arXiv subjects

Xiaoyu Zheng

Publications and source records attributed to Xiaoyu Zheng.

At least 37 records · Page 2Linked to original sources

arXiv2022

Whip dynamics in a freely falling chain

In this work, we examine the whip dynamics in a freely falling chain. We consider an inextensible chain with free ends in the presence of gravity hanging from a fixed pulley. If the configuration is unbalanced, the chain begins to accelerate and eventually may lift off the pulley. We show that after the liftoff, the dynamics of the chain resemble that of a whip whose tip speed diverges. The curved region of the chain plays a key role in the dynamics, lifting the chain. The chain is in free fall, yet it exhibits whip dynamics, with one end snapping upward periodically as the chain falls. We have conducted experiments demonstrating this phenomena.

physics.class-ph↗

arXiv2022

An elastically stabilized spherical invagination

Invaginations are partial enclosures formed by surfaces. Typically formed by biological membranes; they abound in nature. In this paper, we consider fundamentally different structures: elastically stabilized invaginations. Focusing on spherical invaginations formed by elastic membranes, we carried out experiments and mathematical modeling to understand the stress and strain fields underlying stable structures. Friction plays a key role in stabilization, and consequently the required force balance is an inequality. Using a novel scheme, we were able to find stable solutions of the balance equations for different models of elasticity, with reasonable agreement with experiments.

cond-mat.soft↗

arXiv2022

Anticlinic order of long-range repulsive rod-like magnetic particles in 2D

In the field of liquid crystals, it is well-known that rod-like molecules interacting via long-range attractive interactions or short-range repulsive potentials can exhibit orientational order. In this work, we are interested in what would happen to systems of rod-like particles interacting via long-range repulsive potential. In our model, each particle consists of a number of point dipoles uniformly distributed along the particle length, with all dipoles pointing along the $z-$ axis, so that the rod-like particles repel each other when they lie in the $x-y$ plane. Dipoles from different particles interact via an $r^{-3}$potential, where $r$ is the distance between the dipoles. We have considered two model systems, each with $N$ particles in a unit cell with periodic boundary conditions. In the first, particle centers are fixed on a square or triangular lattice but they are free to rotate. In the second, particles are free to translate as well as in cells with variable shapes. Here they self-assemble to form configurations where the stress tensors are isotropic. Our numerical results show that at low temperatures the particles tend to form stripes with alternating orientations, resembling herringbone patterns or the anticlinic Sm-C$_{A}$ liquid crystal phase.

cond-mat.soft↗

arXiv2021

Cavity volume and free energy in many-body systems

Within this work we derive and analyse an expression for the free energy of a single-species system in the thermodynamic limit in terms of a generalised cavity volume, that is exact in general, and in principle applicable to systems across their entire range of density, as well as to particles within a general coordinate space. This provides a universal equation of state, and can thus relate the cavity volume to classical results, such as Mayer's cluster expansions. Through this we are able to provide some insight into the connections between cavity volume and free energy density, as well as their consequences. We use examples which permit explicit computations to further probe these results, reclaiming the exact results for a classical Tonks gas and providing a novel derivation of Onsager's free energy for a single species, isotropic system. Given the complexity of the problem we also provide a local lattice ansatz, exact in one dimension, with which we may approximate the cavity volume for hard sphere systems to provide an accurate equation of state in the cases of hard disks and spheres in both dilute regimes as well as beyond the freezing transition.

cond-mat.stat-mech↗

arXiv2021

The Freedericksz transition in a spatially varying magnetic field

Much is known about the Freedericksz transition induced by uniform electric and magnetic fields in nematic liquid crystals. Here we study the effects of a spatially varying field on the transition. We study the response of a nematic to a magnetic field with cylindrical symmetry, and find that since the field magnitude varies in the plane of the cell, the transition vanishes.

