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Results for "Hao Liu"

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Evidence of s-channel Single Top Quark Production in Events with one Charged Lepton and Bottom Quark Jets at CDFOct 08 2013We report an evidence of \textit{s}-channel single top quark production in $p\bar{p}$ collision at $\sqrt{s}= 1.96 \mathrm{TeV}$ using data with integrated luminosity of $9.4 \mathrm{fb}^{-1}$ collected by the Collider Detector at Fermilab (CDF). We select ... More
Fast Local Voltage Control under Limited Reactive Power: Optimality and Stability AnalysisOct 23 2015High penetration of distributed energy resources presents several challenges and opportunities for voltage regulation in power distribution systems. A local reactive power (VAR) control framework will be developed that can fast respond to voltage mismatch ... More
A remark on Mirzakhani's asymptotic formulaeMar 26 2011Aug 29 2011In this note, we answer a question of Mirzakhani on asymptotic behavior of the one-point volume polynomial of moduli spaces of curves. We also present some applications of Mirzakhani's asymptotic formulae of Weil-Petersson volumes.
Intersection numbers and automorphisms of stable curvesAug 09 2006May 22 2009Due to the orbifold singularities, the intersection numbers on the moduli space of curves $\bar{\sM}_{g,n}$ are in general rational numbers rather than integers. We study the properties of the denominators of these intersection numbers and their relationship ... More
Mirzakharni's recursion formula is equivalent to the Witten-Kontsevich theoremMay 15 2007May 22 2009In this paper, we give a proof of Mirzakhani's recursion formula of Weil-Petersson volumes of moduli spaces of curves using the Witten-Kontsevich theorem. We also describe properties of intersections numbers involving higher degree $\kappa$ classes.
Theory of carrier density in multigated doped graphene sheets with quantum correctionMar 30 2013The quantum capacitance model is applied to obtain an exact solution for the space-resolved carrier density in a multigated doped graphene sheet at zero temperature, with quantum correction arising from the finite electron capacity of the graphene itself ... More
An Energetic Variational Approach for the Cahn--Hilliard Equation with Dynamic Boundary Condition: Model Derivation and Mathematical AnalysisOct 23 2017Jan 23 2019The Cahn--Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In recent years, several types of dynamic boundary conditions have been proposed in order to account for possible short-range interactions ... More
Descendent integrals and tautological rings of moduli spaces of curvesDec 03 2009Apr 11 2010The main objective of this paper is to give a summary of our recent work on recursion formulae for intersection numbers on moduli spaces of curves and their applications. We also present a conjectural relation between tautological rings and the mock theta ... More
Computing top intersections in the tautological ring of $M_g$Jan 25 2010We derive effective recursion formulae of top intersections in the tautological ring $R^*(M_g)$ of the moduli space of curves of genus $g\geq 2$. As an application, we prove a convolution-type tautological relation in $R^{g-2}(M_g)$.
Quantum fluctuations, conformal deformations, and Gromov's topology --- Wheeler, DeWitt, and Wilson meeting GromovSep 13 2015Oct 07 2015The moduli space of isometry classes of Riemannian structures on a smooth manifold was emphasized by J.A.Wheeler in his superspace formalism of quantum gravity. A natural question concerning it is: What is a natural topology on such moduli space that ... More
Neck analysis for biharmonic mapsDec 17 2013In this paper, we study the blow up of a sequence of (both extrinsic and intrinsic) biharmonic maps in dimension four with bounded energy and show that there is no neck in this process. Moreover, we apply the method to provide new proofs to the removable ... More
Novel mobility edges in the off-diagonal disordered tight-binding modelsApr 03 2018We study the one-dimensional tight-binding models which include a slowly varying, incommensurate off-diagonal modulation on the hopping amplitude. Interestingly, we find that the mobility edges can appear only when this off-diagonal (hopping) disorder ... More
On the finite time blow-up of biharmonic map flow in dimension fourJan 24 2014In this paper, we show that for certain initial values, the (extrinsic) biharmonic map flow in dimension four must blow up in finite time.
