Eliminating Flow Separation and Reducing Viscous Drag Through Boundary Layer Analysis and Manipulation

As both computers and flow-analyzing equations have increased in sophistication, Computational Fluid Dynamics (CFD) has evolved into a fixture for advanced aircraft design. While CFD codes have improved in accuracy and efficiency, their ability to encompass viscous effects is lacking in certain areas. For example, current CFD codes cannot accurately predict or correct for the increased drag due to these viscous effects at some flow conditions. However, by analyzing an airfoil's turbulent boundary layer, one can predict not only flow separation via the shape factor parameter, but also viscous drag via the momentum thickness. Various codes have been written which can calculate turbulent boundary layer parameters. The goal of my research is to develop procedures for modifying an airfoil (via its local pressure distribution) to eliminate boundary layer separation and/or to reduce viscous drag. The modifications to the local pressure distribution necessary to achieve these objectives will be determined using a direct-iterative method installed into a turbulent boundary layer analyzer. Furthermore, the modifications should preserve the basic characteristics of the original airfoil

Nonlinear Free Vibration Analysis of Laminated Carbon/Epoxy Curved Panels

Nonlinear frequency responses of the laminated carbon/epoxy composite curved shell panels have been investigated numerically and validated with in-house experimentation. The nonlinear responses have been computed numerically via customised computer code developed in MATLAB environment with the help of current mathematical model in conjunction with the direct iterative method. The mathematical model of the layered composite structure derived using various shear deformable kinematic models (two higher-order theories) in association with Green-Lagrange nonlinear strains. The current model includes all the nonlinear higher-order strain terms in the formulation to achieve generality. Further, the modal test has been conducted experimentally to evaluate the desired frequency values and are extracted via the transformed signals using fast Fourier transform technique. In addition, the results are computed using the simulation model developed in commercial finite element package (ANSYS) via batch input technique. Finally, numerical examples are solved for different geometrical configurations and discussed the effects of other design parameters (thickness ratio, curvature ratio and constraint condition) on the fundamental linear and nonlinear frequency responses in details

Numerical analysis of reversible A + B <-> C reaction-diffusion systems

We develop an effective numerical method of studying large-time properties of reversible reaction-diffusion systems of type A + B C with initially separated reactants. Using it we find that there are three types of asymptotic reaction zones. In particular we show that the reaction rate can be locally negative and concentrations of species A and B can be nonmonotonic functions of the space coordinate x, locally significantly exceeding their initial values.Comment: To appear in EPJ B, 5 pages + 6 figure

Demonstration of Adiabatic Variational Quantum Computing with a Superconducting Quantum Coprocessor

Adiabatic quantum computing enables the preparation of many-body ground states. This is key for applications in chemistry, materials science, and beyond. Realisation poses major experimental challenges: Direct analog implementation requires complex Hamiltonian engineering, while the digitised version needs deep quantum gate circuits. To bypass these obstacles, we suggest an adiabatic variational hybrid algorithm, which employs short quantum circuits and provides a systematic quantum adiabatic optimisation of the circuit parameters. The quantum adiabatic theorem promises not only the ground state but also that the excited eigenstates can be found. We report the first experimental demonstration that many-body eigenstates can be efficiently prepared by an adiabatic variational algorithm assisted with a multi-qubit superconducting coprocessor. We track the real-time evolution of the ground and exited states of transverse-field Ising spins with a fidelity up that can reach about 99%.Comment: 12 pages, 4 figure

Similarity-Aware Spectral Sparsification by Edge Filtering

In recent years, spectral graph sparsification techniques that can compute ultra-sparse graph proxies have been extensively studied for accelerating various numerical and graph-related applications. Prior nearly-linear-time spectral sparsification methods first extract low-stretch spanning tree from the original graph to form the backbone of the sparsifier, and then recover small portions of spectrally-critical off-tree edges to the spanning tree to significantly improve the approximation quality. However, it is not clear how many off-tree edges should be recovered for achieving a desired spectral similarity level within the sparsifier. Motivated by recent graph signal processing techniques, this paper proposes a similarity-aware spectral graph sparsification framework that leverages efficient spectral off-tree edge embedding and filtering schemes to construct spectral sparsifiers with guaranteed spectral similarity (relative condition number) level. An iterative graph densification scheme is introduced to facilitate efficient and effective filtering of off-tree edges for highly ill-conditioned problems. The proposed method has been validated using various kinds of graphs obtained from public domain sparse matrix collections relevant to VLSI CAD, finite element analysis, as well as social and data networks frequently studied in many machine learning and data mining applications

Thermodynamics of the self-gravitating ring model

We present the phase diagram, in both the microcanonical and the canonical ensemble, of the Self-Gravitating-Ring (SGR) model, which describes the motion of equal point masses constrained on a ring and subject to 3D gravitational attraction. If the interaction is regularized at short distances by the introduction of a softening parameter, a global entropy maximum always exists, and thermodynamics is well defined in the mean-field limit. However, ensembles are not equivalent and a phase of negative specific heat in the microcanonical ensemble appears in a wide intermediate energy region, if the softening parameter is small enough. The phase transition changes from second to first order at a tricritical point, whose location is not the same in the two ensembles. All these features make of the SGR model the best prototype of a self-gravitating system in one dimension. In order to obtain the stable stationary mass distribution, we apply a new iterative method, inspired by a previous one used in 2D turbulence, which ensures entropy increase and, hence, convergence towards an equilibrium state

The Periodic Standing-Wave Approximation: Overview and Three Dimensional Scalar Models

The periodic standing-wave method for binary inspiral computes the exact numerical solution for periodic binary motion with standing gravitational waves, and uses it as an approximation to slow binary inspiral with outgoing waves. Important features of this method presented here are: (i) the mathematical nature of the ``mixed'' partial differential equations to be solved, (ii) the meaning of standing waves in the method, (iii) computational difficulties, and (iv) the ``effective linearity'' that ultimately justifies the approximation. The method is applied to three dimensional nonlinear scalar model problems, and the numerical results are used to demonstrate extraction of the outgoing solution from the standing-wave solution, and the role of effective linearity.Comment: 13 pages RevTeX, 5 figures. New version. A revised form of the nonlinearity produces better result

Fixed-Point Algorithms for Solving the Critical Value and Upper Tail Quantile of Kuiper's Statistics

Kuiper's statistic is a good measure for the difference of ideal distribution and empirical distribution in the goodness-of-fit test. However, it is a challenging problem to solve the critical value and upper tail quantile, or simply Kuiper pair, of Kuiper's statistics due to the difficulties of solving the nonlinear equation and reasonable approximation of infinite series. The pioneering work by Kuiper just provided the key ideas and few numerical tables created from the upper tail probability $\alpha$ and sample capacity $n$, which limited its propagation and possible applications in various fields since there are infinite configurations for the parameters $\alpha$ and $n$. In this work, the contributions lie in three perspectives: firstly, the second order approximation for the infinite series of the cumulative distribution of the critical value is used to achieve higher precision; secondly, the principles and fixed-point algorithms for solving the Kuiper pair are presented with details; finally, an error in Kuiper's table of critical value is discovered and fixed. The algorithms are verified and validated by comparing with the table provided by Kuiper. The methods and algorithms proposed are enlightening and worthy of introducing to the college students, computer programmers, engineers, experimental psychologists and so on.Comment: 19 pages, 6 figures, code available on GitHu