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The rare physical property of negative thermal expansion (NTE) is intriguing because materials with large NTE over a wide temperature range can serve as high-performance thermal expansion compensators. However, applications of NTE are hindered by the fact that most of the available NTE materials show small magnitudes of NTE, and/or NTE occurs only in a narrow temperature range. Herein, for the first time, we investigated the effect of anion substitution instead of general Pb/Ti-site substitutions on the thermal expansion properties of a typical ferroelectric NTE material, PbTiO3. Intriguingly, the substitution of S for O in PbTiO3 further increases the tetragonality of PbTiO3. Consequently, an unusually enhanced NTE with an average volumetric coefficient of thermal expansion $\bar{\alpha}_V$ = -2.50 $\times$ 10$^{-5}$/K was achieved over a wide temperature range (300 -- 790 K), which is contrasted to that of pristine PbTiO3 ($\bar{\alpha}_V$ = -1.99 $\times$ 10$^{-5}$/K RT -- 763 K). The intensified NTE is attributed to the enhanced hybridization between Pb/Ti and O/S atoms by the substitution of S, as evidenced by our theoretical investigations. We therefore demonstrate a new technique for introducing mixed anions to achieve large NTE over a wide temperature range in PbTiO3-based ferroelectrics., Comment: 14 pages, 4 figures

Rapid ice recession in the Arctic Ocean, with predictions of ice-free summers by 2060, opens new maritime routes but requires reliable navigation solutions. Current approaches rely heavily on subjective expert judgment, underscoring the need for automated, data-driven solutions. This study leverages machine learning to assess ice conditions using ship-borne optical data, introducing a finely annotated dataset of 946 images, and a semi-manual, region-based annotation technique. The proposed video segmentation model, UPerFlow, advances the SegFlow architecture by incorporating a six-channel ResNet encoder, two UPerNet-based segmentation decoders for each image, PWCNet as the optical flow encoder, and cross-connections that integrate bi-directional flow features without loss of latent information. The proposed architecture outperforms baseline image segmentation networks by an average 38% in occluded regions, demonstrating the robustness of video segmentation in addressing challenging Arctic conditions.

In this work, we demonstrate the equivalency of the Rotating Parallel Ray Omnidirectional Integration (RPR-ODI) and the Pressure Poisson Equation (PPE) for pressure field reconstruction from corrupted image velocimetry data. Building on the work by Zigunov and Charonko (2024b), we show that performing the ODI is equivalent to pursuing the minimum norm least square solution to a Poisson equation with all Neumann boundary conditions, which is an ill-posed problem. Looking through the lenses of the well-posedness of the Poisson equation, linear algebra, as well as regression and optimization, we provide a comprehensive and integrated framework to analyze ODI/PPE-based pressure field reconstruction methods. The new comprehensions on the equivalence of ODI and PPE not only can reduce the immense computational cost of ODI to that of PPE, but more importantly, unveil their shared strengths and limitations. This paves the way for further improvements in ODI/PPE-based pressure field reconstruction by utilizing the extensive literature on fast, robust elliptic solvers and their associated regularization methods. Throughout this work, we include remarks and notes offering theoretical and computational insights valuable to experimentalists. Some of these notes illustrate a ``minimalist" regularization strategy, serving as ``minimal reproducible examples" that provide a foundation for further refinement. Numerical experiments are presented to support and illustrate these arguments.

Recovering pressure fields from image velocimetry measurements has two general strategies: i) directly integrating the pressure gradients from the momentum equation and ii) solving or enforcing the pressure Poisson equation (divergence of the pressure gradients). In this work, we analyze the error propagation of the former strategy and provide some practical insights. For example, we establish the error scaling laws for the Pressure Gradient Integration (PGI) and the Pressure Poisson Equation (PPE). We explain why applying the Helmholtz-Hodge Decomposition (HHD) could significantly reduce the error propagation for the PGI. We also propose to use a novel HHD-based pressure field reconstruction strategy that offers the following advantages: i) effective processing of noisy scattered or structured image velocimetry data on a complex domain and ii) using Radial Basis Functions (RBFs) with curl/divergence-free kernels to provide divergence-free correction to the velocity fields for incompressible flows and curl-free correction for pressure gradients. Complete elimination of divergence-free bias in measured pressure gradient and curl-free bias in the measured velocity field results in superior accuracy. Synthetic velocimetry data based on exact solutions and high-fidelity simulations are used to validate the analysis as well as demonstrate the flexibility and effectiveness of the RBF-HHD solver.

