arXiv subjects

Shanshan Chen

Publications and source records attributed to Shanshan Chen.

At least 37 records · Page 2Linked to original sources

arXiv2022

Evolution of dispersal in advective patchy environments

We study a two-species competition model in a patchy advective environment, where the species are subject to both directional drift and undirectional random dispersal between patches and there are losses of individuals in the downstream end (e.g., due to the flow into a lake or ocean). The two competing species are assumed to have the same growth rates but different advection and random dispersal rates. We focus our studies on the properties of an associated eigenvalue problem which characterizes the extinction/persistence dynamics of the underlying patch population model. We also derive conditions on the advection and random dispersal rates under which a mutating species can or cannot invade the resident species.

math.DS↗

arXiv2022

Pressure-induced superconductivity in flat-band Kagome compounds Pd$_3$P$_2$(S$_{1-x}$Se$_x$)$_8$

We performed high-pressure transport studies on the flat-band Kagome compounds, Pd$_3$P$_2$(S$_{1-x}$Se$_x$)$_8$ ($x$ = 0, 0.25), with a diamond anvil cell. For both compounds, the resistivity exhibits an insulating behavior with pressure up to 17 GPa. With pressure above 20 GPa, a metallic behavior is observed at high temperatures in Pd$_3$P$_2$S$_8$, and superconductivity emerges at low temperatures. The onset temperature of superconducting transition $T_{\rm C}$ rises monotonically from 2 K to 4.8 K and does not saturate with pressure up to 43 GPa. For the Se-doped compound Pd$_3$P$_2$(S$_{0.75}$Se$_{0.25}$)$_8$, the $T_{\rm C}$ is about 1.5 K higher than that of the undoped one over the whole pressure range, and reaches 6.4 K at 43 GPa. The upper critical field with field applied along the $c$ axis at typical pressures is about 50$\%$ of the Pauli limit, suggesting a 3D superconductivity. The Hall coefficient in the metallic phase is low and exhibits a peaked behavior at about 30 K, which suggests either a multi-band electronic structure or an electron correlation effect in the system.

cond-mat.supr-con↗

arXiv2022

Twisted Angle-Dependent Work Functions in CVD-Grown Twisted Bilayer Graphene by Kelvin Probe Force Microscopy

Tailoring the interlayer twist angle of bilayer graphene (BLG) has a significant influence on its electronic properties, including superconductivity, topological transitions, ferromagnetic states and correlated insulating states. These exotic electronic properties are sensitively dependent on the work functions of bilayer graphene samples. Here, the twisted angle-dependent work functions of CVD-grown twisted bilayer graphene (tBLG) are detailed investigated by Kelvin Probe Force Microscopy (KPFM) in combination with Raman spectra. The thickness-dependent surface potentials of Bernal-stacked multilayer graphene were measured. The AB-BLG and tBLG are directly determined by KPFM due to their twist angle-specific surface potentials. The detailed relationship of twist angles and surface potentials are further obtained by the in-situ combination investigation of KPFM and Raman spectra measurements. The thermal stability of tBLG was further explored through controlled annealing process. Our work provides the twisted angle-dependent surface potentials of tBLG and lays the foundation for further exploring their twist-angle-dependent novel electronic properties.

cond-mat.mtrl-sci↗

arXiv2021

Validating CircaCP: a Generic Sleep-Wake Cycle Detection Algorithm

Sleep-wake cycle detection is a key step when extrapolating sleep patterns from actigraphy data. Numerous supervised detection algorithms have been developed with parameters estimated from and optimized for a particular dataset, yet their generalizability from sensor to sensor or study to study is unknown. In this paper, we propose and validate an unsupervised algorithm -- CircaCP -- to detect sleep-wake cycles from minute-by-minute actigraphy data. It first uses a robust cosinor model to estimate circadian rhythm, then searches for a single change point (CP) within each cycle. We used CircaCP to estimate sleep/wake onset times (S/WOTs) from 2125 indviduals' data in the MESA Sleep study and compared the estimated S/WOTs against self-reported S/WOT event markers. Lastly, we quantified the biases between estimated and self-reported S/WOTs, as well as variation in S/WOTs contributed by the two methods, using linear mixed-effects models and variance component analysis. On average, SOTs estimated by CircaCP were five minutes behind those reported by event markers, and WOTs estimated by CircaCP were less than one minute behind those reported by markers. These differences accounted for less than 0.2% variability in SOTs and in WOTs, taking into account other sources of between-subject variations. By focusing on the commonality in human circadian rhythms captured by actigraphy, our algorithm transferred seamlessly from hip-worn ActiGraph data collected from children in our previous study to wrist-worn Actiwatch data collected from adults. The large between- and within-subject variability highlights the need for estimating individual-level S/WOTs when conducting actigraphy research. The generalizability of our algorithm also suggests that it could be widely applied to actigraphy data collected by other wearable sensors.