Recursion formulae of higher Weil-Petersson volumesAug 03 2007May 22 2009In this paper we study effective recursion formulae for computing intersection numbers of mixed $\psi$ and $\kappa$ classes on moduli spaces of curves. By using the celebrated Witten-Kontsevich theorem, we generalize Mulase-Safnuk form of Mirzakhani's ... More
New properties of the intersection numbers on moduli spaces of curvesSep 14 2006Oct 22 2007We present certain new properties about the intersection numbers on moduli spaces of curves $\bar{\sM}_{g,n}$, including a simple explicit formula of $n$-point functions and several new identities of intersection numbers. In particular we prove a new ... More
New results of intersection numbers on moduli spaces of curvesMay 24 2007We present a series of new results we obtained recently about the intersection numbers of tautological classes on moduli spaces of curves, including a simple formula of the n-point functions for Witten's $\tau$ classes, an effective recursion formula ... More
A proof of the Faber intersection number conjectureMar 14 2008Dec 03 2009We prove the famous Faber intersection number conjecture and other more general results by using a recursion formula of $n$-point functions for intersection numbers on moduli spaces of curves. We also present some vanishing properties of Gromov-Witten ... More
An effective recursion formula for computing intersection numbersOct 29 2007We prove a new effective recursion formula for computing all intersection indices (integrals of $\psi$ classes) on the moduli space of curves, inducting only on the genus.
Heat kernel coefficients on Kahler manifoldsNov 21 2013Dec 02 2013Polterovich proved a remarkable closed formula for heat kernel coefficients of the Laplace operator on compact Riemannian manifolds involving powers of Laplacians acting on the distance function. In the case of K\"ahler manifolds, we prove a combinatorial ... More
The n-point functions for intersection numbers on moduli spaces of curvesJan 11 2007Oct 14 2009Using the celebrated Witten-Kontsevich theorem, we prove a recursive formula of the $n$-point functions for intersection numbers on moduli spaces of curves. It has been used to prove the Faber intersection number conjecture and motivated us to find some ... More
A Research on the Force-Freeness of Photosphere Magnetic FieldFeb 01 2019In this paper, the statistical studies on the force-freeness of photosphere magnetic fields are given. The studies are based on the vector magnetic fields observed by Solar Optical Telescope/Spectro-Polarimeter (SOT/SP) on board Hinode. Three parameters ... More
Dynamical quantum phase transitions on cross-stitch flat band networksJan 02 2019Jan 06 2019We study the quench dynamics on cross-stitch flat band networks by a sudden change of the inter-cell hopping strength $J$. For quench processes with $J$ changing as $J=0\rightarrow J\neq0$, we give the analytical expression to the Loschmidt echo which ... More
Topological phase transition in the quasiperiodic disordered Su-Schriffer-Heeger chainMay 10 2018We study the stability of the topological phase in one-dimensional Su-Schrieffer-Heeger chain subject to the quasiperiodic hopping disorder. We investigate two different hopping disorder configurations, one is the Aubry-Andr\'{e} quasiperiodic disorder ... More
Gate-induced carrier density modulation in bulk graphene: Theories and electrostatic simulation using Matlab pdetoolNov 15 2012Apr 03 2013This article aims at providing a self-contained introduction to theoretical modeling of gate-induced carrier density in graphene sheets. For this, relevant theories are introduced, namely, classical capacitance model (CCM), self-consistent Poisson-Dirac ... More
Decentralized Dynamic Optimization for Power Network Voltage ControlJul 23 2016Voltage control in power distribution networks has been greatly challenged by the increasing penetration of volatile and intermittent devices. These devices can also provide limited reactive power resources that can be used to regulate the network-wide ... More
Incompressible Limit of a Compressible Liquid Crystals SystemJan 28 2012May 29 2013This article is devoted to the study of the so-called incompressible limit for solutions of the compressible liquid crystals system. We consider the problem in the whole space $\mathbb{R}^{\mathbb{N}}$ and a bounded domain of $\mathbb{R}^{\mathbb{N}}$ ... More
