1,120 research outputs found
Hydrodynamic Flows on Curved Surfaces: Spectral Numerical Methods for Radial Manifold Shapes
We formulate hydrodynamic equations and spectrally accurate numerical methods
for investigating the role of geometry in flows within two-dimensional fluid
interfaces. To achieve numerical approximations having high precision and level
of symmetry for radial manifold shapes, we develop spectral Galerkin methods
based on hyperinterpolation with Lebedev quadratures for -projection to
spherical harmonics. We demonstrate our methods by investigating hydrodynamic
responses as the surface geometry is varied. Relative to the case of a sphere,
we find significant changes can occur in the observed hydrodynamic flow
responses as exhibited by quantitative and topological transitions in the
structure of the flow. We present numerical results based on the
Rayleigh-Dissipation principle to gain further insights into these flow
responses. We investigate the roles played by the geometry especially
concerning the positive and negative Gaussian curvature of the interface. We
provide general approaches for taking geometric effects into account for
investigations of hydrodynamic phenomena within curved fluid interfaces.Comment: 14 figure
Design, Analysis, and Application of Flipped Product Chaotic System
In this paper, a novel method is proposed to build an improved 1-D discrete chaotic map called flipped product chaotic system (FPCS) by multiplying the output of one map with the output of a vertically flipped second map. Two variants, each with nine combinations, are shown with trade-off between computational cost and performance. The chaotic properties are explored using the bifurcation diagram, Lyapunov exponent, Kolmogorov entropy, and correlation coefficient. The proposed schemes offer a wider chaotic range and improved chaotic performance compared to the constituent maps and several prior works of similar nature. Wide chaotic window and improved chaotic complexity are two desired characteristics for several security applications as these two characteristics ensure enhanced design space with elevated entropic properties. We present a general Field-Programmable Gate Array (FPGA) design framework for the hardware implementation of the proposed flipped-product schemes and the results show good qualitative agreement with the numerical results from MATLAB simulation. Finally, we present a new Pseudo Random Number Generator (PRNG) using the two variants of the proposed chaotic map and validate their excellent randomness property using four standard statistical tests, namely NIST, FIPS, TestU01, and Diehard
Physical limits to sensing material properties
Constitutive relations describe how materials respond to external stimuli
such as forces. All materials respond heterogeneously at small scales, which
limits what a localized sensor can discern about the global constitution of a
material. In this paper, we quantify the limits of such constitutional sensing
by determining the optimal measurement protocols for sensors embedded in
disordered media. For an elastic medium, we find that the least fractional
uncertainty with which a sensor can determine a material constant
is approximately
\begin{equation*}
\frac{\delta \lambda_0}{\lambda_0 } \sim \left( \frac{\Delta_{\lambda} }{
\lambda_0^2} \right)^{1/2} \left( \frac{ d }{ a } \right)^{D/2} \left( \frac{
\xi }{ a } \right)^{D/2} \end{equation*} for , , and , where is the size of the sensor, is
its spatial resolution, is the correlation length of fluctuations in the
material constant, is the local variability of the material
constant, and is the dimension of the medium. Our results reveal how one
can construct microscopic devices capable of sensing near these physical
limits, e.g. for medical diagnostics. We show how our theoretical framework can
be applied to an experimental system by estimating a bound on the precision of
cellular mechanosensing in a biopolymer network.Comment: 33 pages, 3 figure
Pengembangan True Random Number Generator berbasis Citra menggunakan Algoritme Kaotis
The security of most cryptographic systems depends on key generation using a nondeterministic RNG. PRNG generates a random numbers with repeatable patterns over a period of time and can be predicted if the initial conditions and algorithms are known. TRNG extracts entropy from physical sources to generate random numbers. However, most of these systems have relatively high cost, complexity, and difficulty levels. If the camera is directed to a random scene, the resulting random number can be assumed to be random. However, the weakness of a digital camera as a source of random numbers lies in the resulting refractive pattern. The raw data without further processing can have a fixed noise pattern. By applying digital image processing and chaotic algorithms, digital cameras can be used to generate true random numbers. In this research, for preprocessing image data used method of floyd-steinberg algorithm. To solve the problem of several consecutive black or white pixels appearing in the processed image area, the arnold-cat map algorithm is used while the XOR operation is used to combine the data and generate the true random number. NIST statistical tests, scatter and histrogram analyzes show the use of this method can produce truly random number
Analysis and Geometric Singularities
This workshop focused on several of the main areas of current research concerning analysis on singular and noncompact spaces. Topics included harmonic analysis and Hodge theory on, and the theory of compactifications of, locally symmetric spaces, new topological techniques in index theory, nonlinear elliptic problems related to metrics with special geometry, and various more traditional problems in spectral geometry concerning estimation of eigenvalues and the spectral function
Tropical Monte Carlo quadrature for Feynman integrals
We introduce a new method to evaluate algebraic integrals over the simplex
numerically. This new approach employs techniques from tropical geometry and
exceeds the capabilities of existing numerical methods by an order of
magnitude. The method can be improved further by exploiting the geometric
structure of the underlying integrand. As an illustration of this, we give a
specialized integration algorithm for a class of integrands that exhibit the
form of a generalized permutahedron. This class includes integrands for
scattering amplitudes and parametric Feynman integrals with tame kinematics. A
proof-of-concept implementation is provided with which Feynman integrals up to
loop order 17 can be evaluated.Comment: 6 figures, see http://github.com/michibo/tropical-feynman-quadrature
for the referenced program code; v2: typos corrected, version accepted for
publication in Annales de l'Institut Henri Poincar\'e
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