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Jingyi Chen

Publications and source records attributed to Jingyi Chen.

At least 55 records · Page 3Linked to original sources
arXiv2021

Suppressing coherence effects in quantum-measurement based engines

The recent advances in the study of thermodynamics of microscopic processes have driven the search for new developments in energy converters utilizing quantum effects. We here propose a universal framework to describe the thermodynamics of a quantum engine fueled by quantum projective measurements. Standard quantum thermal machines operating in a finite-time regime with a driven Hamiltonian that does not commute in different times have the performance decreased by the presence of coherence, which is associated with a larger entropy production and irreversibility degree. However, we show that replacing the standard hot thermal reservoir by a projective measurement operation with general basis in the Bloch sphere and controlling the basis angles suitably could improve the performance of the quantum engine as well as decrease the entropy change during the measurement process. Our results go in direction of a generalization of quantum thermal machine models where the fuel comes from general sources beyond the standard thermal reservoir.

quant-ph↗
arXiv2021

Regularity of Hamiltonian Stationary Equations in Symplectic manifolds

In this paper, we prove that any $C^{1}$-regular Hamiltonian stationary Lagrangian submanifold in a symplectic manifold is smooth. More broadly, we develop a regularity theory for a class of fourth order nonlinear elliptic equations with two distributional derivatives. Our fourth order regularity theory originates in the geometrically motivated variational problem for the volume functional, but should have applications beyond.

math.DG↗
arXiv2021

Bayesian Poroelastic Aquifer Characterization from InSAR Surface Deformation Data Part II: Quantifying the Uncertainty

Uncertainty quantification of groundwater (GW) aquifer parameters is critical for efficient management and sustainable extraction of GW resources. These uncertainties are introduced by the data, model, and prior information on the parameters. Here we develop a Bayesian inversion framework that uses Interferometric Synthetic Aperture Radar (InSAR) surface deformation data to infer the laterally heterogeneous permeability of a transient linear poroelastic model of a confined GW aquifer. The Bayesian solution of this inverse problem takes the form of a posterior probability density of the permeability. Exploring this posterior using classical Markov chain Monte Carlo (MCMC) methods is computationally prohibitive due to the large dimension of the discretized permeability field and the expense of solving the poroelastic forward problem. However, in many partial differential equation (PDE)-based Bayesian inversion problems, the data are only informative in a few directions in parameter space. For the poroelasticity problem, we prove this property theoretically for a one-dimensional problem and demonstrate it numerically for a three-dimensional aquifer model. We design a generalized preconditioned Crank--Nicolson (gpCN) MCMC method that exploits this intrinsic low dimensionality by using a low-rank based Laplace approximation of the posterior as a proposal, which we build scalably. The feasibility of our approach is demonstrated through a real GW aquifer test in Nevada. The inherently two dimensional nature of InSAR surface deformation data informs a sufficient number of modes of the permeability field to allow detection of major structures within the aquifer, significantly reducing the uncertainty in the pressure and the displacement quantities of interest.

physics.geo-ph↗
arXiv2020

Probing the pathway of an ultrafast structural phase transition to illuminate the transition mechanism in Cu2S

Disentangling the primary order parameter from secondary order parameters in phase transitions is critical to the interpretation of the transition mechanisms in strongly correlated systems and quantum materials. Here we present a study of structural phase transition pathways in superionic Cu2S nanocrystals that exhibit intriguing properties. Utilizing ultrafast electron diffraction techniques sensitive in both momentum-space and the time-domain, we distinguish the dynamics of crystal symmetry breaking and lattice expansion in this system. We are able to follow the transient states along the transition pathway and so observe the dynamics of both the primary and secondary order parameters. Based on these observations we argue that the mechanism of the structural phase transition in Cu2S is dominated by the electron-phonon coupling. This mechanism advances the understanding from previous results where the focus was solely on dynamic observations of the lattice expansion.

cond-mat.str-el↗
arXiv2020

On stability of the fibres of Hopf surfaces as harmonic maps and minimal surfaces

We construct a family of Hermitian metrics on the Hopf surface $ \mathbb{S}^3\times \mathbb{S}^1$, whose fundamental classes represent distinct cohomology classes in the Aeppli cohomology group. These metrics are locally conformally Kähler. Among the toric fibres of $π:\mathbb{S}^{3} \times \mathbb{S}^1\to\mathbb{C} P^1$ two of them are stable minimal surfaces and each of the two has a neighbourhood so that fibres therein are given by stable harmonic maps from 2-torus and outside, far away from the two tori, there are unstable harmonic ones that are also unstable minimal surfaces.

math.DG↗
arXiv2020

Bayesian Poroelastic Aquifer Characterization from InSAR Surface Deformation Data. Part I: Maximum A Posteriori Estimate