Efficient quantum transport simulation for bulk graphene heterojunctionsJun 01 2012Sep 28 2012The quantum transport formalism based on tight-binding models is known to be powerful in dealing with a wide range of open physical systems subject to external driving forces but is, at the same time, limited by the memory requirement's increasing with ... More
On extremal transitions of Calabi-Yau threefolds and the singularity of the associated 7-space from rollingJan 27 1998Dec 18 1998M-theory compactification leads one to consider 7-manifolds obtained by rolling Calabi-Yau threefolds in the web of Calabi-Yau moduli spaces. The resulting 7-space in general has singularities governed by the extremal transition undergone. After providing ... More
Possible associated signal with GW150914 in the LIGO dataSep 27 2016We present a simple method for the identification of weak signals associated with gravitational wave events. Its application reveals a signal with the same time lag as the GW150914 event in the released LIGO strain data with a significance around $3.2\sigma$. ... More
Understanding $B^-\rightarrow X(3823)K^-$ via rescattering mechanism and predicting $B^-\to η_{c2} (^1D_2)/ψ_3(^3D_3)K^-$May 16 2016Jul 20 2016We study the observed $B^-\rightarrow X(3823)K^-$ decay via rescattering mechanism and show that this branching ratio is well reproduced by this mechanism. We further extend this theoretical framework to investigate the decays of $B^-\to\eta_{c2} (^1D_2)/\psi_3(^3D_3)K^-$, ... More
Newly observed $B(5970)$ and the predictions of its spin and strange partnersFeb 03 2014Apr 30 2014Using the effective Lagrangian approach, we study the decay behavior of the newly observed $B(5970)$ meson, which is assigned as the $2^3S_1$ state in the $B$ meson family. What is more important is that we predict the information of the partial and total ... More
Flat space compressible fluid as holographic dual of black hole with curved horizonDec 28 2014Jan 29 2015We consider the fluid dual of $(d+2)$-dimensional vacuum Einstein equation either with or without a cosmological constant. The background solutions admit black hole event horizons and the spatial sections of the horizons are conformally flat. Therefore, ... More
Upstanding Rashba spin in honeycomb lattices: Electrically reversible surface spin polarizationJul 14 2009Dec 13 2009The spin-split states subject to Rashba spin-orbit coupling in two-dimensional systems have long been accepted as pointing inplane and perpendicular to the corresponding wave vectors. This is in general true for free electron model, but exceptions do ... More
Spin precession in inversion-asymmetric two-dimensional systemsApr 18 2006We present a theoretical method to calculate the expectation value of spin in an inversion-asymmetric two-dimensional (2D) system with respect to an arbitrarily spin-polarized electron state, injected via an ideal point contact. The 2D system is confined ... More
Creating and Manipulating Electron Beams in GrapheneAug 05 2016An electron collimator composed of a point-like source and a parabolic pn junction is proposed as a generator of highly focused electron beams in graphene. The collimator is based on negative refraction and Klein collimation, which are unique to pseudo-relativistic ... More
Extended phase space thermodynamics for third order Lovelock black holes in diverse dimensionsMay 16 2014May 22 2014Treating the cosmological constant as thermodynamic pressure and its conjugate as thermodynamic volume, we investigate the critical behavior of the third order Lovelock black holes in diverse dimensions. For black hole horizons with different normalized ... More
Immersed Lagrangian deformations of a branched covering of a special Lagrangian 3-sphere in a Calabi-Yau 3-fold and its deviation from Joyce's criteria: Potential image-support rigidity of A-branes that wrap around a sL $S^3$Sep 09 2011Using a hyperK\"{a}hler rotation on complex structures of a Calabi-Yau 2-fold and rolling of an isotropic 2-submanifold in a symplectic 6-manifold, we construct, by gluing, a natural family of immersed Lagrangian deformations of a branched covering of ... More
Degeneration and gluing of Kuranishi structures in Gromov-Witten theory and the degeneration/gluing axioms for open Gromov-Witten invariants under a symplectic cutSep 18 2006We study the degeneration and the gluing of Kuranishi structures in Gromov-Witten theory under a symplectic cut. This leads us to a degeneration axiom and a gluing axiom for open Gromov-Witten invariants. They provide then a route to the construction ... More
