arXiv subjects

Tianshu Liu

Publications and source records attributed to Tianshu Liu.

18 recordsLinked to original sources

arXiv2026

Unsteady Thin-Airfoil Theory Revisited: An Approximate Analytical Solution and the Self-Similar Wagner Effect in Viscous Flows

An approximate analytical solution for the unsteady lift of a thin airfoil with a general unsteady motion is derived from a viscous-flow perspective, where the wake vortex-sheet strength is given in an explicit convolution-type expression as an approximate solution of the Wagner integral equation. For validation, this analytical solution is applied to the Wagner and Theodorsen problems, giving the explicit integral forms of the Wagner and Theodorsen functions as the reduced cases. Further, this analytical solution is applied to the starting flow with a finite timescale in the generalized Wagner problem, revealing the self-similarity of the re-normalized circulatory lift coefficient and its equivalence to the re-normalized Wagner function in a finite time domain. More importantly, the self-similar Wagner effect is found in numerical simulation of the flow over a starting flat-plate airfoil at low Reynolds numbers even when the flow is moderately separated. This self-similarity represents the Reynolds-number-invariance.

physics.flu-dyn↗

arXiv2026

Quadruple decomposition of boundary vorticity flux

First introduced by Lighthill in 1963 for two-dimensional flows and later generalized by Jie-Zhi Wu to three-dimensional scenarios since 1986, the boundary vorticity flux (BVF) is the cornerstone of boundary vorticity dynamics, which quantifies the vorticity source strength on a solid boundary. Recent advances in vorticity and vortex dynamics have revealed both the rigid-rotation and spin modes of vorticity from multiple perspectives. In the present study, we propose a novel quadruple decomposition of the BVF on a stationary solid wall, which essentially uncovers the boundary creation rates of the elementary vorticity modes for both the tangential and wall-normal BVF components, respectively. The proposed framework is illustrated through skin-friction and surface-pressure measurements for flow over a hill model in a low-speed wind tunnel, revealing a set of intriguing BVF patterns for the first time. These theoretical results are expected to be valuable for global surface flow diagnostics when combined with experiments, as well as for understanding the formation mechanisms of near-wall coherent structures and flow-induced noise.

physics.flu-dyn↗

arXiv2026

Vorticity-dynamical analysis of Richtmyer-Meshkov instability based on orbital-spin vorticity decomposition

The present study provides a detailed vorticity-dynamical analysis of shock-driven hydrodynamic physics in canonical Richtmyer-Meshkov instability (RMI) flows: shock interaction with a single-mode perturbed interface, and a cylindrical air bubble immersed in Krypton. These findings provide insights into vortical flow physics beyond the conventional vorticity paradigm, and the DVD approach holds promise for the diagnosis of practical instability-induced flows.

physics.flu-dyn↗

arXiv2025

A general kinematic theory of fluid-element rotation and intrinsic vorticity decompositions

The present study proposes a general kinematic theory for fluid-element rotation and intrinsic vorticity decompositions within the context of vorticity and vortex dynamics. Both the angular velocities of material line and surface elements comprise a classical contribution driven by volume-element rotation (equal to half the local vorticity), and a strain-rate-induced specific angular velocity. Then, two direction-dependent vorticity decompositions (DVDs) are constructed, revealing the rigid rotation and spin modes of vorticity. We derive intrinsic coupling relations for orthogonal line-surface element pair, elucidating their complementary kinematic and geometric roles. Notably, we rigorously prove that the spin mode (in the surface-element-based DVD) is identical to the relative vorticity in the generalized Caswell formula, thereby faithfully accounting for surface shear stress in Newtonian fluids. Next, within a field-theoretic framework, vorticity decompositions are proposed based on streamline and streamsurface using differential geometry. The physical roles of the six rotational invariants in the characteristic algebraic description (including the the normal-nilpotent decomposition (NND) of the velocity gradient tensor (VGT) and the resulting invariant vorticity decomposition (IVD)) are clarified through unified analysis with the DVD, Caswell formula, and Helmholtz-Hodge decomposition. ... It is found that physical admissible DVD vorticity modes must be bounded by IVD modes in phase space, whereas enforcing a minimization principle naturally yields the Liutex formula. Finally, the effectiveness of theory is validated across diverse flows, from simple to complex. Results show that a coupled IVD-DVD analysis could enhance physical understanding of complex vortical flows under both algebraic and field-theoretic frameworks.