Characterizing the properties of groundwater aquifers is essential for predicting aquifer response and managing groundwater resources. In this work, we develop a high-dimensional scalable Bayesian inversion framework governed by a three-dimensional quasi-static linear poroelastic model to characterize lateral permeability variations in groundwater aquifers. We determine the maximum a posteriori (MAP) point of the posterior permeability distribution from centimeter-level surface deformation measurements obtained from Interferometric Synthetic Aperture Radar (InSAR). The scalability of our method to high parameter dimension is achieved through the use of adjoint-based derivatives, inexact Newton methods to determine the MAP point, and a Matérn class sparse prior precision operator. Together, these guarantee that the MAP point is found at a cost, measured in number of forward/adjoint poroelasticity solves, that is independent of the parameter dimension. We apply our methodology to a test case for a municipal well in Mesquite, Nevada, in which InSAR and GPS surface deformation data are available. We solve problems with up to 320,824 state variable degrees of freedom (DOFs) and 16,896 parameter DOFs. A consistent treatment of noise level is employed so that the aquifer characterization result does not depend on the pixel spacing of surface deformation data. Our results show that the use of InSAR data significantly improves characterization of lateral aquifer heterogeneity, and the InSAR-based aquifer characterization recovers complex lateral displacement trends observed by independent daily GPS measurements.

physics.geo-ph↗
arXiv2019

Compactification of the space of Hamiltonian stationary Lagrangian submanifolds with bounded total extrinsic curvature and volume

For a sequence of immersed connected closed Hamiltonian stationary Lagrangian submaniolds in $\mathbb{C}^{n}$ with uniform bounds on their volumes and the total extrinsic curvatures, we prove that a subsequence converges either to a point or to a Hamiltonian stationary Lagrangian $n$-varifold locally uniformly in $C^{k}$ for any nonnegative integer $k$ away from a finite set of points, and the limit is Hamiltonian stationary in ${\mathbb{C}}^{n}$. We also obtain a theorem on extending Hamiltonian stationary Lagrangian submanifolds $L$ across a compact set $N$ of Hausdorff codimension at least 2 that is locally noncollapsing in volumes matching its Hausdorff dimension, provided the mean curvature of $L$ is in $L^{n}$ and a condition on local volume of $L$ near $N$ is satisfied.

math.DG↗
arXiv2017

On the Regularity of Hamiltonian Stationary Lagrangian manifolds

We prove a Morrey-type theorem for Hamiltonian stationary submanifolds of $\mathbb{C}^{n}$. Namely, if $L$ $\subset$ $\mathbb{C}^{n}$ is a $C^{1}$ Lagrangian submanifold with weakly harmonic Lagrangian phase $θ,$ then $L$ must be smooth. In the process we also discuss a local version of the equation, which is a nonlinear fourth order double divergence equation of the potential function whose gradient graph defines the Hamiltonian stationary submanifolds locally, and we establish full regularity and removability of singular sets of capacity zero for weak solutions with $C^{1,1}$ norm below a dimensional constant.

math.AP↗
arXiv2017

Hamiltonian stationary cones with isotropic links

We show that any closed oriented immersed Hamiltonian stationary isotropic surface $Σ$ with genus $g_Σ$ in $S^{5}\subset\mathbb{C}^{3}$ is (1) Legendrian and minimal if $g_Σ=0$; (2) either Legendrian or with exactly $2g_Σ-2$ Legendrian points if $g_Σ\geq1.$ In general, every compact oriented immersed isotropic submanifold $L^{n-1}\subset S^{2n-1}\subset\mathbb{C}^{n}$ such that the cone $C\left( L^{n-1}\right) $ is Hamiltonian stationary must be Legendrian and minimal if its first Betti number is zero. Corresponding results for non-orientable links are also provided.

math.DG↗
arXiv2016

Radial solutions of a fourth order Hamiltonian stationary equation

We consider smooth radial solutions to the Hamiltonian stationary equation which are defined away from the origin. We show that in dimension two all radial solutions on unbounded domains must be special Lagrangian. In contrast, for all higher dimensions there exist non-special Lagrangian radial solutions over unbounded domains; moreover, near the origin, the gradient graph of such a solution is continuous if and only if the graph is special Lagrangian.

math.AP↗
arXiv2016

Geometry of Lagrangian self-shrinking tori and applications to the Piecewise Lagrangian Mean Curvature Flow