Transformation of algebraic Gromov-Witten invariants of three-folds under flops and small extremal transitions, with an appendix from the stringy and the symplectic viewpointMay 05 2005We study how Gromov-Witten invariants of projective 3-folds transform under a standard flop and a small extremal transition in the algebro-geometric setting from the recent development of algebraic relative Gromov-Witten theory and its applications. This ... More
D-branes and synthetic/$C^{\infty}$-algebraic symplectic/calibrated geometry, I: Lemma on a finite algebraicness property of smooth maps from Azumaya/matrix manifoldsApr 08 2015We lay down an elementary yet fundamental lemma concerning a finite algebraicness property of a smooth map from an Azumaya/matrix manifold with a fundamental module to a smooth manifold. This gives us a starting point to build a synthetic (synonymously, ... More
A mathematical theory of D-string world-sheet instantons, I: Compactness of the stack of $Z$-semistable Fourier-Mukai transforms from a compact family of nodal curves to a projective Calabi-Yau 3-foldFeb 08 2013In a suitable regime of superstring theory, D-branes in a Calabi-Yau space and their most fundamental behaviors can be nicely described mathematically through morphisms from Azumaya spaces with a fundamental module to that Calabi-Yau space. In the earlier ... More
A mathematical theory of D-string world-sheet instantons, II: Moduli stack of $Z$-(semi)stable morphisms from Azumaya nodal curves with a fundamental module to a projective Calabi-Yau 3-foldOct 19 2013In this Part II, D(10.2), of D(10), we take D(10.1) (arXiv:1302.2054 [math.AG]) as the foundation to define the notion of $Z$-semistable morphisms from general Azumaya nodal curves, of genus $\ge 2$, with a fundamental module to a projective Calabi-Yau ... More
Exotic decays of the 125 GeV Higgs boson at future $e^+e^-$ lepton collidersDec 29 2016Mar 31 2017Discovery of unexpected properties of the Higgs boson offers an intriguing opportunity of shedding light on some of the most profound puzzles in particle physics. The Beyond Standard Model (BSM) decays of the Higgs boson could reveal new physics in a ... More
D-branes and Azumaya/matrix noncommutative differential geometry, I: D-branes as fundamental objects in string theory and differentiable maps from Azumaya/matrix manifolds with a fundamental module to real manifoldsJun 04 2014We consider D-branes in string theory and address the issue of how to describe them mathematically as a fundamental object (as opposed to a solitonic object) of string theory in the realm in differential and symplectic geometry. The notion of continuous ... More
$N=1$ fermionic D3-branes in RNS formulation I. $C^\infty$-Algebrogeometric foundations of $d=4$, $N=1$ supersymmetry, SUSY-rep compatible hybrid connections, and $\widehat{D}$-chiral maps from a $d=4$ $N=1$ Azumaya/matrix superspaceAug 15 2018As the necessary background to construct from the aspect of Grothendieck's Algebraic Geometry dynamical fermionic D3-branes along the line of Ramond-Neveu-Schwarz superstrings in string theory, three pieces of the building blocks are given in the current ... More
Further studies of the notion of differentiable maps from Azumaya/matrix supermanifolds I. The smooth case: Ramond-Neveu-Schwarz and Green-Schwarz meeting GrothendieckSep 26 2017In this sequel to works D(11.1) (arXiv:1406.0929 [math.DG]), D(11.2) (arXiv:1412.0771 [hep-th]), and D(11.3.1) (arXiv:1508.02347 [math.DG]), we re-examine --- and reformulate when in need --- several basic notions in super $C^{\infty}$-algebraic geometry ... More
Fate of topological states and mobility edges in one-dimensional slowly varying incommensurate potentialsAug 01 2017We investigate the interplay between disorder and superconducting pairing for a one-dimensional $p$-wave superconductor subject to slowly varying incommensurate potentials with mobility edges. With amplitude increments of the incommensurate potentials, ... More
Thermodynamics and holographic entanglement entropy for spherical black holes in 5D Gauss-Bonnet gravityJun 21 2016Sep 13 2016The holographic entanglement entropy is studied numerically in (4+1)-dimensional spherically symmetric Gauss-Bonnet AdS black hole spacetime with compact boundary. On the bulk side the black hole spacetime undergoes a van der Waals-like phase transition ... More
Gauss-Bonnet coupling constant as a free thermodynamical variable and the associated criticalityNov 13 2013May 12 2014The thermodynamic phase space of Gauss-Bonnet (GB) AdS black holes is extended, taking the inverse of the GB coupling constant as a new thermodynamic pressure $P_{\mathrm{GB}}$. We studied the critical behavior associated with $P_{\mathrm{GB}}$ in the ... More
