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Yunhui Wu

Publications and source records attributed to Yunhui Wu.

At least 37 records · Page 2Linked to original sources
arXiv2023

Polaritonic Waveguide Emits Super-Planckian Thermal Radiation

Classical Planck's theory of thermal radiation predicts an upper limit of the heat transfer between two bodies separated by a distance longer than the dominant radiation wavelength (far-field regime). This limit can be overcome when the dimensions of the absorbent bodies are smaller than the dominant wavelength due to hybrid electromagnetic waves, known as surface phonon-polaritons (SPhPs). Here, we experimentally demonstrate that the far-field radiative heat transfer between two non-absorbent bodies can also overcome Planck's limit, by coating them with an absorbent material to form a polaritonic waveguide. This super-Planckian far-field thermal radiation is confirmed by measuring the radiative thermal conductance between two silicon plates coated with silicon dioxide nanolayers. The observed conductance is twice higher than Planck's limit and agrees with the predictions of our model for the SPhP waveguide modes. Our findings could be applied to thermal management in microelectronics and silicon photonics.

physics.optics↗
arXiv2022

Large genus asymptotics for lengths of separating closed geodesics on random surfaces

In this paper, we investigate basic geometric quantities of a random hyperbolic surface of genus $g$ with respect to the Weil-Petersson measure on the moduli space $\mathcal{M}_g$. We show that as $g$ goes to infinity, a generic surface $X\in \mathcal{M}_g$ satisfies asymptotically: (1) the separating systole of $X$ is about $2\log g$; (2) there is a half-collar of width about $\frac{\log g}{2}$ around a separating systolic curve of $X$; (3) the length of shortest separating closed multi-geodesics of $X$ is about $2\log g$. As applications, we also discuss the asymptotic behavior of the extremal separating systole, the non-simple systole and the expectation value of lengths of shortest separating closed multi-geodesics as $g$ goes to infinity.

math.GT↗
arXiv2022

The Cheeger constants of random Belyi surfaces

Brooks and Makover developed a combinatorial model of random hyperbolic surfaces by gluing certain hyperbolic ideal triangles. In this paper we show that for any $ε>0$, as the number of ideal triangles goes to infinity, a generic hyperbolic surface in Brooks-Makover's model has Cheeger constant less than $\frac{3}{2π}+ε$.

math.DG↗
arXiv2022

Degenerating hyperbolic surfaces and spectral gaps for large genus

In this article we study the differences of two consecutive eigenvalues $λ_{i}-λ_{i-1}$ up to $i=2g-2$ for the Laplacian on hyperbolic surfaces of genus $g$, and show that the supremum of such spectral gaps over the moduli space has infimum limit at least $\frac{1}{4}$ as genus goes to infinity. A min-max principle for eigenvalues on degenerating hyperbolic surfaces is also established.

math.DG↗
arXiv2022

Observation of phonon Poiseuille flow in isotopically-purified graphite ribbons

In recent times, the unique collective transport physics of phonon hydrodynamics motivates theoreticians and experimentalists to explore it in micro- and nanoscale and at elevated temperatures. Graphitic materials have been predicted to facilitate hydrodynamic heat transport with their intrinsically strong normal scattering. However, owing to the experimental difficulties and vague theoretical understanding, the observation of phonon Poiseuille flow in graphitic systems remains challenging. In this study, based on a microscale experimental platform and the pertinent occurrence criterion in anisotropic solids, we demonstrate the phonon Poiseuille flow in a 5 μm-wide suspended graphite ribbon with purified 13C isotope concentration. Our observation is well supported by our theoretical model based on a kinetic theory with fully first-principles inputs. Thus, this study paves the way for deeper insight into phonon hydrodynamics and cutting-edge heat manipulating applications.

cond-mat.mes-hall↗
arXiv2022

A new uniform lower bound on Weil-Petersson distance

In this paper we study the injectivity radius based at a fixed point along Weil-Petersson geodesics. We show that the square root of the injectivity radius based at a fixed point is $ 0.3884$-Lipschitz on Teichmüller space endowed with the Weil-Petersson metric. As an application we reprove that the square root of the systole function is uniformly Lipschitz on Teichmüller space endowed with the Weil-Petersson metric, where the Lipschitz constant can be chosen to be $0.5492$. Applications to asymptotic geometry of moduli space of Riemann surfaces for large genus will also be discussed.