stat.AP↗

arXiv2021

Global dynamics of a Lotka-Volterra competition patch model

The global dynamics of the two-species Lotka-Volterra competition patch model with asymmetric dispersal is classified under the assumptions of weak competition and the weighted digraph of the connection matrix is strongly connected and cycle-balanced. It is shown that in the long time, either the competition exclusion holds that one species becomes extinct, or the two species reach a coexistence equilibrium, and the outcome of the competition is determined by the strength of the inter-specific competition and the dispersal rates. Our main techniques in the proofs follow the theory of monotone dynamical system and a graph-theoretic approach based on the Tree-Cycle identity.

math.CA↗

arXiv2021

Toplayer-Dependent Crystallographic Orientation Imaging in the Bilayer Two-Dimensional Materials with Transverse Shear Microscopy

Nanocontact properties of two-dimensional (2D) materials are closely dependent on their unique nanomechanical systems, such as the number of atomic layers and the supporting substrate. Here, we report a direct observation of toplayer-dependent crystallographic orientation imaging of 2D materials with the transverse shear microscopy (TSM). Three typical nanomechanical systems, MoS2 on the amorphous SiO2/Si, graphene on the amorphous SiO2/Si, and MoS2 on the crystallized Al2O3, have been investigated in detail. This experimental observation reveals that puckering behaviour mainly occurs on the top layer of 2D materials, which is attributed to its direct contact adhesion with the AFM tip. Furthermore, the result of crystallographic orientation imaging of MoS2/SiO2/Si and MoS2/Al2O3 indicated that the underlying crystalline substrates almost do not contribute to the puckering effect of 2D materials. Our work directly revealed the top layer dependent puckering properties of 2D material, and demonstrate the general applications of TSM in the bilayer 2D systems.

cond-mat.mtrl-sci↗

arXiv2020

The stability and Hopf bifurcation of the diffusive Nicholson's blowflies model in spatially heterogeneous environment

In this paper, we consider the diffusive Nicholson's blowflies model in spatially heterogeneous environment when the diffusion rate is large. We show that the ratio of the average of the maximum per capita egg production rate to that of the death rate affects the dynamics of the model. The unique positive steady state is locally asymptotically stable if the ratio is less than a critical value. However, when the ratio is greater than the critical value, large time delay can make the unique positive steady state unstable through Hopf bifurcation. Especially, the first Hopf bifurcation value tends to that of the ''average'' DDE model when the diffusion rate tends to infinity. Moreover, we show that the direction of the Hopf bifurcation is forward, and the bifurcating periodic solution from the first Hopf bifurcation value is orbitally asymptotically stable, which improves the earlier result by Wei and Li (Nonlinear. Anal., 60: 1351-1367, 2005).

math.DS↗

arXiv2020

Double Hopf bifurcation in nonlocal reaction-diffusion systems with spatial average kernel

In this paper, we consider a general reaction-diffusion system with nonlocal effects and Neumann boundary conditions, where a spatial average kernel is chosen to be the nonlocal kernel. By virtue of the center manifold reduction technique and normal form theory, we present a new algorithm for computing normal forms associated with the codimension-two double Hopf bifurcation of nonlocal reaction-diffusion equations. The theoretical results are applied to a predator-prey model, and complex dynamic behaviors such as spatially nonhomogeneous periodic oscillations and spatially nonhomogeneous quasi-periodic oscillations could occur.

math.DS↗

arXiv2019

Hopf bifurcation of a delayed single population model with patch structure

In this paper, we show the existence of Hopf bifurcation of a delayed single population model with patch structure. The effect of the dispersal rate on the Hopf bifurcation is considered. Especially, if each patch is favorable for the species, we show that when the dispersal rate tends to zero, the limit of the Hopf bifurcation value is the minimum of the "local" Hopf bifurcation values over all patches. On the other hand, when the dispersal rate tends to infinity, the Hopf bifurcation value tends to that of the "average" model.