Datta-Das transistor: Significance of channel direction, size-dependence of source contacts, and boundary effectsJul 21 2005Apr 18 2006We analyze the spin expectation values for injected spin-polarized electrons (spin vectors) in a [001]-grown Rashba-Dresselhaus two-dimensional electron gas (2DEG). We generalize the calculation for point spin injection in semi-infinite 2DEGs to finite-size ... More
More on the admissible condition on differentiable maps $\varphi: (X^{\!A\!z},E;\nabla)\rightarrow Y$ in the construction of the non-Abelian Dirac-Born-Infeld action $S_{DBI}(\varphi,\nabla)$Nov 29 2016In D(13.1) (arXiv:1606.08529 [hep-th]), we introduced an admissible condition on differentiable maps $\varphi: (X^{\!A\!z}, E;\nabla)\rightarrow Y$ from an Azumaya/matrix manifold $X^{\!A\!z}$ (with the fundamental module $E$) with a connection $\nabla$ ... More
D0-brane realizations of the resolution of a reduced singular curveNov 21 2011Based on examples from superstring/D-brane theory since the work of Douglas and Moore on resolution of singularities of a superstring target-space $Y$ via a D-brane probe, the richness and the complexity of the stack of punctual D0-branes on a variety, ... More
A Family of Reversible BCH CodesAug 07 2016Cyclic codes are an interesting class of linear codes due to their efficient encoding and decoding algorithms as well as their theoretical importance. BCH codes form a subclass of cyclic codes and are very important in both theory and practice as they ... More
Implication the observed $ψ(3770)\to p\bar{p}π^0$ for studying the $p\bar{p}\to ψ(3770)π^0$ processMay 18 2015Mar 31 2016We study the charmonium $p \bar{p} \to \psi(3770) \pi^0$ reaction using effective lagrangian approach where the contributions from well established $N^*$ states are considered, and all parameters are fixed in the process of $e^+e^- \to p \bar{p}\pi^0$ ... More
Highly sensitive optical sensor for precision measurement of electrical charges based on optomechanically induced difference-sideband generationAug 22 2017Difference-sideband generation in an optomechanical system coupled to a charged object is investigated beyond the conventional linearized description of optomechanical interactions. An exponential decay law for difference-sideband generation in the presence ... More
Majorana Neutrino Masses from Neutrinoless Double-Beta Decays and Lepton-Number-Violating Meson DecaysJun 15 2016Jul 20 2016The Schechter-Valle theorem states that a positive observation of neutrinoless double-beta ($0\nu \beta \beta$) decays implies a finite Majorana mass term for neutrinos when any unlikely fine-tuning or cancellation is absent. In this note, we reexamine ... More
Finite size analysis of zero-temperature jamming transition under applied shear stressDec 10 2013By finding local minima of an enthalpy-like energy, we can generate jammed packings of frictionless spheres under constant shear stress $\sigma$ and obtain the yield stress $\sigma_y$ by sampling the potential energy landscape. For three-dimensional systems ... More
Parameters of two classes of LCD BCH codesAug 09 2016BCH codes are widely employed in data storage, communications systems, and consumer electronics. A new application of LCD codes in cryptography was found recently. It is known that LCD codes are asymptotically good. LCD cyclic codes were referred to as ... More
Cosmological Constraints on Variable Warm Dark MatterFeb 04 2013Mar 10 2013Although $\Lambda$CDM model is very successful in many aspects, it has been seriously challenged. Recently, warm dark matter (WDM) remarkably rose as an alternative of cold dark matter (CDM). In the literature, many attempts have been made to determine ... More
Charged and neutral vector meson under magnetic fieldAug 06 2014The vector meson $\rho$ in the presence of external magnetic field has been investigated in the framework of the Nambu--Jona-Lasinio model, where mesons are constructed by infinite sum of quark-loop chains by using random phase approximation. The $\rho$ ... More
Formal pseudodifferential operators and Witten's r-spin numbersDec 20 2011We derive an effective recursion for Witten's r-spin intersection numbers, using Witten's conjecture relating r-spin numbers to the Gel'fand-Dikii hierarchy (Theorem 4.1). Consequences include closed-form descriptions of the intersection numbers (for ... More
Relativistic SpheresMar 02 1999By analyzing the Einstein's equations for the static sphere, we find that there exists a non-singular static configuration whose radius can approach its corresponding horizon size arbitrarily.