math.DG↗
arXiv2022

Random hyperbolic surfaces of large genus have first eigenvalues greater than $\frac{3}{16}-ε$

Let $M_g$ be the moduli space of hyperbolic surfaces of genus $g$ endowed with the Weil-Petersson metric. In this paper, we show that for any $ε>0$, as genus $g$ goes to infinity, a generic surface $X\in M_g$ satisfies that the first eigenvalue $λ_1(X)>\frac{3}{16}-ε$. As an application, we also show that a generic surface $X\in M_g$ satisfies that the diameter $\mathrm{diam}(X)<(4+ε)\ln(g)$ for large genus.

math.DG↗
arXiv2022

Small eigenvalues of closed Riemann surfaces for large genus

In this article we study the asymptotic behavior of small eigenvalues of Riemann surfaces for large genus. We show that for any positive integer $k$, as the genus $g$ goes to infinity, the smallest $k$-th eigenvalue of Riemann surfaces in any thick part of moduli space of Riemann surfaces of genus $g$ is uniformly comparable to $\frac{1}{g^2}$ in $g$. In the proof of the upper bound, for any constant $ε>0$, we will construct a closed Riemann surface of genus $g$ in any $ε$-thick part of moduli space such that it admits a pants decomposition whose boundary curves all have length equal to $ε$, and the number of separating systole curves in this surface is uniformly comparable to $g$.

math.DG↗
arXiv2021

Observation of quasi-ballistic thermal transport of surface phonon-polaritons over hundreds of micrometres

Long-distance propagation of heat carriers is essential for efficient heat dissipation in microelectronics. However, in dielectric nanomaterials, the primary heat carriers - phonons - can propagate ballistically only for hundreds of nanometres, which limits their heat conduction efficiency. Theory predicts that surface phonon-polaritons (SPhPs) can overcome this limitation and conduct heat without dissipation for hundreds of micrometres. In this work, we experimentally demonstrate such long-distance heat transport by SPhPs. Using the 3$ω$ technique, we measure the in-plane thermal conductivity of SiN nanomembranes for different heater-sensor distances (100 and 200 $μ$m), membrane thicknesses (30 - 200 nm), and temperatures (300 - 400 K). We find that in contrast with thick membranes, thin nanomembranes support heat conduction by SPhPs, as evidenced by an increase in the thermal conductivity with temperature. Remarkably, the thermal conductivity measured 200 $μ$m away from the heater are consistently higher than that measured 100 $μ$m closer. This result suggests that heat conduction by SPhPs is quasi-ballistic over at least hundreds of micrometres. Thus, our findings show that SPhPs can enhance heat dissipation in polar nanomembranes and find applications in thermal management, near-field radiation, and polaritonics.

cond-mat.mes-hall↗
arXiv2021

The simple separating systole for hyperbolic surfaces of large genus

In this note we show that the expected value of the separating systole of a random surface of genus $g$ with respect to Weil-Petersson volume behaves like $2\log g $ as the genus goes to infinity. This is in strong contrast to the behavior of the expected value of the systole which, by results of Mirzakhani and Petri, is independent of genus.

math.GT↗
arXiv2021

Optimal lower bounds for first eigenvalues of Riemann surfaces for large genus

In this article we study the first eigenvalues of closed Riemann surfaces for large genus. We show that for every closed Riemann surface $X_g$ of genus $g$ $(g\geq 2)$, the first eigenvalue of $X_g$ is greater than $\frac{\mathcal{L}_1(X_g)}{g^2}$ up to a uniform positive constant multiplication. Where $\mathcal{L}_1(X_g)$ is the shortest length of multi closed curves separating $X_g$. Moreover,we also show that this new lower bound is optimal as $g \to \infty$.

math.DG↗
arXiv2019

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures

In this article we show that for every finite area hyperbolic surface $X$ of type $(g,n)$ and any harmonic Beltrami differential $μ$ on $X$, then the magnitude of $μ$ at any point of small injectivity radius is uniform bounded from above by the ratio of the Weil-Petersson norm of $μ$ over the square root of the systole of $X$ up to a uniform positive constant multiplication. We apply the uniform bound above to show that the Weil-Petersson Ricci curvature, restricted at any hyperbolic surface of short systole in the moduli space, is uniformly bounded from below by the negative reciprocal of the systole up to a uniform positive constant multiplication. As an application, we show that the average total Weil-Petersson scalar curvature over the moduli space is uniformly comparable to $-g$ as the genus $g$ goes to infinity.

