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Ran Zhuo

Publications and source records attributed to Ran Zhuo.

17 recordsLinked to original sources
arXiv2025

Social Imitation Dynamics of Vaccination Driven by Vaccine Effectiveness and Beliefs

Declines in vaccination coverage for vaccine-preventable diseases, such as measles and chickenpox, have enabled their surprising comebacks and pose significant public health challenges in the wake of growing vaccine hesitancy. Vaccine opt-outs and refusals are often fueled by beliefs concerning perceptions of vaccine effectiveness and exaggerated risks. Here, we quantify the impact of competing beliefs -- vaccine-averse versus vaccine-neutral -- on social imitation dynamics of vaccination, alongside the epidemiological dynamics of disease transmission. These beliefs may be pre-existing and fixed, or coevolving attitudes. This interplay among beliefs, behaviors, and disease dynamics demonstrates that individuals are not perfectly rational; rather, they base their vaccine uptake decisions on beliefs, personal experiences, and social influences. We find that the presence of a small proportion of fixed vaccine-averse beliefs can significantly exacerbate the vaccination dilemma, making the tipping point in the hysteresis loop more sensitive to changes in individuals' perceived costs of vaccination and vaccine effectiveness. However, in scenarios where competing beliefs spread concurrently with vaccination behavior, their double-edged impact can lead to self-correction and alignment between vaccine beliefs and behaviors. The results show that coevolution of vaccine beliefs and behaviors makes populations more sensitive to abrupt changes in perceptions of vaccine cost and effectiveness compared to scenarios without beliefs. Our work provides valuable insights into harnessing the social contagion of even vaccine-neutral attitudes to overcome vaccine hesitancy.

physics.soc-ph↗
arXiv2024

The direct moving sphere for fractional Laplace equation

This paper works on the direct method of moving spheres and establishes a Liouville-type theorem for the fractional elliptic equation \[ (-Δ)^{α/2} u =f(u) ~~~~~~ \text{in } \mathbb{R}^{n} \] with general non-linearity. One of the key improvement over the previous work is that we do not require the usual Lipschitz condition. In fact, we only assume the structural condition that $f(t) t^{- \frac{n+α}{n-α}}$ is monotonically decreasing. This differs from the usual approach such as Chen-Li-Li (Adv. Math. 2017), which needed the Lipschitz condition on $f$, or Chen-Li-Zhang (J. Funct. Anal. 2017), which relied on both the structural condition and the monotonicity of $f$. We also use the direct moving spheres method to give an alternative proof for the Liouville-type theorem of the fractional Lane-Emden equation in a half space. Similarly, our proof does not depend on the integral representation of solutions compared to existing ones. The methods developed here should also apply to problems involving more general non-local operators, especially if no equivalent integral equations exist.

math.AP↗
arXiv2023

In situ tuning of dynamical Coulomb blockade on Andreev bound states in hybrid nanowire devices

Electron interactions in quantum devices can exhibit intriguing phenomena. One example is assembling an electronic device in series with an on-chip resistor. The quantum laws of electricity of the device is modified at low energies and temperatures by dissipative interactions induced by the resistor, a phenomenon known as dynamical Coulomb blockade (DCB). The DCB strength is usually non-adjustable in a fixed environment defined by the resistor. Here, we design an on-chip circuit for InAs-Al hybrid nanowires where the DCB strength can be gate-tuned in situ. InAs-Al nanowires could host Andreev or Majorana zero-energy states. This technique enables tracking the evolution of the same state while tuning the DCB strength from weak to strong. We observe the transition from a zero-bias conductance peak to split peaks for Andreev zero-energy states. Our technique opens the door to in situ tuning interaction strength on zero-energy states.

cond-mat.mes-hall↗
arXiv2023

A localized criterion for the regularity of solutions to Navier-Stokes equations

The Serrin-Prodi-Ladyzhenskaya type $L^{p,q}$ criteria for the regularity of solutions to the incompressible Navier-Stokes equations are fundamental in the study of the millennium problem posted by the Clay Mathematical Institute about the incompressible N-S equations. In this article, we establish some localized $L^{p,q}$ criteria for the regularity of solutions to the equations. In fact, we obtain some a priori estimates of solutions to the equations depend only on some local $L^{p,q}$ type norms. These local $L^{p,q}$ type norms, are small for reasonable initial value and shall remain to be small for global regular solutions. Thus, deriving the smallness or even the boundedness of the local $L^{p,q}$ type norms is necessary and sufficient to affirmatively answer the millennium problem. Our work provides an interesting and plausible approach to study the millennium problem.

math.AP↗
arXiv2023

A priori estimates for higher-order fractional Laplace equations

In this paper, we establish a priori estimates for the positive solutions to a higher-order fractional Laplace equation on a bounded domain by a blowing-up and rescaling argument. To overcome the technical difficulty due to the high-order and fractional order mixed operators, we divide the high-order fractional Laplacian equation into a system, and provide uniform estimates for each equation in the system. Finding a proper scaling parameter for the domain is the crux of rescaling argument to the above system, and the new idea is introduced in the rescaling proof, which may hopefully be applied to many other system problems. In order to derive a contradiction in the blowing-up proof, combining the moving planes method and suitable Kelvin transform, we prove a key Liouville-type theorem under a weaker regularity assumption in a half space.