Nontrivial Azumaya noncommutative schemes, morphisms therefrom, and their extension by the sheaf of algebras of differential operators: D-branes in a $B$-field background à la Polchinski-Grothendieck AnsatzSep 12 2009In this continuation of [L-Y1], [L-L-S-Y], [L-Y2], and [L-Y3] (arXiv:0709.1515 [math.AG], arXiv:0809.2121 [math.AG], arXiv:0901.0342 [math.AG], arXiv:0907.0268 [math.AG]), we study D-branes in a target-space with a fixed $B$-field background $(Y,\alpha_B)$ ... More
D-branes and Azumaya noncommutative geometry: From Polchinski to GrothendieckMar 05 2010We review first Azumaya geometry and D-branes in the realm of algebraic geometry along the line of Polchinski-Grothendieck Ansatz from our earlier work and then use it as background to introduce Azumaya $C^{\infty}$-manifolds with a fundamental module ... More
Further studies on the notion of differentiable maps from Azumaya/matrix manifolds, I. The smooth caseAug 10 2015In this follow-up of our earlier two works D(11.1) (arXiv:1406.0929 [math.DG]) and D(11.2) (arXiv:1412.0771 [hep-th]) in the D-project, we study further the notion of a `differentiable map from an Azumaya/matrix manifold to a real manifold'. A conjecture ... More
Mechanical properties of jammed packings of frictionless spheres under applied shear stressFeb 03 2015By minimizing a thermodynamic-like potential, we unbiasedly sample the potential energy landscape of soft and frictionless spheres under constant shear stress. We obtain zero-temperature jammed states under desired shear stresses and investigate their ... More
Critical points of the cosmic velocity field and the uncertainties in the value of the Hubble constantMay 17 2016May 20 2016The existence of critical points for the peculiar velocity field is a natural feature of the correlated vector field. These points appear at the junctions of velocity domains with different orientations of their averaged velocity vectors. Since peculiar ... More
The Power of Online Learning in Stochastic Network OptimizationApr 06 2014Jul 29 2014In this paper, we investigate the power of online learning in stochastic network optimization with unknown system statistics {\it a priori}. We are interested in understanding how information and learning can be efficiently incorporated into system control ... More
Cloud Server Benchmarks for Performance Evaluation of New Hardware ArchitectureMar 04 2016Adding new hardware features to a cloud computing server requires testing both the functionalities and the performance of the new hardware mechanisms. However, commonly used cloud computing server workloads are not well-represented by the SPEC integer ... More
Survival of charged rho condensation at high temperature and densityJul 21 2015The charged vector $\rho$ mesons in the presence of external magnetic fields at finite temperature $T$ and chemical potential $\mu$ have been investigated in the framework of the Nambu--Jona-Lasinio model. We compute the masses of charged $\rho$ mesons ... More
The effect of the chiral chemical potential on the chiral phase transition in the NJL model with different regularization schemesNov 10 2015We study the chiral phase transition in the presence of the chiral chemical potential $\mu_5$ using the two-flavor Nambu--Jona-Lasinio model. In particular, we analyze the reason why one can obtain two opposite behaviors of the chiral critical temperature ... More
Asymptotic Behavior for a Nematic Liquid Crystal Model with Different Kinematic Transport PropertiesJan 13 2009Oct 29 2010We study the asymptotic behavior of global solutions to hydrodynamical systems modeling the nematic liquid crystal flows under kinematic transports for molecules of different shapes. The coupling system consists of Navier-Stokes equations and kinematic ... More
Two-dimensional ReN$_2$ materials from first principlesDec 08 2016We predict two two-dimensional materials of ReN$_{2}$ by using the first-principles investigation: honeycomb and tetragonal phases. The tetragonal phase has lower energy than the honeycomb one. The phonon spectra establish the dynamical stability for ... More
Battery-Aware Relay Selection for Energy Harvesting Cooperative NetworksAug 19 2014The use of energy harvesting (EH) nodes as cooperative relays is an emerging solution for enabling green wireless systems. In this paper, we consider multiple EH relay nodes harvesting energy from the radio frequency (RF) signal received from the source ... More
Extracting Gromov-Witten invariants of a conifold from semi-stable reduction and relative GW invariants of pairsNov 02 2004Nov 28 2004The study of open/closed string duality and large $N$ duality suggests a Gromov-Witten theory for conifolds that sits on the border of both a closed Gromov-Witten theory and an open Gromov-Witten theory. In this work we employ the result of Jun Li on ... More
