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Zipeng Wang

Publications and source records attributed to Zipeng Wang.

At least 73 records · Page 4Linked to original sources
arXiv2024

Hankel matrices acting on the Dirichlet space

The characterization of the boundedness of operators induced by Hankel matrices on analytic function spaces can be traced back to the work of Z. Nehari and H. Widom on the Hardy space, and has been extensively studied on many other analytic function spaces recently. However, this question remains open in the context of the Dirichlet space [20]. By Carleson measures, the Widom type condition and the reproducing kernel thesis, this paper provides a comprehensive solution to this question. As a beneficial product, characterizations of the boundedness and compactness of operators induced by Cesàro type matrices on the Dirichlet space are given. In addition, we also show that a random Dirichlet function almost surely induces a compact Hankel type operator on the Dirichlet space.

math.CV↗
arXiv2023

Moments of Mandelbrot cascades at critical exponents

We obtain the asymptotic growth rate of the moments of the Mandelbrot random cascades at critical exponents. The key ingredient is a $q$ to $q/2$ reduction method for the moment-estimation, which is obtained by combining the martingale inequalities due to Burkholder and Burkholder-Rosenthal.

math.PR↗
arXiv2023

Universal discontinuous percolation transition in the Earth's terrestrial topography

Based on the Topographic Wetness Index (TWI), we studied the percolation process of water on the Earth's land surface and discovered a universal discontinuous phase transition across scales, with a critical TWI threshold of 0.671 (0.054). The discontinuity is attributed to the long-range correlation and directionality of the percolation process. Furthermore, the criticality is shown to extend from the critical point to a region corresponding to the Griffiths phase, where natural lake systems are found to develop, indicating the governess of self-organized criticality within the Earth system.

physics.geo-ph↗
arXiv2023

Converging trend of global urban land expansion sheds new light on sustainable development

Urban land growth presents a major sustainability challenge, yet its growth patterns and dynamics remain unclear. We quantified urban land evolution by analyzing its statistical distribution in 14 regions and countries over 29 years. The results show a converging temporal trend in urban land expansion from sub-country to global scales, characterized by a coherent shift of urban area distributions from initial power law to exponential distributions, with the consequences of reduced system stability and resilience, and increased exposure of urban populations to extreme heat and air pollution. These changes are attributed to the increased influence from external economies of scale associated with globalization and are predicted to intensify in the future. The findings will advance urban science and direct current land urbanization practices toward sustainable development, especially in developing regions and medium-size cities.

physics.soc-ph↗
arXiv2023

General Relativistic Polarized Proca Stars

Massive vector fields can form spatially localized, non-relativistic, stationary field configurations supported by gravitational interactions. The ground state configurations (p-solitons/vector solitons/dark photon stars/polarized Proca stars) have a time-dependent vector field pointing in the same spatial direction throughout the configuration at any instant of time, can carry macroscopic amounts of spin angular momentum, and are spherically symmetric and monotonic in the energy density. In this paper, we include general relativistic effects, and numerically investigate the stability of compact polarized Proca stars (linear and circularly polarized) and compare them to hedgehog-like field configurations (with radially pointing field directions). Starting with approximate field profiles of such stars, we evolve the system numerically using 3+1 dimensional numerical simulations in general relativity. We find that these initial conditions lead to stable configurations. However, at sufficiently large initial compactness, they can collapse to black holes. We find that the initial compactness that leads to black hole formation is higher for circularly polarized stars (which carry macroscopic spin angular momentum), compared to linearly polarized ones, which in turn is higher than that for hedgehog configurations.

gr-qc↗
arXiv2023

GRDzhadzha: A code for evolving relativistic matter on analytic metric backgrounds

GRDzhadzha is an open-source code for relativistic simulations of matter fields on curved spacetimes that admit an analytic description (e.g. stationary black holes). It is based on the publicly available 3+1D numerical relativity code GRChombo. Such a description is valid where the density of the matter is small compared to the curvature scale of the spacetime, which is the case for many physical scenarios - for example, dark matter environments. The approach offers significant savings on memory and speed compared to running full numerical relativity simulations, since the metric variables and their derivatives are calculated analytically, and therefore are not evolved or stored on the grid. This brief paper introduces the code and gives details of some applications for which it has already been used.

gr-qc↗
arXiv2023

The three-body scattering hypervolume of identical fermions in one dimension

We study the zero-energy collision of three identical spin-polarized fermions with short-range interactions in one dimension. We derive the asymptotic expansions of the three-body wave function when the three fermions are far apart or one pair and the third fermion are far apart, and the three-body scattering hypervolume $D_F$ appears in the coefficients of such expansions. If the two-body interaction is attractive and supports two-body bound states, $D_F$ acquires a negative imaginary part related to the amplitudes of the outgoing waves describing the departure of the resultant bound pair and the remaining free fermion. For weak interaction potentials, we derive an approximate formula of the hypervolume by using the Born expansion. For the square-barrier and the square-well potentials and the Gaussian potential, we solve the three-body Schrödinger equation to compute $D_F$ numerically. We also calculate the shifts of energy and of pressure of spin-polarized one-dimensional Fermi gases due to a nonzero $D_F$ and the three-body recombination rate in one dimension.

cond-mat.quant-gas↗
arXiv2023

Singular integrals of non-convolution type on product spaces

We study a new class of pseudo differential operators whose symbols satisfy the differential inequality with a mixture of homogeneities. On the other hand, by taking singular integral realization, it can be equivalently defined by kernels carrying certain characteristic properties on product spaces. We prove that these operators are bounded on L^p-spaces for 1<p<infinity. Moreover, they form an algebra.