We propose a simple boundary condition regularization strategy to reduce error propagation in pressure field reconstruction from corrupted image velocimetry data. The core idea is to replace the canonical Neumann boundary conditions with Dirichlet ones obtained by integrating the tangential part of the pressure gradient along the boundaries. Rigorous analysis and numerical experiments justify the effectiveness of this regularization.

The three-dimensional Time-Resolved Lagrangian Particle Tracking (3D TR-LPT) technique has recently advanced flow diagnostics by providing high spatiotemporal resolution measurements under the Lagrangian framework. To fully exploit its potential, accurate and robust data processing algorithms are needed. These algorithms are responsible for reconstructing particle trajectories, velocities, and differential quantities (e.g., pressure gradients, strain- and rotation-rate tensors, and coherent structures) from raw LPT data. In this paper, we propose a three-dimensional (3D) divergence-free Lagrangian reconstruction method, where three foundation algorithms -- Constrained Least Squares (CLS), stable Radial Basis Function (RBF-QR), and Partition-of-Unity Method (PUM) -- are integrated into one comprehensive reconstruction strategy. Our method, named CLS-RBF PUM, is able to (i) directly reconstruct flow fields at scattered data points, avoiding Lagrangian-to-Eulerian data conversions; (ii) assimilate the flow diagnostics in Lagrangian and Eulerian descriptions to achieve high-accuracy flow reconstruction; (iii) process large-scale LPT data sets with more than hundreds of thousand particles in two dimensions (2D) or 3D; (iv) enable spatiotemporal super-resolution while imposing physical constraints (e.g., divergence-free for incompressible flows) at arbitrary time and location. Validation based on synthetic and experimental LPT data confirmed that our method can consistently achieve the above advantages with accuracy and robustness., Comment: 30 pages, 11 figures

The dynamics of cavitation bubbles in the vicinity of a solid cylinder or fibre are seen in water treatment, demolition and/or cleaning of composite materials, as well as bio-medical scenarios such as ultrasound-induced bubbles near the tubular structures in the body. When the bubble collapses near the surface, violent fluid jets may be generated. Understanding whether these jets occur and predicting their directions -- departing or approaching the solid surface -- is crucial for assessing their potential impact on the solid phase. However, the criteria for classifying the onset and directions of the jets created by cavitation near a curved surface of a cylinder have not been established. In this research, we present models to predict the occurrence and directions of the jet in such scenarios. The onset criteria and the direction(s) of the jets are dictated by the bubble stand-off distance and the cylinder diameter. Our models are validated by comprehensive experiments. The results not only predict the jetting behaviour but can serve as guidelines for designing and controlling the jets when a cavitation bubble collapses near a cylinder, whether for protective or destructive purposes.

The transient process accompanied by extreme acceleration in the conical sections of hydraulic systems (e.g., draft tube, diffuser) can induce large cavitation bubbles both at the closed ends and in the bulk liquid. The collapses of the large cavitation bubbles can cause severe damage to the solid walls. We conduct experiments in the tubes with different conical-frustum shaped closed ends with the `tube-arrest' method and observe bubbles generated at these two locations. For the bubbles generated at the close end of the tube, we propose the onset criteria, consisting of two universal non-dimensional parameters $Ca_1$ and $Ca_2$, of large cavitation bubbles separating the water column. We investigate their dynamics including the collapse time and speed. The results indicate that the larger the conical angle, the faster the bubbles collapse. For the bubbles generated in the bulk liquid, we numerically study the collapse time, the jet characteristics and the pressure pulse at bubble collapse. We observe a much stronger jet and pressure pulse of bubbles in tubes, comparing with a bubble near an infinite plate. Our results can provide guidance in the design and safe operation of hydraulic machinery with complex geometries, considering the cavitation during the transient process.

