# Browsing by Author "Ohsawa, Tomoki"

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Item Controlled Lagrangians and Stabilization of Euler-Poincaré Mechanical Systems with Broken Symmetry(2021-02-26) Contreras, Cesar; Ohsawa, TomokiShow more We extend the method of Controlled Lagrangians to Euler-Poincaré mechanical systems with broken symmetry, and find asymptotic stabilizing controls of unstable equilibria of such mechanical systems. Our motivating example is a top spinning on a movable base: The gravity breaks the symmetry with respect to the three-dimensional rotations and translations of the system, and also renders the upright spinning equilibrium unstable. We formulate the system as Euler-Poincaré equations with advected parameters using semidirect Lie group $\mathsf{SE}(3) \ltimes (\mathbb{R}^{4})^*$, and find a control that is applied to the base to asymptotically stabilize the equilibrium.Show more Item Dual Pairs and Regularization of Kummer Shapes in Resonances(American Institute of Mathematical Sciences, 2019-06) Ohsawa, Tomoki; Ohsawa, TomokiShow more We present an account of dual pairs and the Kummer shapes for n : m resonances that provides an alternative to Holm and Vizman’s work. The advantages of our point of view are that the associated Poisson structure on su(2)* is the standard (+)-Lie–Poisson bracket independent of the values of (n, m) as well as that the Kummer shape is regularized to become a sphere without any pinches regardless of the values of (n, m). A similar result holds for n : −m resonance with a paraboloid and su(1, 1)* . The result also has a straightforward generalization to multidimensional resonances as well. ©2019 American Institute of Mathematical SciencesShow more Item Ergodic Properties of Generalized Billiards(December 2023) Sechkin, Georgii 1992-; Arnold, Maxim; Zhu, Hejun; Dragovic, Vladimir; Ohsawa, Tomoki; Coskunuzer, BarisShow more We consider the generalization of the classical billiard map via different reflection laws. We study several dynamical properties of the resulting dynamical systems with the emphasis on the ergodic properties of the dynamic.Show more Item Existence and Spatio-temporal Patterns of Periodic Solutions to Non-autonomous Second Order Equivariant Delayed Systems(2022-05-01T05:00:00.000Z) Ye, Xiaoli; Malko, Anton V.; Krawcewicz, Wieslaw; Lou, Yifei; Ohsawa, Tomoki; Balanov, Zalman I.Show more In this dissertation, we study the existence and spatio-temporal symmetric patterns of peri- odic solutions to second order reversible equivariant non-autonomous periodic systems with multiple delays under the Hartman-Nagumo growth conditions. Our method is based on the usage of the Brouwer D1 × Z2 × Γ-equivariant degree theory, where D1 is related to the reversing symmetry, Z2 is related to the oddness of the right-hand-side and Γ reflects the symmetric character of the coupling in the corresponding network. Abstract results are supported by a concrete example with Γ = Dn – the dihedral group of order 2n.Show more Item Geometric Integrators for Non-separable Hamiltonian Systems(2022-08-01T05:00:00.000Z) Jayawardana, Buddhika Chathuranga Bandara; Ohsawa, Tomoki; Winkler , Duane; Rachinskiy, Dmitry; Zweck, John; Lou, YifeiShow more In this thesis, we consider non-separable Hamiltonian systems, and we develop an integrator that combines Pihajoki’s expanded approach to phase space with the symmetric projection technique. Through this, we construct a semiexplicit numerical integrator, meaning that the primary time evolution step is explicit but the symmetric projection step is implicit. The symmetric projection fixes the major disadvantage of the extended phase space technique by binding possibly divergent copies of solutions. In addition, our semiexplicit approach gives the first extended phase space integrator that is symplectic in the original phase space. This is in contrast to those explicit extended phase space integrators of Pihajoki and Tao, which are symplectic only in the extended phase space. Our integrator tends to preserve invariants better than Tao’s. Moreover, for some higher-order implementations and higher-dimensional problems, ours is faster than Tao’s explicit method despite being partially implicit.Show more Item Geometry and Dynamics of Gaussian Wave Packets and Their Wigner Transforms(Amer Inst Physics, 2018-09-24) Ohsawa, Tomoki; Tronci, Cesare; 0000-0001-9406-132X (Ohsawa, T); Ohsawa, TomokiShow more We find a relationship between the dynamics of the Gaussian wave packet and the dynamics of the corresponding Gaussian Wigner function from the Hamiltonian/symplectic