physics.flu-dyn↗

arXiv2025

Deformation Driven Suction Cups: A Mechanics-Based Approach to Wearable Electronics

Wearable electronics are emerging as essential tools for health monitoring, haptic feedback, and human-computer interactions. While stable contact at the device-body interface is critical for these applications, it remains challenging due to the skin's softness, roughness, and mechanical variability. Existing methods, such as grounding structures or adhesive tapes, often suffer from contact loss, limited repeatability, and restrictions on the types of electronics they can support. Suction-based adhesives offer a promising alternative by generating negative pressure without requiring tight bands or chemical adhesives. However, most existing cup designs rely on rigid-surface assumptions and overlook mechanical interactions between suction cups and skin. Inspired by traditional cupping therapies, we present a suction-based adhesive system that attaches through elastic deformation and recovery. Using analytical modeling, numerical simulations, and experiments, we present a mechanics-based framework showing how suction performance depends on cup geometry, substrate compliance, and interfacial adhesion. We show that cup geometry should be tailored to substrate stiffness. Wide, flat suction cups perform well on rigid surfaces but fail on soft ones like skin due to substrate intrusion into the chamber. Narrow and tall domes better preserve recoverable volume and generate stronger suction. To improve sealing on rough, dry skin, we introduce a soft, tacky interfacial layer informed by a contact mechanics model. Using our design principles for skin suction adhesives, we demonstrate secure attachment of rigid and flexible components including motion sensors, haptic actuators, and electrophysiological electrodes across diverse anatomical regions. These findings provide a fundamental basis for designing the next generation of skin-friendly adhesives for wearable electronics.

physics.med-ph↗

arXiv2024

Boundary sources of velocity gradient tensor and its invariants

The present work elucidates the boundary behaviors of the velocity gradient tensor ($\bm{A}\equiv\bm{\nabla}\bm{u}$) and its principal invariants ($P,Q,R$) for compressible flow interacting with a stationary rigid wall. Firstly, it is found that the well-known Caswell formula exhibits an inherent physical structure being compatible with the normal-nilpotent decomposition, where both the strain-rate and rotation-rate tensors contain the physical effects from the spin component of the vorticity. Secondly, we derive the kinematic and dynamic forms of the boundary $\bm{A}$-flux from which the known boundary fluxes can be recovered by applying the symmetric-antisymmetric decomposition. Then, we obtain the explicit expression of the boundary $Q$ flux as a result of the competition among the boundary fluxes of squared dilatation, enstrophy and squared strain-rate. Importantly, we emphasize that both the coupling between the spin and surface pressure gradient, and the spin-curvature quadratic interaction, are \textit{not} responsible for the generation of the boundary $Q$ flux, although they contribute to both the boundary fluxes of enstrophy and squared strain-rate. Moreover, we prove that the boundary $R$ flux must vanish on a stationary rigid wall. Finally, the boundary fluxes of the invariants of the strain-rate and rotation-rate tensors are also discussed. It is revealed that the boundary flux of the third invariant of the strain-rate tensor is proportional to the wall-normal derivative of the vortex stretching term, which serves as a source term accounting for the the spatiotemporal evolution rate of the wall-normal enstrophy flux. These theoretical results provide a unified description of boundary vorticity and vortex dynamics, which could be valuable in understanding the formation mechanisms of complex near-wall coherent structures and the boundary sources of flow noise.

physics.flu-dyn↗

arXiv2024

Efficient aerodynamic coefficients prediction with a long sequence neural network