A conceptual model for targeted particle delivery is proposed using controlled vortex ring reconnection. Entrained particles can be efficiently transported within the core of the vortex ring which is propelled via self-induction. A pair of these particle-transporting vortices travelling in the streamwise direction along parallel trajectories will mutually interact resulting in vortex reconnection. The reconnection causes a topological change to the vortex rings which is accompanied by a rapid repulsion in a perpendicular plane to the direction of travel; effectively, transporting the particles to the desired delivery site on the sidewalls. This work explains the physics of the process and the considerations for targeted delivery.

Extreme cavitation scenarios such as water column separations in hydraulic systems during transient processes caused by large cavitation bubbles can lead to catastrophic destruction. In the present paper, we study the onset criteria and dynamics of large cavitation bubbles in a tube. A new cavitation number $Ca_2 = {l^*}^{-1} Ca_0$ is proposed to describe the maximum length $L_{\max}$ of the cavitation bubble, where $l^*$ is a non-dimensional length of the water column indicating its slenderness, and $Ca_0$ is the classic cavitation number. Combined with the onset criteria for acceleration-induced cavitation ($Ca_1<1$, Pan et al. (2017)), we show that the occurrence of large cylindrical cavitation bubbles requires both $Ca_2<1$ and $Ca_1<1$ simultaneously. We also establish a Rayleigh-type model for the dynamics of large cavitation bubbles in a tube. The bubbles collapse at a finite end speed, and the time from the maximum bubble size to collapse is $T_c=\sqrt{2}\sqrt{lL_{\max}}\sqrt{\frac{\rho}{p_\infty}}$, where $l$ is the length of the water column, $L_{\max}$ is the maximum bubble length, $\rho$ is the liquid density, and $p_{\infty}$ is the reference pressure in the far field. The analytical results are validated against systematic experiments using a modified 'tube-arrest' apparatus, which can decouple acceleration and velocity. The results in the current work can guide design and operation of hydraulic systems encountering transient processes.

Understanding the behavior of entities is critical to the development of new policies and technologies aiming at global health and wellbeing; this paper presents a unified model developed and validated for the deposition of entities, ranging from a few Angstroms to tens of nanometers,on nanofibers. The transport of entities is based on convective diffusion and interfacial interactive diffusion. As the size of entities decreases to intermediate sizes - between gas molecules and nanoparticles - adhesion probability on the surface is less than unity, which is determined by the interfacial interactions and kinetics of adhesion. Dimensionless surface coverage provides a better understanding of adhesion kinetic by considering the effects of initial concentration and time. The model is validated by available experimental data in the literature.

A turbulent boundary layer is an essential flow case of fundamental and applied fluid mechanics. However, accurate measurements of turbulent boundary layer parameters (e.g., friction velocity $u_\tau$ and wall shear $\tau_w$), are challenging, especially for high speed flows (Smits et al., 2011). Many direct and/or indirect diagnostic techniques have been developed to measure wall shear stress (Vinuesa et al., 2017). However, based on different principles, these techniques usually give different results with different uncertainties. The current study introduces a nonlinear data assimilation framework based on the Unscented Kalman Filter that can fuse information from i) noisy and gappy measurements from Stereo Particle Image Velocimetry, a Preston tube, and a MEMS shear stress sensor, as well as ii) the uncertainties of the measurements to estimate the parameters of a turbulent boundary layer. A direct numerical simulation of a fully developed turbulent boundary layer flow at Mach 0.3 is used first to validate the data assimilation algorithm. The algorithm is then applied to experimental data of a flow at Mach 0.3, which are obtained in a blowdown wind tunnel facility. The UKF-based data assimilation algorithm is robust to uncertain and gappy experimental data and is able to provide accurate estimates of turbulent boundary layer parameters., Comment: To be appeared in Measurement Science and Technology (2020)