point of view. The main result states that the momentum map corresponding to the natural action of the symplectic group on the Siegel upper half space yields the covariance matrix of the corresponding Gaussian Wigner function. This fact, combined with Kostant's coadjoint orbit covering theorem, establishes a symplectic/Poisson-geometric connection between the two dynamics. The Hamiltonian formulation naturally gives rise to corrections to the potential terms in the dynamics of both the wave packet and the Wigner function, thereby resulting in slightly different sets of equations from the conventional classical ones. We numerically investigate the effect of the correction term and demonstrate that it improves the accuracy of the dynamics as an approximation to the dynamics of expectation values of observables.Show more Item Optimal Control Problems with Symmetry Breaking Cost Functions(SIAM Publications) Bloch, Anthony M.; Colombo, Leonardo J.; Gupta, Rohit; Ohsawa, Tomoki; Ohsawa, TomokiShow more We investigate symmetry reduction of optimal control problems for left-invariant control affine systems on Lie groups, with partial symmetry breaking cost functions. Our approach emphasizes the role of variational principles and considers a discrete-time setting as well as the standard continuous time formulation. Specifically, we recast the optimal control problem as a constrained variational problem with a partial symmetry breaking Lagrangian and obtain the Euler-Poincare equations from a variational principle. By using a Legendre transformation, we recover the Lie Poisson equations obtained by Borum and Bretl [IEEE Trans. Automat. Control, 62 (2017), pp. 3209-3224] in the same context. We also discretize the variational principle in time and obtain the discrete-time Lie Poisson equations. We illustrate the theory with some practical examples including a motion planning problem in the presence of an obstacle.Show more Item Stabilization of Nonholonomic Euler–poincaré Mechanical Systems With Broken Symmetry by Controlled Lagrangians(2022-12-01T06:00:00.000Z) Garcia, Jorge Silva; Ohsawa, Tomoki; Stelling, Allison; Dragovic, Vladimir; Ramakrishna, Viswanath; Pereira, L. FelipeShow more We extend the method of Controlled Lagrangians to nonholonomic Euler–Poincaré mechanical systems with broken symmetry by considering the problem of stabilizing what we call a pendulum skate, a simple model of a figure skater developed by Gzenda and Putkaradze. By exploiting the symmetry of the system as well as taking care of the part of the symmetry broken by the gravity, the equations of motion are given as nonholonomic Euler–Poincaré equation with advected parameters. After that, we discovered the general form of the equilibrium points and presented the classification of two special ones, designated as sliding and spinning. Of our main interest is the stability of the sliding and spinning equilibria of the system. We show that the former is unstable and the latter is stable only under certain conditions. We use the method of Controlled Lagrangians to find a control to stabilize the sliding equilibrium and also show how to achieve the stabilization for the general equilibrium point.Show more Item Symmetry and Conservation Laws in Semiclassical Wave Packet Dynamics(American Institute of Physics Inc., 2015-03-18) Ohsawa, Tomoki; Ohsawa, TomokiShow more We formulate symmetries in semiclassical Gaussian wave packet dynamics and find the corresponding conserved quantities, particularly the semiclassical angular momentum, via Noether's theorem. We consider two slightly different formulations of Gaussian wave packet dynamics; one is based on earlier works of Heller and Hagedorn and the other based on the symplectic-geometric approach by Lubich and others. In either case, we reveal the symplectic and Hamiltonian nature of the dynamics and formulate natural symmetry group actions in the setting to derive the corresponding conserved quantities (momentum maps). The semiclassical angular momentum inherits the essential properties of the classical angular momentum as well as naturally corresponds to the quantum picture.Show more Item The Hagedorn–Hermite Correspondence(Birkhäuser Boston) Ohsawa, Tomoki; Ohsawa, TomokiShow more We investigate the relationship between the semiclassical wave packets of Hagedorn and the Hermite functions by establishing a relationship between their ladder operators. This Hagedorn–Hermite correspondence provides a unified view as well as simple proofs of some essential results on the Hagedorn wave packets. Particularly, we show that Hagedorn’s ladder