light. The images reconstructed using cone beam geometry is seen to deteriorate in some planes as those regions are not scanned. Refraction correction is important and needs to be taken in to consideration to achieve quantitatively accurate dose reconstructions. Refraction modeling is crucial in array based scanners as it is not possible to identify refracted rays in the sinogram space.