In order to establish the correlation between the magnetoelectric coupling and magnetic instability, we have studied the structural, magnetic, and ferroelectric properties of \textit{x}BaTiO${_3}$-(1-\textit{x})BiCoO${_3}$ as a function of BaTiO$_3$ concentration ($x$) and volume.The $G-$type antiferromagnetic ordering is found to be energetically favorable for $x<$ 0.45 and higher concentrations stabilize with nonmagnetic states. We observe metamagnetic spin state transitions associated with paraelectric to ferrolectric transitions as a function of volume and $x$ using synchrotron diffraction and computational studies, indicating a strong magnetoelectric coupling. Specifically for $x=$ 0.33 composition, a pressure induced high spin (HS) to low spin (LS) transition occurs when the volume is compressed below 5\%. Our orbital$-$projected density of states show a HS state for Co$^{3+}$ in the ferroelectric ground state for $x<$ 0.45 and the corresponding paraelectric phase is stable in the nonmagnetic state due to the stabilization of LS state as evident from our fixed$-$spin$-$moment calculations and magnetic measurements. High values of spontaneous ferroelectric polarizations are predicted for lower $x$ values which inversely vary with $x$ because of the reduction of tetragonality ($c/a$) with increase in $x$. Moreover, we find that the HS$-$LS transition point and magnetoelectric coupling strength can be varied by $x$., Comment: 30 pages

The discovery of unusual negative thermal expansion (NTE) provides the opportunity to control the common but much desired property of thermal expansion, which is valuable not only in scientific interests but also in practical applications. However, most of the available NTE materials are limited to a narrow temperature range, and the NTE effect is generally weakened by means of various modifications. Here, we report an enhanced NTE effect that occurs over a wide temperature range (\alpha V = -5.24 * 10-5 {\deg}C^-1, 25-575 {\deg} C), and this NTE effect is accompanied by an abnormal enhanced tetragonality, a large spontaneous polarization, and a G-type antiferromagnetic ordering in the present perovskite-type ferroelectric of (1-x)PbTiO3-xBiCoO3. Specifically, for the composition of 0.5PbTiO3-0.5BiCoO3, an extensive volumetric contraction of ~4.8 % has been observed near the Curie temperature of 700 {\deg}C, which represents the highest level in PbTiO3-based ferroelectrics. According to our experimental and theoretical results, the giant NTE originates from a synergistic effect of the ferroelectrostriction and spin-crossover of cobalt on the crystal lattice. The actual NTE mechanism is contrasted with previous functional NTE materials, in which the NTE is simply coupled with one ordering such as electronic, magnetic, or ferroelectric ordering. The present study sheds light on the understanding of NTE mechanisms and it attests that NTE could be simultaneouslycoupled with different orderings, which will pave a new way toward the design of large NTE materials., Comment: 30 pages

An analytical framework for the propagation of velocity errors into PIV-based pressure calculation is extended. Based on this framework, the optimal spatial resolution and the corresponding minimum field-wide error level in the calculated pressure field are determined. This minimum error can be viewed as the smallest resolvable pressure. We find that the optimal spatial resolution is a function of the flow features (patterns and length scales), fundamental properties of the flow domain (e.g., geometry of the flow domain and the type of the boundary conditions), in addition to the error in the PIV experiments, and the choice of numerical methods. Making a general statement about pressure sensitivity is difficult. The minimum resolvable pressure depends on competing effects from the experimental error due to PIV and the truncation error from the numerical solver, which is affected by the formulation of the solver. This means that PIV experiments motivated by pressure measurements should be carefully designed so that the optimal resolution (or close to the optimal resolution) is used. Flows ($Re = 1.27 \times 10^4$ and $5\times 10^4$) with exact solutions are used as examples to validate the theoretical predictions of the optimal spatial resolutions and pressure sensitivity. The numerical experimental results agree well with the rigorous analytical predictions. We also propose an \textit{a posterior} method to estimate the contribution of truncation error using Richardson extrapolation and that of PIV error by adding artificially overwhelming noise. We also provide an introductory analysis of the effects of interrogation window overlap in PIV in the context of the pressure calculation., Comment: This is a significant extension of the previous version. Correspondence and requests should be addressed to Zhao Pan (email: zhao.pan@uwaterloo.ca)