math.DS↗

arXiv2019

Asymptotic profiles of the steady states for an SIS epidemic patch model with asymmetric connectivity matrix

The dynamics of an SIS epidemic patch model with asymmetric connectivity matrix is analyzed. It is shown that the basic reproduction number $R_0$ is strictly decreasing with respect to the dispersal rate of the infected individuals, and the model has a unique endemic equilibrium if $R_0>1$. The asymptotic profiles of the endemic equilibrium for small dispersal rates are characterized. In particular, it is shown that the endemic equilibrium converges to a limiting disease-free equilibrium as the dispersal rate of susceptible individuals tends to zero, and the limiting disease-free equilibrium has a positive number of susceptible individuals on each low-risk patch. Moreover a sufficient and necessary condition is found to guarantee that the limiting disease-free equilibrium has no positive number of susceptible individuals on each high-risk patch. Our results extend earlier results for symmetric connectivity matrix, and we also partially solve an open problem by Allen et al. (SIAM J. Appl. Math., 67: 1283-1309, 2007).

math.DS↗

arXiv2019

Spectral Monotonicity of Perturbed Quasi-positive Matrices with Applications in Population Dynamics

Threshold values in population dynamics can be formulated as spectral bounds of matrices, determining the dichotomy of population persistence and extinction. For a square matrix $μA + Q$, where $A$ is a quasi-positive matrix describing population dispersal among patches in a heterogeneous environment and $Q$ is a diagonal matrix encoding within-patch population dynamics, the monotonicy of its spectral bound with respect to dispersal speed/coupling strength/travel frequency $μ$ is established via two methods. The first method is an analytic derivation utilizing a graph-theoretic approach based on Kirchhoff's Matrix-Tree Theorem; the second method employs Collatz-Wielandt formula from matrix theory and complex analysis arguments. It turns out that our established result is a slightly strengthen version of Karlin-Altenberg's Theorem, which has previously been discovered independently while investigating reduction principle in evolution biology and evolution dispersal in patchy landscapes. Nevertheless, our result provides a new and effective approach in stability analysis of complex biological systems in a heterogeneous environment. We illustrate this by applying our result to well-known ecological models of single species, predator-prey and competition, and an epidemiological model of susceptible-infected-susceptible (SIS) type. We successfully solve some open problems in the literature of population dynamics.

math.DS↗

arXiv2019

Asymptotic profiles of basic reproduction number for epidemic spreading in heterogeneous environment

The effect of diffusion rates on the basic reproduction number of a general compartmental reaction-diffusion epidemic model in a heterogeneous environment is considered. It is shown when the diffusion rates tend to zero, the limit of the basic reproduction number is the maximum value of the local reproduction number on the spatial domain. On the other hand when the diffusion rates tend to infinity, the basic reproduction number tends to the spectral radius of the "average"~next generation matrix. These asymptotic limits of basic reproduction number hold for a class of general spatially heterogeneous compartmental epidemic models, and they are applied to a wide variety of examples.

math.DS↗

arXiv2019

Global dynamics of the diffusive Lotka-Volterra competition model with stage structure

The global asymptotic behavior of the classical diffusive Lotka-Volterra competition model with stage structure is studied. A complete classification of the global dynamics is given for the weak competition case. It is shown that under otherwise same conditions, the species with shorter maturation time prevails. The method is also applied to the global dynamics of another delayed competition models.

math.DS↗

arXiv2019

A Generic Algorithm for Sleep-Wake Cycle Detection using Unlabeled Actigraphy Data

One key component when analyzing actigraphy data for sleep studies is sleep-wake cycle detection. Most detection algorithms rely on accurate sleep diary labels to generate supervised classifiers, with parameters optimized for a particular dataset. However, once the actigraphy trackers are deployed in the field, labels for training models and validating detection accuracy are often not available. In this paper, we propose a generic, training-free algorithm to detect sleep-wake cycles from minute-by-minute actigraphy. Leveraging a robust nonlinear parametric model, our proposed method refines the detection region by searching for a single change point within bounded regions defined by the parametric model. Challenged by the absence of ground truth labels, we also propose an evaluation metric dedicated to this problem. Tested on week-long actigraphy from 112 children, the results show that the proposed algorithm improves on the baseline model consistently and significantly (p<3e-15). Moreover, focusing on the commonality in human circadian rhythm captured by actigraphy, the proposed method is generic to data collected by various actigraphy trackers, circumventing the laborious label collection step in developing customized classifiers for sleep detection.

