arXiv subjects

Ruowen Liu

Publications and source records attributed to Ruowen Liu.

7 recordsLinked to original sources

arXiv2024

Some $3$-designs invariant under $2.P{\Sigma}L(2,49).$

We construct a ternary [49,25,7] code from the row span of a Jacobsthal matrix. It is equivalent to a Generalized Quadratic Residue (GQR) code in the sense of van Lint and MacWilliams (1978). These codes are the abelian generalizations of the quadratic residue (QR) codes which are cyclic. The union of the [50,25,8] extension of the said code and its dual supports a 3-(50,14,1248) design. The automorphism group of the latter design is a double cover of the permutation part of the automorphism group of the [50,25,8] code, which is isomorphic to $P{\Sigma}L(2,49).$ Other weights in this code, other GQR codes, and other QR codes yield other 3-designs by the same process. A simple group action argument is provided to explain this behaviour of isodual codes.

cs.IT↗

arXiv2024

Shape optimization of slip-driven axisymmetric microswimmers

In this work, we develop a computational framework that aims at simultaneously optimizing the shape and the slip velocity of an axisymmetric microswimmer suspended in a viscous fluid. We consider shapes of a given reduced volume that maximize the swimming efficiency, i.e., the (size-independent) ratio of the power loss arising from towing the rigid body of the same shape and size at the same translation velocity to the actual power loss incurred by swimming via the slip velocity. The optimal slip and efficiency (with shape fixed) are here given in terms of two Stokes flow solutions, and we then establish shape sensitivity formulas of adjoint-solution that provide objective function derivatives with respect to any set of shape parameters on the sole basis of the above two flow solutions. Our computational treatment relies on a fast and accurate boundary integral solver for solving all Stokes flow problems. We validate our analytic shape derivative formulas via comparisons against finite-difference gradient evaluations, and present several shape optimization examples.

math.OC↗

arXiv2023

Demystifying the RSA Algorithm: An Intuitive Introduction for Novices in Cybersecurity

Given the escalating importance of cybersecurity, it becomes increasingly beneficial for a diverse community to comprehend fundamental security mechanisms. Among these, the RSA algorithm stands out as a crucial component in public-key cryptosystems. However, understanding the RSA algorithm typically entails familiarity with number theory, modular arithmetic, and related concepts, which can often exceed the knowledge base of beginners entering the field of cybersecurity. In this study, we present an intuitively crafted, student-oriented introduction to the RSA algorithm. We assume that our readers possess only a basic background in mathematics and cybersecurity. Commencing with the three essential goals of public-key cryptosystems, we provide a step-by-step elucidation of how the RSA algorithm accomplishes these objectives. Additionally, we employ a toy example to further enhance practical understanding. Our assessment of student learning outcomes, conducted across two sections of the same course, reveals a discernible improvement in grades for the students.

cs.CR↗

arXiv2021

Shape optimization of peristaltic pumps transporting rigid particles in Stokes flow

This paper presents a computational approach for finding the optimal shapes of peristaltic pumps transporting rigid particles in Stokes flow. In particular, we consider shapes that minimize the rate of energy dissipation while pumping a prescribed volume of fluid, number of particles and/or distance traversed by the particles over a set time period. Our approach relies on a recently developed fast and accurate boundary integral solver for simulating multiphase flows through periodic geometries of arbitrary shapes. In order to fully capitalize on the dimensionality reduction feature of the boundary integral methods, shape sensitivities must ideally involve evaluating the physical variables on the particle or pump boundaries only. We show that this can indeed be accomplished owing to the linearity of Stokes flow. The forward problem solves for the particle motion in a slip-driven pipe flow while the adjoint problems in our construction solve quasi-static Dirichlet boundary value problems backwards in time, retracing the particle evolution. The shape sensitivities simply depend on the solution of one forward and one adjoint (for each shape functional) problems. We validate these analytic shape derivative formulas by comparing against finite-difference based gradients and present several examples showcasing optimal pump shapes under various constraints.

math.OC↗

arXiv2021

Optimal Ciliary Locomotion of Axisymmetric Microswimmers

Many biological microswimmers locomote by periodically beating the densely-packed cilia on their cell surface in a wave-like fashion. While the swimming mechanisms of ciliated microswimmers have been extensively studied both from the analytical and the numerical point of view, the optimization of the ciliary motion of microswimmers has received limited attention, especially for non-spherical shapes. In this paper, using an envelope model for the microswimmer, we numerically optimize the ciliary motion of a ciliate with an arbitrary axisymmetric shape. The forward solutions are found using a fast boundary integral method, and the efficiency sensitivities are derived using an adjoint-based method. Our results show that a prolate microswimmer with a 2:1 aspect ratio shares similar optimal ciliary motion as the spherical microswimmer, yet the swimming efficiency can increase two-fold. More interestingly, the optimal ciliary motion of a concave microswimmer can be qualitatively different from that of the spherical microswimmer, and adding a constraint to the ciliary length is found to improve, on average, the efficiency for such swimmers.

cond-mat.soft↗

arXiv2020

Optimal slip velocities of micro-swimmers with arbitrary axisymmetric shapes

This article presents a computational approach for determining the optimal slip velocities on any given shape of an axisymmetric micro-swimmer suspended in a viscous fluid. The objective is to minimize the power loss to maintain a target swimming speed, or equivalently to maximize the efficiency of the micro-swimmer. Owing to the linearity of the Stokes equations governing the fluid motion, we show that this PDE-constrained optimization problem reduces to a simpler quadratic optimization problem, whose solution is found using a high-order accurate boundary integral method. We consider various families of shapes parameterized by the reduced volume and compute their swimming efficiency. {Among those, prolate spheroids were found to be the most efficient micro-swimmer shapes for a given reduced volume. We propose a simple shape-based scalar metric that can determine whether the optimal slip on a given shape makes it a pusher, a puller, or a neutral swimmer.}

physics.flu-dyn↗

arXiv2019

Shape optimization of Stokesian peristaltic pumps using boundary integral methods

This article presents a new boundary integral approach for finding optimal shapes of peristaltic pumps that transport a viscous fluid. Formulas for computing the shape derivatives of the standard cost functionals and constraints are derived. They involve evaluating physical variables (traction, pressure, etc.) on the boundary only. By emplyoing these formulas in conjuction with a boundary integral approach for solving forward and adjoint problems, we completely avoid the issue of volume remeshing when updating the pump shape as the optimization proceeds. This leads to significant cost savings and we demonstrate the performance on several numerical examples.

math.OC↗