Traditionally, deriving aerodynamic parameters for an airfoil via Computational Fluid Dynamics requires significant time and effort. However, recent approaches employ neural networks to replace this process, it still grapples with challenges like lack of end-to-end training and interpretability. A novel and more efficient neural network is proposed in this paper, called AirfoilNet. AirfoilNet seamlessly merges mathematical computations with neural networks, thereby augmenting interpretability. It encodes grey-scale airfoil images into a lower-dimensional space for computation with Reynolds number, angle of attack, and geometric coordinates of airfoils. The calculated features are then fed into prediction heads for aerodynamic coefficient predictions, and the entire process is end-to-end. Furthermore, two different prediction heads, Gated Recurrent Unit Net(GRUNet) and Residual Multi-Layer Perceptron(ResMLP), designed to support our iteratively refined prediction scheme. Comprehensive analysis of experimental results underscores AirfoilNet's robust prediction accuracy, generalization capability, and swift inference.

physics.flu-dyn↗

arXiv2022

Boundary vorticity dynamics of two-phase viscous flow

From the Navier-Stokes-Korteweg (NSK) equations, the exact relations between the fundamental surface physical quantities for two-phase viscous flow with diffuse interface are derived, including density gradient, shear stress, vorticity, pressure, enstrophy flux and surface curvature. These theoretical results provide a solid foundation of the boundary/interfacial vorticity dynamics and a new tool for analysis of complex interfacial phenomena in two-phase viscous flows. To demonstrate the application of the developed results, simulation of a droplet impacting and spreading on a solid wall is conducted by using a recently developed well-balanced discrete unified gas kinetic scheme (WB-DUGKS), focusing on spreading process when the separation bubbles form inside the droplet. The distributions of shear stress, pressure and enstrophy flux at the interface and wall are analyzed, particularly near the moving contact points and other characteristic points. This example gives an unique perspective to the physics of droplet impingement on a wall.

physics.flu-dyn↗

arXiv2022

Lamb dilatation and its hydrodynamic viscous flux in near-wall incompressible flows

In this paper, we introduce a new physical concept referred to as the wall-normal Lamb dilatation flux (WNLDF), which is defined as the wall-normal derivative of the Lamb dilatation (namely, the divergence of the Lamb vector) multiplied by the dynamic viscosity for incompressible viscous flows. It is proved that the boundary Lamb dilatation flux (BLDF, namely the wall-normal Lamb dilatation flux at the wall) is determined by the boundary enstrophy flux (BEF) and the surface curvature-induced contribution. As the first step to explore this new concept, the present study only considers flow past a stationary no-slip flat wall without curvature-fluid dynamic coupling effects. It is found that the temporal-spatial evolution rate of the WNLDF is contributed by four source terms, which can be explicitly expressed using the fundamental surface quantities including skin friction (or surface vorticity) and surface pressure. Therefore, the instantaneous near-wall flow structures are directly related to the WNLDF in both laminar and turbulent flows. As an example, for the turbulent channel flow at $Re_{\tau}=180$, the intensification of the temporal-spatial evolution rate of the WNLDF is caused by the strong wall-normal velocity event (SWNVE) associated with quasi-streamwise vortices and high intermittency of the viscous sublayer. In addition, near the SWNVE, this evolution rate is mainly contributed by the coupling between skin friction and the boundary enstrophy gradient, as well as the coupling between the skin friction divergence and the boundary enstrophy. The exact results presented in this paper could provide new physical insights into complex near-wall flows.

physics.flu-dyn↗

arXiv2021

A tuned mass amplifier for enhanced haptic feedback

Vibro-tactile feedback is, by far the most common haptic interface in wearable or touchable devices. This feedback can be amplified by controlling the wave propagation characteristics in devices, by utilizing phenomena such as structural resonance. However, much of the work in vibro-tactile haptics has focused on amplifying local displacements in a structure by increasing local compliance. In this paper, we show that engineering the resonance mode shape of a structure with embedded localized mass amplifies the displacements without compromising on the stiffness or resonance frequency. The resulting structure, i.e., a tuned mass amplifier, produces higher tactile forces (7.7 times) compared to its counterpart without a mass, while maintaining a low frequency. We optimize the proposed design using a combination of a neural network and sensitivity analysis, and validate the results with experiments on 3-D printed structures. We also study the performance of the device on contact with a soft material, to evaluate the interaction with skin. Potential avenues for future work are also presented, including small form factor wearable haptic devices and remote haptics.