We study geometric properties of the Lagrangian self-shrinking tori in $\mathbb R^4$. When the area is bounded above uniformly, we prove that the entropy for the Lagrangian self-shrinking tori can only take finitely many values; this is done by deriving a Łojasiewicz-Simon type gradient inequality for the branched conformal self-shrinking tori and then combining with the compactness theorem in \cite{CMa}. When the area bound is small, we show that any Lagrangian self-shrinking torus in $\mathbb R^4$ with small area is embedded with uniform curvature estimates, and the space of such tori is compact. Using the finiteness of entropy values, we construct a piecewise Lagrangian mean curvature flow for Lagrangian immersed tori in $\mathbb R^4$, along which the Lagrangian condition is preserved, area is decreasing, and the type I singularities that are compact with a fixed area upper bound can be perturbed away in finite steps. This is a Lagrangian version of the construction for embedded surfaces in $\mathbb R^3$ in \cite{CM}.

math.DG↗
arXiv2015

Extendability of conformal structures on punctured surfaces

For a smooth immersion $f$ from the punctured disk $D\backslash\{0\}$ into $\mathbb{R}^n$ extendable continuously at the puncture, if its mean curvature is square integrable and the measure of $f(D)\cap B_{r_k}=o(r_k)$ for a sequence $r_k\to 0$, we show that the Riemannian surface $(D_r\backslash\{0\},g)$ where $g$ is the induced metric is conformally equivalent to the unit Euclidean punctured disk, for any $r\in(0,1)$. For a locally $W^{2,2}$ Lipschitz immersion $f$ from the punctured disk $D_2\backslash\{0\}$ into $\mathbb{R}^n$, if $\|\nabla f\|_{L^\infty}$ is finite and the second fundamental form of $f$ is in $L^2$, we show that there exists a homeomorphism $ϕ:D\to D$ such that $f\circϕ$ is a branched $W^{2,2}$-conformal immersion from the Euclidean unit disk $D$ into $\mathbb{R}^n$.

math.DG↗
arXiv2014

Liouville type theorems for the p-harmonic functions

We show that the Dirichlet problem at infinity is unsolvable for the p-Laplace equation for any nonconstant continuous boundary data, for certain range of p>n, on an n-dimensional Cartan-Hadamard manifold constructed from a complete noncompact shrinking gradient Ricci soliton. Using the steady gradient Ricci soliton, we find an incomplete Riemannian metric on ${\mathbb R}^2$ with positive Gauss curvature such that every positive p-harmonic function must be constant for $p\geq 4$.

math.DG↗
arXiv2014

Radially Symmetric Solutions To The Graphic Willmore Surface Equation

We show that a smooth radially symmetric solution $u$ to the graphic Willmore surface equation is either a constant or the defining function of a half sphere in ${\mathbb R}^3$. In particular, radially symmetric entire Willmore graphs in ${\mathbb R}^3$ must be flat. When $u$ is a smooth radial solution over a punctured disk $D(ρ)\backslash\{0\}$ and is in $C^1(D(ρ))$, we show that there exist a constant $λ$ and a function $β$ in $C^0(D(ρ))$ such that $u''(r) =\fracλ{2}\log r+β(r)$; moreover, the graph of $u$ is contained in a graphical region of an inverted catenoid which is uniquely determined by $λ$ and $β(0)$. It is also shown that a radial solution on the punctured disk extends to a $C^1$ function on the disk when the mean curvature is square integrable.

math.DG↗
arXiv2014

The space of compact self-shrinking solutions to the Lagrangian Mean Curvature Flow in $\mathbb C^2$

Let $F_n :(Σ, h_n) \to \mathbb C^2$ be a sequence of conformally immersed Lagrangian self-shrinkers with a uniform area upper bound to the mean curvature flow, and suppose that the sequence of metrics $\{h_n\}$ converges smoothly to a Riemannian metric $h$. We show that a subsequence of $\{F_n\}$ converges smoothly to a branched conformally immersed Lagrangian self-shrinker $F_\infty : (Σ, h)\to \mathbb C^2$. When the area bound is less than $16π$, the limit $F_\infty$ is an embedded torus. When the genus of $Σ$ is one, we can drop the assumption on convergence $h_n\to h$. When the genus of $Σ$ is zero, we show that there is no branched immersion of $Σ$ as a Lagrangian shrinker, generalizing the rigidity result of Smoczyk in dimension two by allowing branch points.

math.DG↗
arXiv2013

Homotopy classes of harmonic maps of the stratified 2-spheres and applications to geometric flows

We show that the set of harmonic maps from the 2-dimensional stratified spheres with uniformly bounded energies contains only finitely many homotopy classes. We apply this result to construct infinitely many harmonic map flows and mean curvature flows of 2-sphere in the connected sum of two closed 3-dimensional manifolds $M_1\not=S^3$ and $M_2\not=S^3,\R¶^3$, which must develop finite time singularity.

math.DG↗