TY - JOUR
TI - Optimal boundary control of a model thin-film fiber coating model
AU - Biswal, Shiba
AU - Ji, Hangjie
AU - Elamvazhuthi, Karthik
AU - Bertozzi, Andrea L.
T2 - PHYSICA D-NONLINEAR PHENOMENA
AB - This paper considers the control of fluid on a solid vertical fiber, where the fiber radius is larger than the film thickness. The fluid dynamics is governed by a fourth-order partial differential equation (PDE) that models this flow regime. Fiber coating is affected by the Rayleigh-Plateau instability that leads to breakup into moving droplets. In this work, we show that control of the film profile can be achieved by dynamically altering the input flux to the fluid system that appears as a boundary condition of the PDE. We use the optimal control methodology to compute the control function. This method entails solving a minimization of a given cost function over a time horizon. We formally derive the optimal control conditions, and numerically verify that subject to the domain length constraint, the thin film equation can be controlled to generate a desired film profile with a single point of actuation. Specifically, we show that the system can be driven to both constant film profiles and traveling waves of certain speeds.
DA - 2024/1//
PY - 2024/1//
DO - 10.1016/j.physd.2023.133942
VL - 457
SP -
SN - 1872-8022
KW - Thin-film equation
KW - Optimal control
KW - Boundary control
KW - PDE control
KW - Distributed parameter systems
ER -
TY - JOUR
TI - A positivity-preserving numerical method for a thin liquid film on a vertical cylindrical fiber
AU - Kim, Bohyun
AU - Ji, Hangjie
AU - Bertozzi, Andrea L.
AU - Sadeghpour, Abolfazl
AU - Ju, Y. Sungtaek
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - When a thin liquid film flows down on a vertical fiber, one can observe the complex and captivating interfacial dynamics of an unsteady flow. Such dynamics are applicable in various fluid experiments due to their high surface area-to-volume ratio. Recent studies verified that when the flow undergoes regime transitions, the magnitude of the film thickness changes dramatically, making numerical simulations challenging. In this paper, we present a computationally efficient numerical method that can maintain the positivity of the film thickness as well as conserve the volume of the fluid under the coarse mesh setting. A series of comparisons to laboratory experiments and previously proposed numerical methods supports the validity of our numerical method. We also prove that our method is second-order consistent in space and satisfies the entropy estimate.
DA - 2024/1/1/
PY - 2024/1/1/
DO - 10.1016/j.jcp.2023.112560
VL - 496
SP -
SN - 1090-2716
KW - Surface tension
KW - Fiber coating
KW - Positivity preserving
KW - Finite difference scheme
ER -
TY - JOUR
TI - A note on Cauchy's formula
AU - Jing, Naihuan
AU - Li, Zhijun
T2 - ADVANCES IN APPLIED MATHEMATICS
AB - We use the correlation functions of vertex operators to give a proof of Cauchy's formula∏i=1K∏j=1N(1−xiyj)=∑μ⊆[K×N](−1)|μ|sμ{x}sμ′{y}. As an application of the interpretation, we obtain an expansion of ∏i=1∞(1−qi)i−1 in terms of half plane partitions.
DA - 2024/2//
PY - 2024/2//
DO - 10.1016/j.aam.2023.102630
VL - 153
SP -
SN - 1090-2074
KW - Schur functions
KW - Cauchy's identity
KW - Vertex operator
KW - Charged free bosons
ER -
TY - JOUR
TI - Segre-driven radicality testing
AU - Helmer, Martin
AU - Tsigaridas, Elias
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - We present a probabilistic algorithm to test if a homogeneous polynomial ideal I defining a scheme X in Pn is radical using Segre classes and other geometric notions from intersection theory which is applicable for certain classes of ideals. If all isolated primary components of the scheme X are reduced and it has no embedded components outside of the singular locus of Xred=V(I), then the algorithm is not applicable and will return that it is unable to decide radically; in all the other cases it will terminate successfully and in either case its complexity is singly exponential in n. The realm of the ideals for which our radical testing procedure is applicable and for which it requires only single exponential time includes examples which are often considered pathological, such as the ones drawn from the famous Mayr-Meyer set of ideals which exhibit doubly exponential complexity for the ideal membership problem.
DA - 2024///
PY - 2024///
DO - 10.1016/j.jsc.2023.102262
VL - 122
SP -
SN - 1095-855X
KW - Radical ideals
KW - Segre class
KW - Rational univariate representation
KW - Testing if a polynomial ideal is radical
KW - Intersection theory
KW - Equidimensional decomposition
ER -
TY - JOUR
TI - The geometry of monotone operator splitting methods (to appear, available on arxiv)
T2 - Acta Numerica
DA - 2024///
PY - 2024///
ER -
TY - JOUR
TI - Settling a Tomoe-sen: Wrestling with Chip Firing
AU - Maultsby, Bevin
T2 - Math Horizons
AB - Click to increase image sizeClick to decrease image size Disclosure statementNo potential conflict of interest was reported by the author.Additional informationNotes on contributorsBevin MaultsbyBevin Maultsby is an associate teaching professor at North Carolina State University. Prior to that, she taught for two years in the University of Minnesota Talented Youth Mathematics Program (UMTYMP).
DA - 2024/9/1/
PY - 2024/9/1/
DO - 10.1080/10724117.2023.2224671
VL - 31
IS - 1
SP - 12-15
UR - http://dx.doi.org/10.1080/10724117.2023.2224671
ER -