The forces on an object impacting the water are extreme in the early moments of water entry and can cause structural damage to biological and man-made bodies alike. These early-time forces arise primarily from added mass, peaking when the submergence is much less than one body length. We experimentally investigate a means of reducing impact forces on rigid spheres by making a jet of water strike the quiescent water surface prior to the object impacting. The water jet accelerates the pool liquid and forms a cavity into which a sphere falls. Through on-board accelerometer measurements and high speed imaging, we quantify the force reduction compared to the case of a sphere entering a quiescent pool. Finally, we find the emergence of a critical jet volume required to maximize force reduction; the critical volume is rationalized using scaling arguments informed by near-surface particle image velocimetry (PIV) data.

Inspired by the huge droplets attached on cypress tree leaf tips after rain, we find that a bent fibre can hold significantly more water in the corner than a horizontally placed fibre (typically up to three times or more). The maximum volume of the liquid that can be trapped is remarkably affected by the bending angle of the fibre and surface tension of the liquid. We experimentally find the optimal included angle ($\sim {36}{^\circ}$) that holds the most water. Analytical and semi-empirical models are developed to explain these counter-intuitive experimental observations and predict the optimal angle. The data and models could be useful for designing microfluidic and fog harvesting devices.

A recent study investigated the propagation of error in a Velocimetry-based Pressure (V-Pressure) field reconstruction problem by directly analyzing the properties of the pressure Poisson equation (Pan et al., 2016). In the present work, we extend these results by quantifying the effect of the error profile in the data field (shape/structure of the error in space) on the resultant error in the reconstructed pressure field. We first calculate the mode of the error in the data that maximizes error in the pressure field, which is the most dangerous error (called the worst error in the present work). This calculation of the worst error is equivalent to finding the principle mode of, for example, an Euler-Bernoulli beam problem in one-dimension and the Kirchhoff-Love plate in two-dimensions, thus connecting the V-Pressure problem from experimental fluid mechanics to buckling elastic bodies from elastic mechanics. Taking advantage of this analogy, we then analyze how the error profile (e.g., spatial frequency of the error and the location of the most concentrated error) in the data field coupled with fundamental features of the flow domain (i.e., size, shape, and dimension of the domain, and the configuration of boundary conditions) significantly affects the error propagation from data to the reconstructed pressure. Our analytical results lend to practical applications in two ways. First, minimization of error propagation can be achieved by avoiding low-frequency error profiles in data similar to the worst case scenarios and error concentrated at sensitive locations. Second, small amounts of the error in the data, if the error profile is similar to the worst error case, can cause significant error in the reconstructed pressure field; such a synthetic error can be used to benchmark V-Pressure algorithms., Comment: this article is significantly extended from the previous version

A positive linear recurrence sequence is of the form $H_{n+1} = c_1 H_n + \cdots + c_L H_{n+1-L}$ with each $c_i \ge 0$ and $c_1 c_L > 0$, with appropriately chosen initial conditions. There is a notion of a legal decomposition (roughly, given a sum of terms in the sequence we cannot use the recurrence relation to reduce it) such that every positive integer has a unique legal decomposition using terms in the sequence; this generalizes the Zeckendorf decomposition, which states any positive integer can be written uniquely as a sum of non-adjacent Fibonacci numbers. Previous work proved not only that a decomposition exists, but that the number of summands $K_n(m)$ in legal decompositions of $m \in [H_n, H_{n+1})$ converges to a Gaussian. Using partial fractions and generating functions it is easy to show the mean and variance grow linearly in $n$: $a n + b + o(1)$ and $C n + d + o(1)$, respectively; the difficulty is proving $a$ and $C$ are positive. Previous approaches relied on delicate analysis of polynomials related to the generating functions and characteristic polynomials, and is algebraically cumbersome. We introduce new, elementary techniques that bypass these issues. The key insight is to use induction and bootstrap bounds through conditional probability expansions to show the variance is unbounded, and hence $C > 0$ (the mean is handled easily through a simple counting argument)., Comment: Version 1.0, 7 pages

