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SST-1M is a prototype of a single-mirror Small Size Telescope developed by a consortium of institutes from Poland, Switzerland and the Czech Republic. With a wide field of view of 9 degrees, SST-1Ms are designed to detect gamma-rays in the energy range between 1 and 300 TeV. The design of the SST-1M follows the Davies-Cotton concept, with a 9.42m2 multi-segment mirror. SST-1M is equipped with DigiCam camera, which features a fully digital readout and trigger system using 250 MHz ADC, and a compact Photo-Detector Plane (PDP) composed of 1296 pixels, each made of a hexagonal light guide coupled to silicone photomultipliers (SiPM). Two SST-1M telescopes are currently being commissioned at the Ondrejov Observatory in the Czech Republic, where they are successfully observing Cerenkov events in stereo. This contribution will present an overview of calibration strategies and performance evaluation based on data collected at the observatory., Comment: Volume 444 - 38th International Cosmic Ray Conference (ICRC2023)

The SST-1M is a Small-Sized Telescope (SST) designed to provide a cost-effective and high-performance solution for gamma-ray astrophysics, particularly for energies beyond a few TeV. The goal is to integrate this telescope into an array of similar instruments, leveraging its lightweight design, earthquake resistance, and established Davies-Cotton configuration. Additionally, its optical system is designed to function without a protective dome, allowing it to withstand the harsh atmospheric conditions typical of mountain environments above 2000 m. The SST-1M utilizes a fully digitizing camera system based on silicon photomultipliers (SiPMs). This camera is capable of digitizing all signals from the UV-optical light detectors, allowing for the implementation of various triggers and data analysis methods. We detail the process of designing, prototyping, and validating this system, ensuring that it meets the stringent requirements for gamma-ray detection and performance. An SST-1M stereo system is currently operational and collecting data at the Ond\v{r}ejov observatory in the Czech Republic, situated at 500 m. Preliminary results from this system are promising. A forthcoming paper will provide a comprehensive analysis of the performance of the telescopes in detecting gamma rays and operating under real-world conditions., Comment: 28 pages, 45 figures, 9 tables, to be sumitted to JCAP

Experiments conducted by NASA measured the pressure drop due to gas-liquid flow through a packed-bed reactor under microgravity conditions. From these experiments, we develop correlations for the gas-liquid $f_{gl}$ interphase drag in a two-fluid model (TFM). We use an Ergun-type closure for liquid-solid drag. Then, under a 1D flow assumption, $f_{gl}$ is the only unknown in the TFM. Using a data-driven approach, we determine $f_{gl}$ and correlate it (via composite fits) with the liquid and gas Reynolds numbers, $Re_{l}$ and $Re_{g}$, respectively, and the Suratman number $Su_{l}$. To validate the proposed $f_{gl}(Re_{l},Re_{g},Su_{l})$ closure, we perform two-dimensional transient simulations at microgravity conditions using ANSYS Fluent and employing an Euler-Euler formulation. We find good agreement between the simulations based on the proposed $f_{gl}$ closure and the experimental data., Comment: 25 pages, 5 figures, preprint mode; v2: minor updates/enhancements

We employ the Lorentz reciprocal theorem to derive a closed-form expression for the pressure drop reduction due to the coupling between shear-thinning fluid flow and a weakly deformable channel wall in terms of the shear rate and the viscosity function (and its derivative) of the underlying rigid-channel flow. The methodology is applied in parallel to fluids for which the generalized Newtonian viscosity depends on either the shear rate or the shear stress magnitude. When the viscosity model allows for a closed-form solution for the axial velocity profile in a straight and rigid channel, the pressure drop reduction can be evaluated in closed form, which we demonstrate for the power-law and Ellis viscosity models as featured examples and to enable comparisons to previous works. Importantly, the pressure drop reduction under the Ellis model is valid for both small and large Carreau (or Ellis) numbers, and we show that it reduces to the analytical expression under the power-law model for large Carreau (small Ellis) numbers., Comment: 11 pages, 3 figures; v2: minor revisions, published in JNNFM

We show how bright, fully coherent, hard x-ray beams can be generated through nonlinear upconversion of femtosecond laser light. By using longer-wavelength mid-infrared driving lasers of moderate peak intensity, full phase matching of the high harmonic generation process can extend, in theory, into the hard x-ray region of the spectrum. We identify the dominant phase matching mechanism for long wavelength driving lasers, and verify our predictions experimentally by demonstrating phase-matched up-conversion into the soft x-ray region of the spectrum around 330 eV using an extended, high-pressure, gas medium that is weakly ionized by the laser. Scaling of the overall conversion efficiency is surprisingly favorable as the wavelength of the driving laser is increased, making useful, fully coherent, multi-keV x-ray sources feasible. Finally, we show that the rapidly decreasing microscopic single-atom yield at longer driving wavelengths is compensated macroscopically by an increasing optimal pressure for phase matching and a rapidly decreasing reabsorption of the generated light at higher photon energies., Comment: 43 pages, 8 figures, 1 table

High-harmonic generation is one of the most extreme nonlinear-optical processes observed to date. By focusing an intense laser pulse into a gas, the light-atom interaction that occurs during the process of ionising the atoms results in the generation of harmonics of the driving laser frequency, that extend up to order ~300 (corresponding to photon energies from 4 to >500eV). Because this technique is simple to implement and generates coherent, laser-like, soft-x-ray beams, it is currently being developed for applications in science and technology including probing of dynamics in chemical and materials systems and for imaging. In this work we demonstrate that by carefully controlling the shape of intense light pulses of 6-8 optical cycles, we can control the interaction of light with an atom as it is being ionised, in a way that improves the efficiency of x-ray generation by an order of magnitude. Furthermore, we demonstrate that it is possible to control the spectral characteristics of the emitted radiation and to channel the interaction between different-order nonlinear processes. The result is an increased utility of harmonic generation as a light source, as well as the first demonstration of optical pulse-shaping techniques to control high-order nonlinear processes., Comment: 16 pages, 3 figures