math.DG↗
arXiv2019

Surface phonon-polaritons enhance thermal conduction in SiN nanomembranes

Surface phonon-polaritons can carry energy on the surface of dielectric films and thus are expected to contribute to heat conduction. However, the contribution of surface phonon-polaritons (SPhPs) to thermal transport has not been experimentally demonstrated yet. In this work, we experimentally measure the effective in-plane thermal conductivity of amorphous silicon nitride membrane and show that it can indeed be increased by SPhPs significantly when the membrane thickness scales down. In particular, by heating up a thin membrane (<100 nm) from 300 to 800 K, the thermal conductivity increases twice due to SPhPs contribution.

cond-mat.mes-hall↗
arXiv2018

On positive scalar curvature and moduli of curves

In this article we first show that any finite cover of the moduli space of closed Riemann surfaces of genus $g$ with $g\geq 2$ does not admit any Riemannian metric $ds^2$ of nonnegative scalar curvature such that $ds^2 \succ ds_{T}^2$ where $ds_{T}^2$ is the Teichmüller metric. Our second result is the proof that any cover $M$ of the moduli space $\mathbb{M}_{g}$ of a closed Riemann surface $S_{g}$ does not admit any complete Riemannian metric of uniformly positive scalar curvature in the quasi-isometry class of the Teichmüller metric, which implies a conjecture of Farb-Weinberger.

math.DG↗
arXiv2018

The Weil-Petersson curvature operator on the universal Teichmüller space

The universal Teichmüller space is an infinitely dimensional generalization of the classical Teichmüller space of Riemann surfaces. It carries a natural Hilbert structure, on which one can define a natural Riemannian metric, the Weil-Petersson metric. In this paper we investigate the Weil-Petersson Riemannian curvature operator $\tilde{Q}$ of the universal Teichmüller space with the Hilbert structure, and prove the following: (i) $\tilde{Q}$ is non-positive definite. (ii) $\tilde{Q}$ is a bounded operator. (iii) $\tilde{Q}$ is not compact; the set of the spectra of $\tilde{Q}$ is not discrete. As an application, we show that neither the Quaternionic hyperbolic space nor the Cayley plane can be totally geodesically immersed in the universal Teichmüller space endowed with the Weil-Petersson metric.

math.DG↗
arXiv2018

Growth of the Weil-Petersson inradius of moduli space

In this paper we study the systole function along Weil-Petersson geodesics. We show that the square root of the systole function is uniformly Lipschitz on Teichmüller space endowed with the Weil-Petersson metric. As an application, we study the growth of the Weil-Petersson inradius of moduli space of Riemann surfaces of genus $g$ with $n$ punctures as a function of $g$ and $n$. We show that the Weil-Petersson inradius is comparable to $\sqrt{\ln{g}}$ with respect to $g$, and is comparable to $1$ with respect to $n$. Moreover, we also study the asymptotic behavior, as $g$ goes to infinity, of the Weil-Petersson volumes of geodesic balls of finite radii in Teichmüller space. We show that they behave like $o((\frac{1}{g})^{(3-ε)g})$ as $g\to \infty$, where $ε>0$ is arbitrary.

math.GT↗
arXiv2018

Uniform Bounds for Weil-Petersson Curvatures

We find bounds for Weil-Petersson holomorphic sectional curvature, and the Weil-Petersson curvature operator in several regimes, that do not depend on the topology of the underlying surface. Among other results, we show that the minimal (most negative) eigenvalue of the curvature operator at any point in the Teichmüller space $\Teich(S_g)$ of a closed surface $S_g$ of genus $g$ is uniformly bounded away from zero. Restricting to a thick part of $\Teich(S_g)$, we show that the minimal eigenvalue is uniformly bounded below by an explicit constant which does not depend on the topology of the surface but only on the given bound on injectivity radius. We also show that the minimal Weil-Petersson holomorphic sectional curvature of a sufficiently thick hyperbolic surface is comparable to $-1$.

math.DG↗