math.AP↗
arXiv2022

On the Dirichlet problem for fractional Laplace equation on a general domain

In this paper, we study Dirichlet problems of fractional Laplace (Poisson) equations on a general bounded domain in $\mathbb{R}^n$. Green's functions and Poisson kernels are important tools needed in our study. We first establish the existence of Green's function by an application of Perron's method. After that, the Poisson kernel is constructed based on the Green's function. Several important properties of Green's functions and Poisson kernels are proved. Finally, we show that the solution of a fractional Laplace (Poisson) equation under a given condition must be unique and be given by our Green's function and Poisson kernel.

math.AP↗
arXiv2022

Qualitative properties of solutions for system involving fractional Laplacian

In this paper, we consider the following nonlinear system involving the fractional Laplacian \begin{equation} \left\{\begin{array}{ll} (-Δ)^{s} u (x)= f(u,\,v), \\ (-Δ)^{s} v (x)= g(u,\,v), \end{array} \right. (1) \end{equation} in two different types of domains, one is bounded, and the other is unbounded, where $0<s<1$. To investigate the qualitative properties of solutions for fractional equations, the conventional methods are extension method and moving planes method. However, the above methods have technical limits in asymmetric and convex domains and so on. In this work, we employ the direct sliding method for fractional Laplacian to derive the monotonicity of solutions for (1) in $x_n$ variable in different types of domains. Meanwhile, we develop a new iteration method for systems in the proofs which hopefully can be applied to solve other problems.

math.AP↗
arXiv2022

Plateau regions for zero-bias peaks within 5% of the quantized conductance value $2e^2/h$

Probing an isolated Majorana zero mode is predicted to reveal a tunneling conductance quantized at $2e^2/h$ at zero temperature. Experimentally, a zero-bias peak (ZBP) is expected and its height should remain robust against relevant parameter tuning, forming a quantized plateau. Here, we report the observation of large ZBPs in a thin InAs-Al hybrid nanowire device. The ZBP height can stick close to $2e^2/h$, mostly within $5\%$ tolerance, by sweeping gate voltages and magnetic field. We further map out the phase diagram and identify two plateau regions in the phase space. Despite the presence of disorder and quantum dots, our result constitutes a step forward towards establishing Majorana zero modes.

cond-mat.mes-hall↗
arXiv2022

Large Andreev bound state zero bias peaks in a weakly dissipative environment

We study Andreev bound states in hybrid InAs-Al nanowire devices. The energy of these states can be tuned to zero by gate voltage or magnetic field, revealing large zero bias peaks (ZBPs) near 2e^2/h in tunneling conductance. Probing these large ZBPs using a weakly dissipative lead reveals non-Fermi liquid temperature (T) dependence due to environmental Coulomb blockade (ECB), an interaction effect from the lead acting on the nanowire junction. By increasing T, these large ZBPs either show a height increase or a transition from split peaks to a ZBP, both deviate significantly from non-dissipative devices where a Fermi-liquid T dependence is revealed. Our result demonstrates the competing effect between ECB and thermal broadening on Andreev bound states.

cond-mat.mes-hall↗
arXiv2021

Large-composition-range pure-phase homogeneous InAs$_{1-x}$Sb$_x$ nanowires

Narrow bandgap InAs$_{1-x}$Sb$_x$ nanowires show broad prospects for applications in wide spectrum infrared detectors, high-performance transistors and quantum computation. Realizing such applications require the fine control of composition and crystal structure of nanowires. However, to date, the fabrication of large-composition-range pure-phase homogeneous InAs$_{1-x}$Sb$_x$ nanowires remains a huge challenge. Here, we first report the growth of large-composition-range stemless InAs$_{1-x}$Sb$_x$ nanowires (x = 0-0.63) on Si (111) substrates by molecular-beam epitaxy. It is found that pure-phase InAs$_{1-x}$Sb$_x$ nanowires can be successfully obtained by controlling the antimony content x, nanowire diameter and nanowire growth direction. Detailed EDS data show that the antimony is uniformly distributed along the axial and radial directions of InAs$_{1-x}$Sb$_x$ nanowires and no spontaneous core-shell nanostructures form in the nanowires. Based on field-effect measurements, we confirm that InAs$_{1-x}$Sb$_x$ nanowires exhibit good conductivity and their mobilities can be up to 4200 cm^2/V.s at 7 K. Our work lays the foundation for the development of InAs$_{1-x}$Sb$_x$ nanowire optoelectronic, electronic and quantum devices.

physics.app-ph↗
arXiv2021

Suppressing Andreev bound state zero bias peaks using a strongly dissipative lead