math.FA↗
arXiv2023

Size distributions reveal regime transition of lake systems under different dominant driving forces

Power law size distribution is found to associate with fractal, self-organized behaviors and patterns of complex systems. Such distribution also emerges from natural lakes, with potentially important links to the dynamics of lake systems. But the driving mechanism that generates and shapes this feature in lake systems remains unclear. Moreover, the power law itself was found inadequate for fully describing the size distribution of lakes, due to deviations at the two ends of size range. Based on observed and simulated lakes in 11 hydro-climatic zones of China, we established a conceptual model for lake systems, which covers the whole size range of lake size distribution and reveals the underlying driving mechanism. The full lake size distribution is composed of three components, with three phases featured by exponential, stretched-exponential and power law distribution. The three phases represent system states with successively increasing degrees of heterogeneity and orderliness, and more importantly, indicate the dominance of exogenic and endogenic forces, respectively. As the dominant driving force changes from endogenic to exogenic, a phase transition occurs with lake size distribution shifted from power law to stretched-exponential and further to exponential distribution. Apart from compressing the power law phase, exogenic force also increases its scaling exponent, driving the corresponding lake size power spectrum into the regime of blue noise. During this process, the autocorrelation function of the lake system diverges with a possibility of going to infinity, indicating the loss of system resilience.

cond-mat.stat-mech↗
arXiv2023

Learning Spatial-Temporal Implicit Neural Representations for Event-Guided Video Super-Resolution

Event cameras sense the intensity changes asynchronously and produce event streams with high dynamic range and low latency. This has inspired research endeavors utilizing events to guide the challenging video superresolution (VSR) task. In this paper, we make the first attempt to address a novel problem of achieving VSR at random scales by taking advantages of the high temporal resolution property of events. This is hampered by the difficulties of representing the spatial-temporal information of events when guiding VSR. To this end, we propose a novel framework that incorporates the spatial-temporal interpolation of events to VSR in a unified framework. Our key idea is to learn implicit neural representations from queried spatial-temporal coordinates and features from both RGB frames and events. Our method contains three parts. Specifically, the Spatial-Temporal Fusion (STF) module first learns the 3D features from events and RGB frames. Then, the Temporal Filter (TF) module unlocks more explicit motion information from the events near the queried timestamp and generates the 2D features. Lastly, the SpatialTemporal Implicit Representation (STIR) module recovers the SR frame in arbitrary resolutions from the outputs of these two modules. In addition, we collect a real-world dataset with spatially aligned events and RGB frames. Extensive experiments show that our method significantly surpasses the prior-arts and achieves VSR with random scales, e.g., 6.5. Code and dataset are available at https: //vlis2022.github.io/cvpr23/egvsr.

cs.CV↗
arXiv2022

Scattering Hypervolume of Fermions in Two Dimensions

We define the three-body scattering hypervolume $D_F$ for identical spin-polarized fermions in two dimensions, by considering the wave function of three such fermions colliding at zero energy and zero orbital angular momentum. We derive the asymptotic expansions of such a wave function when three fermions are far apart or one pair and the third fermion are far apart, and $D_F$ appears in the coefficients of such expansions. For weak interaction potentials, we derive an approximate formula of $D_F$ by using the Born expansion. We then study the shift of energy of three such fermions in a large periodic area due to $D_F$. This shift is proportional to $D_F$ times the square of the area of the triangle formed by the momenta of the fermions. We also calculate the shifts of energy and of pressure of spin-polarized two-dimensional Fermi gases due to a nonzero $D_F$ and the three-body recombination rate of spin-polarized ultracold atomic Fermi gases in two dimensions.

cond-mat.quant-gas↗
arXiv2022

Superradiance in massive vector fields with spatially varying mass

Superradiance is a process by which massive bosonic particles can extract energy from spinning black holes, leading to the build up of a "cloud" if the particle has a Compton wavelength comparable to the black hole's Schwarzschild radius. One interesting possibility is that superradiance may occur for photons in a diffuse plasma, where they gain a small effective mass. Studies of the spin-0 case have indicated that such a build up is suppressed by a spatially varying effective mass, supposed to mimic the photons' interaction with a physically realistic plasma density profile. We carry out relativistic simulations of a massive Proca field evolving on a Kerr background, with modifications to account for the spatially varying effective mass. This allows us to treat the spin-1 case directly relevant to photons, and to study the effect of thinner disk profiles in the plasma. We find similar qualitative results to the scalar case, and so support the conclusions of that work: either a constant asymptotic mass or a shell-like plasma structure is required for superradiant growth to occur. We study thin disks and find a leakage of the superradiant cloud that suppresses its growth, concluding that thick disks are more likely to support the instability.

gr-qc↗
arXiv2022

Stein-Weiss inequality on product spaces

We give a classification between weighted norm inequalities of strong fractional integral operators, and their associated multi-parameter Muckenhoupt characteristics, bu considering the weights to be power functions. As a result, we extend the classical Stein-Weiss theorem to product spaces.

math.CA↗
arXiv2022

Hardy-Littlewood-Sobolev inequality on product spaces

We study a family of fractional integral operator defined on an homogeneous space with a "rectangle doubling" measure. As a result, we give an extension of the classical Hardy-Littlewood-Sobolev theorem to a multi-parameter setting.

math.CA↗