Azumaya-type noncommutative spaces and morphisms therefrom: Polchinski's D-branes in string theory from Grothendieck's viewpointSep 11 2007We explain how Polchinski's work on D-branes re-read from a noncommutative version of Grothendieck's equivalence of local geometries and function rings gives rise to an intrinsic prototype definition of D-branes (of B-type) as an Azumaya-type noncommutative ... More
A degeneration formula of Gromov-Witten invariants with respect to a curve class for degenerations from blow-upsAug 11 2004In two very detailed, technical, and fundamental works, Jun Li constructed a theory of Gromov-Witten invariants for a singular scheme of the gluing form $Y_1\cup_D Y_2$ that arises from a degeneration $W/{\Bbb A}^1$ and a theory of relative Gromov-Witten ... More
D-branes and Azumaya/matrix noncommutative differential geometry,II: Azumaya/matrix supermanifolds and differentiable maps therefrom -- with a view toward dynamical fermionic D-branes in string theoryDec 02 2014In this Part II of D(11), we introduce new objects: super-$C^k$-schemes and Azumaya super-$C^k$-manifolds with a fundamental module (or, synonymously, matrix super-$C^k$-manifolds with a fundamental module), and extend the study in D(11.1) ([L-Y3], arXiv:1406.0929 ... More
Azumaya structure on D-branes and deformations and resolutions of a conifold revisited: Klebanov-Strassler-Witten vs. Polchinski-GrothendieckJul 02 2009In this sequel to [L-Y1], [L-L-S-Y], and [L-Y2] (respectively arXiv:0709.1515 [math.AG], arXiv:0809.2121 [math.AG], and arXiv:0901.0342 [math.AG]), we study a D-brane probe on a conifold from the viewpoint of the Azumaya structure on D-branes and toric ... More
Physicists' $d=3+1$, $N=1$ superspace-time and supersymmetric QFTs from a tower construction in complexified ${\Bbb Z}/2$-graded $C^\infty$-Algebraic Geometry and a purge-evaluation/index-contracting mapFeb 17 2019The complexified ${\Bbb Z}/2$-graded $C^\infty$-Algebraic Geometry aspect of a superspace(-time) $\widehat{X}$ in Sec.\,1 of D(14.1) (arXiv:1808.05011 [math.DG]) together with the Spin-Statistics Theorem in Quantum Field Theory, which requires fermionic ... More
Fingerprints of Galactic Loop I on the Cosmic Microwave BackgroundApr 07 2014Jul 29 2014We investigate possible imprints of galactic foreground structures such as the "radio loops" in the derived maps of the cosmic microwave background. Surprisingly there is evidence for these not only at radio frequencies through their synchrotron radiation, ... More
Understanding the LIGO GW150914 eventApr 21 2016Aug 09 2016We present a simplified method for the extraction of meaningful signals from Hanford and Livingstone 32 seconds data for the GW150914 event made publicly available by the LIGO collaboration and demonstrate its ability to reproduce the LIGO collaboration's ... More
Regularity Analysis for an Abstract System of Coupled Hyperbolic and Parabolic EquationsApr 24 2014In this paper, we provide a complete regularity analysis for an abstract system of coupled hyperbolic and parabolic equations in a complex Hilbert space. We are able to decompose the unit square of the parameters into three parts where the semigroup associated ... More
Diffusion limit of kinetic equations for multiple species charged particlesJun 13 2013Jul 08 2014In ionic solutions, there are multi-species charged particles (ions) with different properties like mass, charge etc. Macroscopic continuum models like the Poisson-Nernst-Planck (PNP) systems have been extensively used to describe the transport and distribution ... More
Spontaneous generation of local CP violation and inverse magnetic catalysisApr 28 2014Sep 14 2014In the chiral symmetric phase, the polarized instanton--anti-instanton molecule pairing induces a nontrivial repulsive interaction in the iso-scalar axial-vector channel. As a consequence, one unusual property is observed that in the chiral restoration ... More
Large-scale anomalies of the CMB in the curvaton scenarioFeb 25 2013Aug 28 2013We extend the curvaton scenario presented by Erickcek et al. (2008, 2009), to explain how the even-odd multipole asymmetry of the Cosmic Microwave Background (CMB) (also called parity asymmetry, (Kim & Naselsky 2010)) and power anisotropies can be generated ... More
Fluids and vortex from constrained fluctuations around C-metric black holeNov 26 2015Dec 03 2015By foliating the four-dimensional C-metric black hole spacetime, we consider a kind of initial-value-like formulation of the vacuum Einstein's equation, the holographic inception data is a double consisting of the induced metric and the Brown-York energy ... More
Compressible forced viscous fluid from product Einstein manifoldsJan 21 2015Jan 29 2015We consider the fluctuation modes around a hypersurface $\Sigma_c$ in a $(d+2)$-dimensional product Einstein manifold, with $\Sigma_c$ taken either near the horizon or at some finite cutoff from the horizon. By mapping the equations that governs the lowest ... More