Hybrid semiconductor-superconductor nanowires are predicted to host Majorana zero modes, manifested as zero-bias peaks (ZBPs) in tunneling conductance. ZBPs alone, however, are not sufficient evidence due to the ubiquitous presence of Andreev bound states in the same system. Here, we implement a strongly resistive normal lead in our InAs-Al nanowire devices and show that most of the expected ZBPs, corresponding to zero-energy Andreev bound states, can be suppressed, a phenomenon known as environmental Coulomb blockade. Our result is the first experimental demonstration of this dissipative interaction effect on Andreev bound states and can serve as a possible filter to narrow down ZBP phase diagram in future Majorana searches.

cond-mat.mes-hall↗
arXiv2021

Large zero bias peaks and dips in a four-terminal thin InAs-Al nanowire device

We report electron transport studies of a thin InAs-Al hybrid semiconductor-superconductor nanowire device using a four-terminal design. Compared to previous works, thinner InAs nanowire (diameter less than 40 nm) is expected to reach fewer sub-band regime. The four-terminal device design excludes electrode contact resistance, an unknown value which has inevitably affected previously reported device conductance. Using tunneling spectroscopy, we find large zero-bias peaks (ZBPs) in differential conductance on the order of $2e^2/h$. Investigating the ZBP evolution by sweeping various gate voltages and magnetic field, we find a transition between a zero-bias peak and a zero-bias dip while the zero-bias conductance sticks close to $2e^2/h$. We discuss a topologically trivial interpretation involving disorder, smooth potential variation and quasi-Majorana zero modes.

cond-mat.mes-hall↗
arXiv2020

In Situ Epitaxy of Pure Phase Ultra-Thin InAs-Al Nanowires for Quantum Devices

Hybrid semiconductor-superconductor InAs-Al nanowires with uniform and defect-free crystal interfaces are one of the most promising candidates used in the quest for Majorana zero modes (MZMs). However, InAs nanowires often exhibit a high density of randomly distributed twin defects and stacking faults, which result in an uncontrolled and non-uniform InAs-Al interface. Furthermore, this type of disorder can create potential inhomogeneity in the wire, destroy the topological gap, and form trivial sub-gap states mimicking MZM in transport experiments. Further study shows that reducing the InAs nanowire diameter from growth can significantly suppress the formation of these defects and stacking faults. Here, we demonstrate the in situ growth of ultra-thin InAs nanowires with epitaxial Al film by molecular-beam epitaxy. Our InAs diameter (~ 30 nm) is only one-third of the diameters (~ 100 nm) commonly used in literatures. The ultra-thin InAs nanowires are pure phase crystals for various different growth directions, suggesting a low level of disorder. Transmission electron microscopy confirms an atomically sharp and uniform interface between the Al shell and the InAs wire. Quantum transport study on these devices resolves a hard induced superconducting gap and $2e^-$ periodic Coulomb blockade at zero magnetic field, a necessary step for future MZM experiments. A large zero bias conductance peak with a peak height reaching 80% of $2e^2/h$ is observed.

cond-mat.mtrl-sci↗
arXiv2020

The A Priori Estimate and Existence of the Positive Solution for A Nonlinear System Involving the Fractional Laplacian

In the paper, we consider the fractional elliptic system \begin{equation*}\left\{\begin{array}{ll} (- Δ)^{\frac{α_1}{2}}u(x)+\sum\limits^n_{i=1}b_i(x)\frac{\partial u}{\partial x_i}+B(x)u(x)=f(x,u,v),& \mbox { in } Ω,\\ (- Δ)^{\frac{α_2}{2}}v(x)+\sum\limits^n_{i=1}c_i(x)\frac{\partial v}{\partial x_i}+C(x)v(x)=g(x,u,v),& \mbox { in } Ω,\\ u=v=0, & \mbox { in } \mathbb{R}^n\setminusΩ, \end{array} \right.\label{a-1.2} \end{equation*} where $Ω$ is a bounded domain with $C^2$ boundary in $\mathbb{R}^n$ and $n>\max\{α_1,α_2\}$. We first utilize the blowing-up and re-scaling method to derive the a priori estimate for positive solutions when $1<α_1,α_2 <2$. Then for $0<α_1,α_2 <1$, we obtain the regularity estimate of positive solutions. On top of this, using the topological degree theory we prove the existence of positive solutions.

math.AP↗
arXiv2016

A Liouville Theorem for the Higher Order Fractional Laplacian

We deal with the higher-order fractional Laplacians by two methods: the integral method and the system method. The former depends on the integral equation equivalent to the differential equation. The latter works directly on the differential equations. We first derive nonexistence of positive solutions, often known as the Liouville type theorem, for the integral and differential equations. Then through an delicate iteration, we show symmetry for positive solutions.

math.AP↗
arXiv2014

A Liouville Theorem for the Fractional Laplacian

We extend the classical Liouville Theorem from Laplacian to the fractional Laplacian, that is, we prove Every $α$-harmonic function bounded either above or below in all of $R^n$ must be constant.

math.AP↗