cond-mat.soft↗

arXiv2021

Leaky Cell Model of Hard Spheres

We study packings of hard spheres on lattices. The partition function, and therefore the pressure, may be written solely in terms of the accessible free volume, i.e. the volume of space that a sphere can explore without touching another sphere. We compute these free volumes using a leaky cell model, in which the accessible space accounts for the possibility that spheres may escape from the local cage of lattice neighbors. We describe how elementary geometry may be used to calculate the free volume exactly for this leaky cell model in two- and three-dimensional lattice packings and compare the results to the well-known Carnahan-Starling and Percus-Yevick liquid models. We provide formulas for the free volumes of various lattices and use the common tangent construction to identify several phase transitions between them in the leaky cell regime, indicating the possibility of coexistence in crystalline materials.

cond-mat.soft↗

arXiv2021

Wavelength selection in a buckling garden hose

We consider sinusoidal undulations which appear on certain garden hoses under normal use. We propose an explanation and provide a model for this phenomenon, and make a connection with biological structures as well as self-buckling. We compare observations with model predictions, and suggest potential applications in the area of shape-changing materials.

cond-mat.soft↗

arXiv2021

Light induced stress and work in photomechanical materials

Increasingly important photomechanical materials produce stress and mechanical work when illuminated. We propose experimentally accessible performance metrics for photostress and photowork, enabling comparison of materials performance. We relate these metrics to material properties, providing a framework for the design and optimization of photomechanical materials.

cond-mat.mtrl-sci↗

arXiv2021

Impedance Matching in an Elastic Actuator

We optimize the performance of an elastic actuator consisting of an active core in a host which performs mechanical work on a load. The system, initially with localized elastic energy in the active component, relaxes and distributes energy to the rest of the system. Using the linearized Mooney-Rivlin hyperelastic model in a cylindrical geometry and assuming the system to be overdamped, we show that the value of the Young's modulus of the impedance matching host which maximizes the energy transfer from the active component to the load is the geometric mean of Young's moduli of the active component and the elastic load. This is similar to the classic results for impedance matching for maximizing the transmittance of light propagating through dielectric media.

cond-mat.soft↗

arXiv2019

Morphy: A Datamorphic Software Test Automation Tool

This paper presents an automated tool called Morphy for datamorphic testing. It classifies software test artefacts into test entities and test morphisms, which are mappings on testing entities. In addition to datamorphisms, metamorphisms and seed test case makers, Morphy also employs a set of other test morphisms including test case metrics and filters, test set metrics and filters, test result analysers and test executers to realise test automation. In particular, basic testing activities can be automated by invoking test morphisms. Test strategies can be realised as complex combinations of test morphisms. Test processes can be automated by recording, editing and playing test scripts that invoke test morphisms and strategies. Three types of test strategies have been implemented in Morphy: datamorphism combination strategies, cluster border exploration strategies and strategies for test set optimisation via genetic algorithms. This paper focuses on the datamorphism combination strategies by giving their definitions and implementation algorithms. The paper also illustrates their uses for testing both traditional software and AI applications with three case studies.

cs.SE↗

arXiv2019

Surface Anchoring Energy of Cholesteric Liquid Crystals

In this paper, we propose a suitable surface energy expression for cholesteric liquid crystals. We show that there exists a symmetry allowed term for chiral nematics that doesn't appear in the traditional Rapini-Papoular surface energy form. We discuss some consequences of this new surface anchoring term.

cond-mat.soft↗

arXiv2018

Contributions of Repulsive and Attractive Interactions to Nematic Order

Both repulsive and attractive molecular interactions can be used to explain the onset of nematic order. The object of this paper is to combine these two nematogenic molecular interactions in a unified theory. This attempt is not unprecedented; what is perhaps new is the focus on the understanding of nematics in the high density limit. There, the orientational probability distribution is shown to exhibit a unique feature: it has compact support on configuration space. As attractive interactions are turned on, the behavior changes, and at a critical attractive interaction strength, thermotropic behavior of the Maier-Saupe type is attained.

