arXiv subjects

Wei Gu

Publications and source records attributed to Wei Gu.

51 records · Page 3Linked to original sources

arXiv2022

Boost Distribution System Restoration with Emergency Communication Vehicles Considering Cyber-Physical Interdependence

Enhancing restoration capabilities of distribution systems is one of the main strategies for resilient power systems to cope with extreme events. However, most of the existing studies assume the communication infrastructures are intact for distribution automation, which is unrealistic. Motivated by the applications of the emergency communication vehicles (ECVs) in quickly setting up wireless communication networks after disasters, in this paper, we propose an integrated distribution system restoration (DSR) framework and optimization models, which can coordinate the repair crews, the distribution system (physical sectors), and the emergency communication (cyber sectors) to pick up unserved power loads as quickly as possible. Case studies validated the effectiveness of the proposed models and proved the benefit of considering ECVs and cyber-physical interdependencies in DSR.

eess.SY↗

arXiv2022

Discrimination-Based Double Auction for Maximizing Social Welfare in the Electricity and Heating Market Considering Privacy Preservation

This paper proposes a doubled-sided auction mechanism with price discrimination for social welfare (SW) maximization in the electricity and heating market. In this mechanism, energy service providers (ESPs) submit offers and load aggregators (LAs) submit bids to an energy trading center (ETC) to maximize their utility; in turn, the selfless ETC as an auctioneer leverages dis-criminatory price weights to regulate the behaviors of ESPs and LAs, which combines the individual benefits of each stakeholder with the overall social welfare to achieve the global optimum. Nash games are employed to describe the interactions between players with the same market role. Theoretically, we first prove the existence and uniqueness of the Nash equilibrium; then, considering the requirement of game players to preserve privacy, a distributed algorithm based on the alternating direction method of multipliers is developed to implement distributed bidding and analytical target cascading algorithm is applied to reach the balance of demand and supply. We validated the proposed mechanism using case studies on a city-level distribution system. The results indicated that the achieved SW improved by 4%-15% compared with other mechanisms, and also verified the effectiveness of the distributed algorithm.

cs.GT↗

arXiv2021

Vacuum Structures Revisited

We consider the relationship between the higher symmetry and the dynamical decomposition in supersymmetric gauge theory in various dimensions by studying the semi-classical potential energy. We observe that besides the scalar moduli we shall also include the field strength $F_{0\cdots d}$ in the vacuum moduli in the 1+d dimensional theory along with a $\mathbb{Z}_{p}$ $d$-form symmetry. In gauge theory for charge-$p$ matters with this symmetry, we find that the vacua decompose into $p$ different universes at an intermediate scale, which means no dynamical domain wall can interpolate between them. In our setup, we re-derive the existing results on the decomposition in various dimensions. In four dimensions, we propose a UV gauge theory for the generalized super Yang-Mills theory, whose instanton sectors are restricted to the topological number with integer multiples of $p$.

hep-th↗

arXiv2021

Hierarchical Electricity and Carbon Trading in Transmission and Distribution Networks Based on Virtual Federated Prosumer

Facing the dilemma of growing energy demand and mitigating carbon emissions, this paper proposes an energy sharing mechanism based on virtual federated prosumers (VFPs) with budget allocation for joint electricity and carbon market to incentivize distributed energy resources to participate in the hierarchical market and reduce carbon emissions. At the transmission level, the regional transmission operator coordinates transactions between two markets, the inter-VFP energy sharing market and the wholesale market, intending to minimize the overall cost of VFPs. The energy sharing market clearing problem is formulated as a generalized Nash game, for which we develop a first-order response algorithm to obtain the equilibrium. At the distribution level, the VFPs play the role of selfless auctioneer that leverage discriminatory weights and benchmark prices to allocate the electricity-carbon budget among entities in the VFP to maximize social welfare. The Nash game is exploited to characterize the budget allocation problem, for which a distributed feedback allocation algorithm is proposed. The entire hierarchical electricity and carbon trading is modeled as an equilibrium problem and is solved iteratively. Case studies based on a practical regional grid verify the effectiveness of the proposed algorithm and show that the mechanism is effective in improving energy efficiency and reducing carbon emissions.