stat.AP↗

arXiv2018

Hopf bifurcation for a delayed diffusive logistic population model in the advective heterogeneous environment

In this paper, we investigate a delayed reaction-diffusion-advection equation, which models the population dynamics in the advective heterogeneous environment. The existence of the nonconstant positive steady state and associated Hopf bifurcation are obtained. A weighted inner product associated with the advection rate is introduced to compute the normal forms, which is the main difference between Hopf bifurcation for delayed reaction-diffusion-advection model and that for delayed reaction-diffusion model. Moreover, we find that the spatial scale and advection can affect Hopf bifurcation in the heterogenous environment.

math.DS↗

arXiv2018

Global stability of epidemic models with imperfect vaccination and quarantine on scale-free networks

Public health services are constantly searching for new ways to reduce the spread of infectious diseases, such as public vaccination of asymptomatic individuals, quarantine (isolation) and treatment of symptomatic individuals. Epidemic models have a long history of assisting in public health planning and policy making. In this paper, we introduce epidemic models including variable population size, degree-related imperfect vaccination and quarantine on scale-free networks. More specifically, the models are formulated both on the population with and without permanent natural immunity to infection, which corresponds respectively to the susceptible-vaccinated-infected-quarantined-recovered (SVIQR) model and the susceptible-vaccinated-infected-quarantined (SVIQS) model. We develop different mathematical methods and techniques to study the dynamics of two models, including the basic reproduction number, the global stability of disease-free and endemic equilibria. For the SVIQR model, we show that the system exhibits a forward bifurcation. Meanwhile, the disease-free and unique endemic equilibria are shown to be globally asymptotically stable by constructing suitable Lyapunov functions. For the SVIQS model, conditions ensuring the occurrence of multiple endemic equilibria are derived. Under certain conditions, this system cannot undergo a backward bifurcation. The global asymptotical stability of disease-free equilibrium, and the persistence of the disease are proved. The endemic equilibrium is shown to be globally attractive by using monotone iterative technique. Finally, stochastic network simulations yield quantitative agreement with the deterministic mean-field approach.

q-bio.PE↗

arXiv2018

Ni Foam Assisted Synthesis of High Quality Hexagonal Boron Nitride with Large Domain Size and Controllable Thickness

The scalable synthesis of two-dimensional (2D) hexagonal boron nitride (h-BN) is of great interest for its numerous applications in novel electronic devices. Highly-crystalline h-BN films, with single-crystal sizes up to hundreds of microns, are demonstrated via a novel Ni foam assisted technique reported here for the first time. The nucleation density of h-BN domains can be significantly reduced due to the high boron solubility, as well as the large specific surface area of the Ni foam. The crystalline structure of the h-BN domains is found to be well aligned with, and therefore strongly dependent upon, the underlying Pt lattice orientation. Growth-time dependent experiments confirm the presence of a surface mediated self-limiting growth mechanism for monolayer h-BN on the Pt substrate. However, utilizing remote catalysis from the Ni foam, bilayer h-BN films can be synthesized breaking the self-limiting effect. This work provides further understanding of the mechanisms involved in the growth of h-BN and proposes a facile synthesis technique that may be applied to further applications in which control over the crystal alignment, and the numbers of layers is crucial.

cond-mat.mtrl-sci↗

arXiv2018

Spatial nonhomogeneous periodic solutions induced by nonlocal prey competition in a diffusive predator-prey model

The diffusive Holling-Tanner predator-prey model with no-flux boundary conditions and nonlocal prey competition is considered in this paper. We show the existence of spatial nonhomogeneous periodic solutions, which is induced by nonlocal prey competition. In particular, the constant positive steady state can lose the stability through Hopf bifurcation when the given parameter passes through some critical values, and the bifurcating periodic solutions near such values can be spatially nonhomogeneous and orbitally asymptotically stable. This phenomenon is different from that in models without nonlocal effect.

math.DS↗