cond-mat.soft↗

arXiv2017

On a paradox in the impact dynamics of smooth rigid bodies

Paradoxes in the impact dynamics of rigid bodies are known to arise in the presence of friction. We show here that, on specificc occasions, in the absence of friction, the conservation laws of classical mechanics are also incompatible with the collisions of smooth, strictly convex rigid bodies. Under the assumption that the impact impulse is along the normal direction to the surface at the contact point, two convex rigid bodies which are well separated can come into contact, and then interpenetrate each other. This paradox can be constructed in both 2D and 3D when the collisions are tangential, in which case no momentum or energy transfer between the two bodies is possible. The postcollisional interpenetration can be realized through the contact points or through neighboring points only. The penetration distance is shown to be O(t^3). The conclusion is that rigid body dynamics is not compatible with the conservation laws of classical mechanics.

physics.class-ph↗

arXiv2017

Onsager's missing steps retraced

Onsager's paper on phase transition and phase coexistence in anisotropic colloidal systems is a landmark in the theory of lyotropic liquid crystals. However, an uncompromising scrutiny of Onsager's original derivation reveals that it would be rigorously valid only for ludicrous values of the system's number density (of the order of the reciprocal of the number of particles) Based on Penrose's tree identity and an appropriate variant of the mean-field approach for purely repulsive, hard-core interactions, our theory shows that Onsager's theory is indeed valid for a reasonable range of densities.

cond-mat.soft↗

arXiv2017

Density functional theory for dense nematics with steric interactions

The celebrated work of Onsager on hard particle systems, based on the truncated second order virial expansion, is valid at relatively low volume fractions for large aspect ratio particles. While it predicts the isotropic-nematic phase transition, it fails to provide a realistic equation of state in that the pressure remains finite for arbitrarily high densities. In this work, we derive a mean field density functional form of the Helmholtz free energy for nematics with hard core repulsion. In addition to predicting the isotropic-nematic transition, the model provides a more realistic equation of state. The energy landscape is much richer, and the orientational probability distribution function in the nematic phase possesses a unique feature: it vanishes on a nonzero measure set in orientational space.

cond-mat.soft↗

arXiv2016

Global Continuous Optimization with Error Bound and Fast Convergence

This paper considers global optimization with a black-box unknown objective function that can be non-convex and non-differentiable. Such a difficult optimization problem arises in many real-world applications, such as parameter tuning in machine learning, engineering design problem, and planning with a complex physics simulator. This paper proposes a new global optimization algorithm, called Locally Oriented Global Optimization (LOGO), to aim for both fast convergence in practice and finite-time error bound in theory. The advantage and usage of the new algorithm are illustrated via theoretical analysis and an experiment conducted with 11 benchmark test functions. Further, we modify the LOGO algorithm to specifically solve a planning problem via policy search with continuous state/action space and long time horizon while maintaining its finite-time error bound. We apply the proposed planning method to accident management of a nuclear power plant. The result of the application study demonstrates the practical utility of our method.

math.OC↗

arXiv2015

The "coin-through-the-rubber" trick: an elastically stabilized invagination

A spectacular trick of close-up magicians involves the apparent passing of a coin through a rubber sheet. The magic is based on the unusual elastic response of a thin rubber sheet: the formation of an invagination, stabilized by friction and elasticity, which holds the coin. By pressing on the coin, the invagination becomes unstable, and the coin is released. We describe the deformation analytically using a simple Hookean description, and examine the stability of the invagination. We finally compare the prediction of the Hookean analysis with numerical solutions of the neo-Hookean model, and provide a brief commentary on the origins of the trick.

physics.pop-ph↗

arXiv2014

Dimensional Analysis and the Time Required to Urinate

According to the recently discovered 'Law of Urination', mammals, ranging in size from mice to elephants, take, on the average, 21s to urinate. We attempt to gain insights into the physical processes responsible for this uniformity using simple dimensional analysis. We assume that the biological apparatus for urination in mammals simply scales with linear size, and consider the scenarios where the driving force is gravity or elasticity, and where the response is dominated by inertia or viscosity. We ask how the time required for urination depends on the length scale, and find that for the time to be independent of body size, the dominant driving force must be elasticity, and the dominant response viscosity. Our note demonstrates that dimensional analysis can indeed readily give insights into complex physical and biological processes.

physics.med-ph↗