Zeckendorf's theorem states every positive integer has a unique decomposition as a sum of non-adjacent Fibonacci numbers. This result has been generalized to many sequences $\{a_n\}$ arising from an integer positive linear recurrence, each of which has a corresponding notion of a legal decomposition. Previous work proved the number of summands in decompositions of $m \in [a_n, a_{n+1})$ becomes normally distributed as $n\to\infty$, and the individual gap measures associated to each $m$ converge to geometric random variables, when the leading coefficient in the recurrence is positive. We explore what happens when this assumption is removed in two special sequences. In one we regain all previous results, including unique decomposition; in the other the number of legal decompositions exponentially grows and the natural choice for the legal decomposition (the greedy algorithm) only works approximately 92.6\% of the time (though a slight modification always works). We find a connection between the two sequences, which explains why the distribution of the number of summands and gaps between summands behave the same in the two examples. In the course of our investigations we found a new perspective on dealing with roots of polynomials associated to the characteristic polynomials. This allows us to remove the need for the detailed technical analysis of their properties which greatly complicated the proofs of many earlier results in the subject, as well as handle new cases beyond the reach of existing techniques., Comment: Version 1.0, 39 pages, 1 figure (added link in bibliography)

Obtaining pressure field data from particle image velocimetry (PIV) is an attractive technique in fluid dynamics due to its noninvasive nature. The application of this technique generally involves integrating the pressure gradient or solving the pressure Poisson equation using a velocity field measured with PIV. However, very little research has been done to investigate the dynamics of error propagation from PIV-based velocity measurements to the pressure field calculation. Rather than measure the error through experiment, we investigate the dynamics of the error propagation by examining the Poisson equation directly. We analytically quantify the error bound in the pressure field, and are able to illustrate the mathematical roots of why and how the Poisson equation based pressure calculation propagates error from the PIV data. The results show that the error depends on the shape and type of boundary conditions, the dimensions of the flow domain, and the flow type.

Learn-to-Fly (L2F) is a new framework that aims to replace the traditional iterative development paradigm for aerial vehicles with a combination of real-time aerodynamic modeling, guidance, and learning control. To ensure safe learning of the vehicle dynamics on the fly, this paper presents an L1 adaptive control (L1AC) based scheme, which actively estimates and compensates for the discrepancy between the intermediately learned dynamics and the actual dynamics. First, to incorporate the periodic update of the learned model within the L2F framework, this paper extends the L1AC architecture to handle a switched reference system subject to unknown time-varying parameters and disturbances. The paper also includes analysis of both transient and steady-state performance of the L1AC architecture in the presence of non-zero initialization error for the state predictor. Second, the paper presents how the proposed L1AC scheme is integrated into the L2F framework, including its interaction with the baseline controller and the real-time modeling module. Finally, flight tests on an unmanned aerial vehicle (UAV) validate the efficacy of the proposed control and learning scheme.

We demonstrate our simple strategy for renormalization with QED at one-loop level, basing on an elaboration of the effective field theory philosophy. No artificial regularization or deformation of the original theory is introduced here and hence no manipulation of infinities, ambiguities arise instead of infinities. Ward identities first come to reduce the number of ambiguities, the residual ones could in principle be removed by imposing physical boundary conditions. Renormalization group equations arise as "decoupling theorems" in the underlying theory perspective. In addition, a technical theorem concerning routing of external momenta is also presented and illustrated with the self-energy and vertex function as examples., Comment: 25 pages, 2 figures, revtex4, publsihed in Int. J. Mod. Phys. A