operators are a natural set of ladder operators obtained from the position and momentum operators using the symplectic group. This construction reveals an algebraic structure of the Hagedorn wave packets, and explains the relative simplicity of Hagedorn’s parametrization compared to the rather intricate construction of the generalized squeezed states. We apply our formulation to show the existence of minimal uncertainty products for the Hagedorn wave packets, generalizing Hagedorn’s one-dimensional result to multi-dimensions. The Hagedorn–Hermite correspondence also leads to an alternative derivation of the generating function for the Hagedorn wave packets based on the generating function for the Hermite functions. This result, in turn, reveals the relationship between the Hagedorn polynomials and the Hermite polynomials. © 2018 Springer Science+Business Media, LLC, part of Springer NatureShow more Item Tracking the Biochemical Activities in Cultured Cancer Cells Using Nuclear Magnetic Resonance(August 2022) Feizi, Wirya; Lumata, Lloyd; Ohsawa, Tomoki; Glosser, Robert; Izen, Joseph M.; Zakhidov, Anvar A.; Slinker, Jason D.Show more The human body, on average, is made up of approximately 30 to 40 trillion cells which are divided into subgroups as organs and tissues with specific roles and functions, along with a regular and controlled growth mechanism. Cancer forms when some of these cells mutate and become rebellious, manifesting in uncontrollable growth and abnormally rapid proliferation. As cancer cells multiply rapidly, there is an immediate need for new raw materials and nutrients to sustain its hyperactive metabolic machinery. Thus, most of the biochemical pathways in cancer are abnormally hyperactive to satisfy its voracious appetite to multiply into new cells. This Ph.D. dissertation entails a discussion of using nuclear magnetic resonance (NMR) spectroscopy to track the aberrant biochemical activities of cancer cells at the molecular level. Chapter 1 of this dissertation includes an introductory discussion on the 3 cancer cell types that I have investigated: pancreatic ductal adenocarcinoma (PDAC), colorectal cancer (CRC), and glioblastoma multiforme (GBM) cell lines, and the experimental techniques that I used to study these cells: NMR spectroscopy, electron spin resonance (ESR), Western blot, and the NMR enhancing technique Overhauser effect dynamic nuclear polarization (DNP). In this chapter, I also discussed the fundamental principles of NMR and the basic details of the other experimental techniques. Chapter 2 of this thesis is about the effect of the chemotherapeutic drug beta-lapachone on the metabolism of the biochemical tracer [1,3-13C2] ethyl acetoacetate (EAA) in PDAC and CRC cells. The main finding of this study was that the metabolism of EAA is reasonably rapid in these cells, with acetate and beta-hydroxybutyrate as some of the metabolic byproducts. The enzyme NQO1 converts β-lapachone into a cancer-killing reactive oxygen species; details of its effects on EAA metabolism in PDAC and CRC cells will be discussed. Chapter 3 discusses the use of the biochemical tracer [1-13C1]α-ketoisocaproate (KIC) to study the hyperactivity of the branched-chain amino acid transferase (BCAT) enzyme in glioblastoma cells. 13C NMR results revealed that 13C-labeled KIC was converted abundantly into the amino acid leucine due to overexpressed and hyperactive BCAT enzymatic activity in SFxL glioblastoma cells. Further study was done using a BCATc inhibitor in which 13C NMR unveiled specific details as to the disruption of this metabolic pathway by this inhibitor ting details from microscopy and Western blot results. Chapter 4 details the fundamentals, instrumental setup, and preliminary results of the Overhauser effect DNP. Herein, the mechanism of electron spin polarization transfer to the nuclear spins is provided as well as the detailed instrumental assembly and setup of the homebuilt Overhauser DNP machine. This DNP setup is a combination of NMR and microwave technologies in pursuit of enhancing the NMR signals at room temperature. This project is still ongoing, but preliminary proton NMR results are presented. The rest of the dissertation entails technical details on the operation and data acquisition of various instruments and techniques used in this thesis. Overall, this PhD thesis provides a compilation of research works on tracking the abnormal biochemical activities in cancer cells using 13C NMR spectroscopy to turn these metabolic aberrations into diagnostic advantages for early detection and metabolic assessment of this disease.Show more