cond-mat.mtrl-sci↗

arXiv2020

Correlation functions of symmetric orbifold from AdS$_3$ string theory

The paper examines correspondence among correlation functions of symmetric orbifold and string theory on AdS3 described by sl(2) Wess-Zumino-Novikov-Witten (WZNW) model. We start by writing down n-point function of twist operators in the symmetric orbifold in terms of the data of effective Riemann surface. It is then shown that the correlation function can be reproduced from the sl(2) WZNW model. The computation is based on the claim that string worldsheet is given by the same Riemann surface and the reduction method from sl(2) WZNW model to Liouville field theory. We first consider the genus zero surface and then generalize the analysis to the case of generic genus. The result should be an important ingredient for deriving AdS$_3$/CFT$_2$ correspondence with tensionless superstrings to all orders in string perturbation theory.

hep-th↗

arXiv2020

Correspondences among CFTs with different W-algebra symmetry

W-algebras are constructed via quantum Hamiltonian reduction associated with a Lie algebra $\mathfrak{g}$ and an $\mathfrak{sl}(2)$-embedding into $\mathfrak{g}$. We derive correspondences among correlation functions of theories having different W-algebras as symmetry algebras. These W-algebras are associated to the same $\mathfrak{g}$ but distinct $\mathfrak{sl}(2)$-embeddings. For this purpose, we first explore different free field realizations of W-algebras and then generalize previous works on the path integral derivation of correspondences of correlation functions. For $\mathfrak{g}=\mathfrak{sl}(3)$, there is only one non-standard (non-regular) W-algebra known as the Bershadsky-Polyakov algebra. We examine its free field realizations and derive correlator correspondences involving the WZNW theory of $\mathfrak{sl}(3)$, the Bershadsky-Polyakov algebra and the principal $W_3$-algebra. There are three non-regular W-algebras associated to $\mathfrak{g}=\mathfrak{sl}(4)$. We show that the methods developed for $\mathfrak{g}=\mathfrak{sl}(3)$ can be applied straightforwardly. We briefly comment on extensions of our techniques to general $\mathfrak{g}$.

hep-th↗

arXiv2019

Unitary and non-unitary $N=2$ minimal models

The unitary $N = 2$ superconformal minimal models have a long history in string theory and mathematical physics, while their non-unitary (and logarithmic) cousins have recently attracted interest from mathematicians. Here, we give an efficient and uniform analysis of all these models as an application of a type of Schur-Weyl duality, as it pertains to the well-known Kazama-Suzuki coset construction. The results include straightforward classifications of the irreducible modules, branching rules, (super)characters and (Grothendieck) fusion rules.

math-ph↗

arXiv2018

Cosets, characters and fusion for admissible-level $\mathfrak{osp}(1 \vert 2)$ minimal models

We study the minimal models associated to $\mathfrak{osp}(1 \vert 2)$, otherwise known as the fractional-level Wess-Zumino-Witten models of $\mathfrak{osp}(1 \vert 2)$. Since these minimal models are extensions of the tensor product of certain Virasoro and $\mathfrak{sl}_2$ minimal models, we can induce the known structures of the representations of the latter models to get a rather complete understanding of the minimal models of $\mathfrak{osp}(1 \vert 2)$. In particular, we classify the irreducible relaxed highest-weight modules, determine their characters and compute their Grothendieck fusion rules. We also discuss conjectures for their (genuine) fusion products and the projective covers of the irreducibles.

hep-th↗

arXiv2016

Magnetically Localizing Heat or Enhancing Equilibration in a Quasi 1D Magnetic Fluid