Shear induced solidification of athermal systems with weak attractionMar 08 2016We find that unjammed packings of frictionless particles with rather weak attraction can always be driven into solid-like states by shear. The structure of shear-driven solids evolves continuously with packing fraction from gel-like to jamming-like, but ... More
Spin-dependent Klein tunneling in graphene: Role of Rashba spin-orbit couplingDec 02 2011Feb 03 2012Within an effective Dirac theory the low-energy dispersions of monolayer graphene in the presence of Rashba spin-orbit coupling and spin-degenerate bilayer graphene are described by formally identical expressions. We explore implications of this correspondence ... More
Anomalous spin Hall effects in Dresselhaus (110) quantum wellsMay 17 2010Sep 27 2010Anomalous spin Hall effects that belong to the intrinsic type in Dresselhaus (110) quantum wells are discussed. For the out-of-plane spin component, antisymmetric current-induced spin polarization induces opposite spin Hall accumulation, even though there ... More
Nonuniform Rashba-Dresselhaus spin precession along arbitrary pathsJul 04 2006Nov 03 2006Electron spin precession in nonuniform Rashba-Dresselhaus two-dimensional electron systems along arbitrary continuous paths is investigated. We derive an analytical formula to describe the spin vectors (expectation values of the injected spin) in such ... More
On the General Ericksen-Leslie System: Parodi's Relation, Well-posedness and StabilityMay 11 2011Oct 03 2012In this paper we investigate the role of Parodi's relation in the well-posedness and stability of the general Ericksen-Leslie system modeling nematic liquid crystal flows. First, we give a formal physical derivation of the Ericksen-Leslie system through ... More
D-branes of A-type, their deformations, and Morse cobordism of A-branes on Calabi-Yau 3-folds under a split attractor flow: Donaldson/Alexander-Hilden-Lozano-Montesinos-Thurston/Hurwitz/Denef-Joyce meeting Polchinski-GrothendieckDec 02 2010In [L-Y5] (D(6): arXiv:1003.1178 [math.SG]) we introduced the notion of Azumaya $C^{\infty}$-manifolds with a fundamental module and morphisms therefrom to a complex manifold. In the current sequel, we use this notion to give a prototypical definition ... More
Extending Adversarial Attacks and Defenses to Deep 3D Point Cloud ClassifiersJan 10 2019Feb 02 20193D object classification and segmentation using deep neural networks has been extremely successful. As the problem of identifying 3D objects has many safety-critical applications, the neural networks have to be robust against adversarial changes to the ... More
Azumaya structure on D-branes and resolution of ADE orbifold singularities revisited: Douglas-Moore vs. Polchinski-GrothendieckJan 03 2009In this continuation of [L-Y1] and [L-L-S-Y], we explain how the Azumaya structure on D-branes together with a netted categorical quotient construction produces the same resolution of ADE orbifold singularities as that arises as the vacuum manifold/variety ... More
Long time dynamics of defocusing energy critical 3 + 1 dimensional wave equation with potential in the radial caseMar 22 2014Using channel of energy inequalities developed by T.Duyckaerts, C.Kenig and F.Merle, we prove that, modulo a free radiation, any finite energy radial solution to the defocusing energy critical wave equation with radial potential in 3 + 1 dimensions converges ... More
Dynamics of D-branes II. The standard action --- an analogue of the Polyakov action for (fundamental, stacked) D-branesApr 11 2017We introduce a new action $S_{standard}^{(\rho,h; \Phi,g,B,C)}$ for D-branes that is to D-branes as the Polyakov action is to fundamental strings. This `standard action' is abstractly a non-Abelian gauged sigma model --- based on maps $\varphi: (X^{\!A\!z},E;\nabla)\rightarrow ... More
Dynamics of D-branes I. The non-Abelian Dirac-Born-Infeld action, its first variation, and the equations of motion for D-branes --- with remarks on the non-Abelian Chern-Simons/Wess-Zumino termJun 28 2016In earlier works, D(1) (arXiv:0709.1515 [math.AG]), D(11.1) (arXiv:1406.0929 [math.DG]), D(11.2) (arXiv:1412.0771 [hep-th]), and D(11.3.1) (arXiv:1508.02347 [math.DG]), we have explained why a D-brane in string theory, when treated as a fundamental dynamical ... More
Generation and amplification of high-order sideband induced by two-level atoms in a hybrid optomechanical systemDec 08 2017It is quite important to enhance and control the optomechanically induced high-order sideband generation to achieve low-power optical comb and high-sensitivity sensing with an integratable structure. Here we present and analyze a proposal for enhancement ... More