math.OC↗

arXiv2021

On Phases of 3d ${\cal N}=2$ Chern-Simons-Matter Theories

We investigate phases of 3d ${\cal N}=2$ Chern-Simons-matter theories, extending to three dimensions the celebrated correspondence between 2d gauged Wess-Zumino-Witten (GWZW) models and non-linear sigma models (NLSMs) with geometric targets. We find that although the correspondence in 3d and 2d are closely related by circle compactification, an important subtlety arises in this process, changing the phase structure of the 3d theory. Namely, the effective theory obtained from the circle compactification of a phase of a 3d ${\cal N}=2$ gauge theory is, in general, different from the phase of the 3d ${\cal N}=2$ theory on ${\mathbb R}^2\times S^{1}$, which means taking phases of a 3d gauge theory does not necessarily commute with compactification. We compute the Witten index of each effective theory to check this observation. Furthermore, when the matter fields have the same non-minimal charges, the 3d ${\cal N}=2$ Chern-Simons-matter theory with a proper Chern-Simons level will decompose into several identical 2d gauged linear sigma models (GLSMs) for the same target upon reduction to 2d. To illustrate this phenomenon, we investigate how vacua of the 3d gauge theory for a weighted projective space $W\mathbb{P}_{[l,\cdots,l]}$ move on the field space when we change the radius of $S^{1}$.

hep-th↗

arXiv2020

Nonabelian mirrors and Gromov-Witten invariants

We propose Picard-Fuchs equations for periods of nonabelian mirrors in this paper. The number of parameters in our Picard-Fuchs equations is the rank of the gauge group of the nonabelian GLSM, which is eventually reduced to the actual number of Kähler parameters. These Picard-Fuchs equations are concise and novel. We justify our proposal by reproducing existing mathematical results, namely Picard-Fuchs equations of Grassmannians and Calabi-Yau manifolds as complete intersections in Grassmannians. Furthermore, our approach can be applied to other nonabelian GLSMs, so we compute Picard-Fuchs equations of some other Fano-spaces, which were not calculated in the literature before. Finally, the cohomology-valued generating functions of mirrors can be read off from our Picard-Fuchs equations. Using these generating functions, we compute Gromov-Witten invariants of various Calabi-Yau manifolds, including complete intersection Calabi-Yau manifolds in Grassmannians and non-complete intersection Calabi-Yau examples such as Pfaffian Calabi-Yau threefold and Gulliksen-Negård Calabi-Yau threefold, and find agreement with existing results in the literature. The generating functions we propose for non-complete intersection Calabi-Yau manifolds are genuinely new.

hep-th↗

arXiv2020

A rim-hook rule for quiver flag varieties

The rim-hook rule for quantum cohomology of the Grassmannian allows one to reduce quantum calculations to classical calculations in the cohomology of the Grassmannian. We use the Abelian/non-Abelian correspondence for cohomology to prove a rim-hook removal rule for the cohomology of quiver flag varieties. Quiver flag varieties are generalisations of type A flag varieties; this result is new even in the flag case. This gives an effective way of computing products in their cohomology, reducing computations to that in the cohomology ring of the Grassmannian. We then prove a quantum rim-hook rule for Fano quiver flag varieties (including type A flag varieties). As a corollary, we see that the Gu--Sharpe mirror to a Fano quiver flag variety computes its quantum cohomology.

math.AG↗

arXiv2020

Correlation functions in massive Landau-Ginzburg orbifolds and tests of dualities

In this paper we discuss correlation function computations in massive topological Landau-Ginzburg orbifolds, extending old results of Vafa. We then apply these computations to provide further tests of the nonabelian mirrors proposal and two-dimensional Hori-Seiberg dualities with $(S)O_{\pm}$ gauge groups and their mirrors.

hep-th↗

arXiv2020

Resonant Precession Modulation Based Magnetic Field Receivers

Antenna technology provides the crucial interface between electronic devices and electromagnetic waves required for wireless communications. This technology has operated under largely the same general principles for over a century, resulting in stagnation of advancements in modern times and fundamentally limiting the extent to which potential applications of wireless communications may be realized. Herein we propose a novel concept for antenna operation employing the nonlinear precession dynamics of subatomic spins. An electromagnetic wave incident on a precessing spin will serve to modulate the spin frequency of precession. Antennas operating based on a detection of these spin dynamics are then able to fully characterize the incident wave while achieving substantial amplifications, higher sensitivities, and smaller form factors as compared to conventional antennas. A preliminary experimental implementation of the proposed concept establishes its feasibility and is already able to demonstrate significant amplification and size benefits.