Using two different configurations of temperature and magnetic field gradients, we observed that, in a quasi one-dimensional magnetic fluid, magnetic force either reduces the temperature difference across the sample when the two gradients are parallel to each other (PL), or increase the temperature difference when the two gradients are antiparallel (AP), where the single convection roll in zero field was replaced by two localized flows at the two ends of the sample cell. This flow structure stops the heat flow of approaching to thermal equilibrium in the system, causing the temperature at hot side of the sample cell getting hotter and cold side becoming colder. None of these phenomena can be described by the existing theories of magnetically-induced instabilities. The underlying physics for observed results for AP configuration has been proposed as the mechanism to drive a new type of heat engines that has much higher efficiency than Carnot engines and has no pollution to the environment, our results point to the potential feasibility of this proposed mechanism.

cond-mat.soft↗

arXiv2016

Optical-flow-based background-oriented schlieren technique for measuring a laser-induced underwater shock wave

The background-oriented schlieren (BOS) technique with the physics-based optical flow method (OF-BOS) is developed for measuring the pressure field of a laser-induced underwater shock wave. Compared to BOS with the conventional cross-correlation method in PIV (called PIV-BOS), by using the OF-BOS, the displacement field generated by the small density gradient in water can be obtained at the spatial resolution of one vector per pixel. The corresponding density and pressure fields can be further extracted. It is particularly demonstrated that the sufficiently high spatial resolution of the extracted displacement vector field is required in the tomographic reconstruction to correctly infer the pressure field of the spherical underwater shock wave. The capability of the OF-BOS is critically evaluated based on synchronized hydrophone measurements. Special emphasis is placed on direct comparison between the OF-BOS with the PIV-BOS.

physics.flu-dyn↗

arXiv2014

Indentation of a Rigid Sphere into an Elastic Substrate with Surface Tension and Adhesion

The surface tension of compliant materials such as gels provides resistance to deformation in addition to and sometimes surpassing that due to elasticity. This article studies how surface tension changes the contact mechanics of a small hard sphere indenting a soft elastic substrate. Previous studies have examined the special case where the external load is zero, so contact is driven by adhesion alone. Here, we tackle the much more complicated problem where, in addition to adhesion, deformation is driven by an indentation force. We present an exact solution based on small strain theory. The relation between indentation force (displacement) and contact radius is found to depend on a single dimensionless parameter: $\omega=\sigma(\mu R)^{-2/3}(9\pi W_{\textrm{ad}}/4)^{-1/3}$, where $\sigma$ and $\mu$ are the surface tension and shear modulus of the substrate, $R$ is the sphere radius, and $W_{\textrm{ad}}$ is the interfacial work of adhesion. Our theory reduces to the Johnson-Kendall-Roberts theory and Young-Dupr\'e equation in the limits of small and large $\omega$ respectively, and compares well with existing experimental data. Our results show that, although surface tension can significantly affect the indentation force, the magnitude of the pull-off load in the partial wetting liquid-like limit is reduced only by 1/3 compared with the JKR limit, and the pull-off behavior is completely determined by $\omega$.

cond-mat.soft↗

arXiv2013

Lift Enhancement by Dynamically Changing Wingspan in Forward Flapping Flight

Stretching and retracting wingspan has been widely observed in the flight of birds and bats, and its effects on the aerodynamic performance particularly lift generation are intriguing. The rectangular flat-plate flapping wing with a sinusoidally stretching and retracting wingspan is proposed as a simple model of biologically-inspired dynamic morphing wings. Direct numerical simulations of the low-Reynolds-number flows around the flapping morphing wing in a parametric space are conducted by using immersed boundary method. It is found that the instantaneous and time-averaged lift coefficients of the wing can be significantly enhanced by dynamically changing wingspan in a flapping cycle. The lift enhancement is caused not only by changing the lifting surface area, but also manipulating the flow structures that are responsible to the generation of the vortex lift. The physical mechanisms behind the lift enhancement are explored by examining the three-dimensional flow structures around the flapping wing.

physics.flu-dyn↗