physics.app-ph↗

arXiv2019

More nonabelian mirrors and some two-dimensional dualities

In this paper we extend the nonabelian mirror proposal of two of the authors from two-dimensional gauge theories with connected gauge groups to the case of O(k) gauge groups with discrete theta angles. We check our proposed extension by counting and comparing vacua in mirrors to known dual two-dimensional (S)O(k) gauge theories. The mirrors in question are Landau-Ginzburg orbifolds, and for mirrors to O(k) gauge theories, the critical loci of the mirror superpotential often intersect fixed-point loci, so that to count vacua, one must take into account twisted sector contributions. This is a technical novelty relative to mirrors of gauge theories with connected gauge groups, for which critical loci do not intersect fixed-point loci and so no orbifold twisted sector contributions are pertinent. The vacuum computations turn out to be a rather intricate test of the proposed mirrors, in particular as untwisted sector states in the mirror to one theory are often exchanged with twisted sector states in the mirror to the dual. In cases with nontrivial IR limits, we also check that central charges computed from the Landau-Ginzburg mirrors match those expected for the IR SCFTs.

hep-th↗

arXiv2019

Supersymmetric Localization in GLSMs for Supermanifolds

In this paper we apply supersymmetric localization to study gauged linear sigma models (GLSMs) describing supermanifold target spaces. We use the localization method to show that A-twisted GLSM correlation functions for certain supermanifolds are equivalent to A-twisted GLSM correlation functions for hypersurfaces in ordinary spaces under certain conditions. We also argue that physical two-sphere partition functions are the same for these two types of target spaces. Therefore, we reproduce the claim of arXiv:hep-th/9404186, arXiv:hep-th/9506070. Furthermore, we explore elliptic genera and (0,2) deformations and find similar phenomena.

hep-th↗

arXiv2016

Localization of twisted $\mathcal{N}{=}(0,2)$ gauged linear sigma models in two dimensions

We study two-dimensional $\mathcal{N}{=}(0,2)$ supersymmetric gauged linear sigma models (GLSMs) using supersymmetric localization. We consider $\mathcal{N}{=}(0,2)$ theories with an $R$-symmetry, which can always be defined on curved space by a pseudo-topological twist while preserving one of the two supercharges of flat space. For GLSMs which are deformations of $\mathcal{N}{=}(2,2)$ GLSMs and retain a Coulomb branch, we consider the $A/2$-twist and compute the genus-zero correlation functions of certain pseudo-chiral operators, which generalize the simplest twisted chiral ring operators away from the $\mathcal{N}{=}(2,2)$ locus. These correlation functions can be written in terms of a certain residue operation on the Coulomb branch, generalizing the Jeffrey-Kirwan residue prescription relevant for the $\mathcal{N}{=}(2,2)$ locus. For abelian GLSMs, we reproduce existing results with new formulas that render the quantum sheaf cohomology relations and other properties manifest. For non-abelian GLSMs, our methods lead to new results. As an example, we briefly discuss the quantum sheaf cohomology of the Grassmannian manifold.

hep-th↗

arXiv2014

The Statistics of Vacuum Geometry

We investigate the vacuum moduli space of supersymmetric gauge theories en masse by probing the space of such vacua from a statistical standpoint. Using quiver gauge theories with ${\cal N}=1$ supersymmetry as a testing ground, we sample over a large number of vacua as algebraic varieties, computing explicitly their dimension, degree and Hilbert series. We study the distribution of these geometrical quantities, and also address the question of how likely it is for the moduli space to be Calabi-Yau.

hep-th↗

arXiv2011

The origin of entropy production in spacetime thermodynamics

We find that the ambiguity term of approximate Killing vector field is responsible for the entropy production term. Without the ambiguity term, pure Einstein theory and $f(R)$ satisfy the relation of thermodynamic equilibrium. Considering such an ambiguity term of approximate Killing vector field, we can get the entropy production term and the entropy in $f(R)$ with a form defined by Jacobson. In pure Einstein theory, the shear term is the only geometric contribution of entropy production term, while in $f(R)$ it can also contribute. We believe our approach and conclusion can be generalized to other gravity theory.

hep-th↗

arXiv2010

A New Entropic Force Scenario and Holographic Thermodynamics

We propose a new holographic program of gravity in which we introduce a surface stress tensor. Our proposal differs from Verlinde's in several aspects. First, we use an open or a closed screen, a temperature is not necessary but a surface energy density and pressure are introduced. The surface stress tensor is proportional to the extrinsic curvature. The energy we use is Brown-York energy and the equipartiton theorem is violated by a non-vanishing surface pressure. We discuss holographic thermodynamics of a gas of weak gravity and find a chemical potential, and show that Verlinde's program does not lead to a reasonable thermodynamics. The holographic entropy is similar to the Bekenstein entropy bound.

hep-th↗