We present spatial coherence measurements of extreme-ultraviolet light generated using the process of high-harmonic upconversion of a femtosecond laser. Using a phase-matched hollow-fiber geometry, the generated beam is found to exhibit essentially full spatial coherence. The coherence of this laser-like EUV source is demonstrated by recording Gabor holograms of small objects. This work demonstrates the capability to do EUV holography using a tabletop experimental setup. Such an EUV source, with low divergence and high spatial coherence, can be used for experiments such as high-precision metrology, inspection of optical components for EUV lithography (1), and for microscopy and holography (2) with nanometer resolution. Furthermore, the short time duration of the EUV radiation (a few femtoseconds) will enable EUV microscopy and holography to be performed with ultrahigh time resolution., Comment: 16 pages, 4 figures

A linear sixth-order partial differential equation (PDE) of ``parabolic'' type describes the dynamics of thin liquid films beneath surfaces with elastic bending resistance when deflections from the equilibrium film height are small. On a finite domain, the associated sixth-order eigenvalue problem is self-adjoint for the boundary conditions corresponding to a thin film in a closed trough, and the eigenfunctions form a complete orthonormal set. Using these eigenfunctions, we derive the Green's function for the governing sixth-order PDE on a finite interval and compare it to the known infinite-line solution. Further, we propose a Galerkin spectral method based on the constructed sixth-order eigenfunctions and their derivative expansions. The system of ordinary differential equations for the time-dependent expansion coefficients is solved by standard numerical methods. The numerical approach is applied to versions of the governing PDE with a second-order spatial derivative (in addition to the sixth-order one), which arises from gravity acting on the film. In the absence of gravity, we demonstrate the self-similar intermediate asymptotics of initially localized disturbances on the film surface, at least until the disturbances ``feel'' the finite boundaries, and show that the derived Green's function is an attractor for such solutions. In the presence of gravity, we use the proposed Galerkin numerical method to demonstrate that self-similar behavior persists, albeit for shortened intervals of time, even for large values of the gravity-to-bending ratio.\\[1mm], Comment: 25 pages, 7 figures; accepted for publication in the Journal of Engineering Mathematics' Special Collection in Memory of Prof. Steve Davis

We provide an experimental framework to measure the flow rate--pressure drop relation for Newtonian and shear-thinning fluids in two common deformable configurations: (\textit{i}) a rectangular channel and (\textit{ii}) an axisymmetric tube. Using the Carreau model to describe the shear-dependent viscosity, we identify the key dimensionless rheological number, $Cu$, which characterizes shear thinning, and we show that our experiments lie within the power-law regime of shear rates. To rationalize the experimental data, we derive the flow rate-pressure drop relation taking into account the two-way-coupled fluid-structure interaction between the flow and its compliant confining boundaries. We thus identify the second key dimensionless number, $\alpha$, which characterizes the compliance of the conduit. We then compare the theoretical flow rate-pressure drop relation to our experimental measurements, finding excellent agreement between the two. We further contrast our results for shear-thinning and Newtonian fluids to highlight the influence of $Cu$ on the flow rate-pressure drop relation. Finally, we delineate four distinct physical regimes of flow and deformation by mapping our experimental flow rate-pressure drop data for Newtonian and shear-thinning fluids into a $Cu-\alpha$ plane., Comment: 10 pages, 4 figures; v2 accepted for publication in Physical Review Fluids

We demonstrate the use of the Lorentz reciprocal theorem in obtaining corrections to the flow rate for oscillatory flow in channels. We start from the unsteady Stokes equations and derive the suitable reciprocity relations for both rigid and deformable channels, assuming all quantities can be expressed as time-harmonic phasors. For the case of a rigid channel, the auxiliary problem is a steady flow solution, and the reciprocal theorem allows us to calculate the first-order correction in the Womersley number to the steady flow rate. For the case of a deformable channel, we account for the fluid--structure interaction using domain perturbation under the assumption of a small compliance number. Using the oscillatory flow solution in a rigid channel as the auxiliary problem, we obtain the first-order correction in the compliance number to the rigid channel flow rate. This correction, validated against numerical simulations, provides the leading-order effect of the interplay between the oscillations of the fluid flow and the compliance of the channel for arbitrary values of the Womersley number., Comment: 13 pages, 4 figures

Gas-liquid flows through packed bed reactors (PBRs) are challenging to predict due to the tortuous flow paths that fluid interfaces must traverse. Experiments at the International Space Station showed that bubble and pulse flows are predominately observed under microgravity conditions, while the trickle and spray flows observed under terrestrial conditions are not present in microgravity. To understand the physics behind the former experiments, we simulate bubble flow through a PBR for different packing-particle-diameter-based Weber numbers and under different gravity conditions. We demonstrate different pore-scale mechanisms, such as capillary entrapment, buoyancy entrapment, and inertia-induced bubble displacement. Then, we perform a quantitative analysis by introducing new dynamic scales, dependent upon the evolving gas-liquid interfacial area, to understand the dynamic trade-offs between the inertia, capillary, and buoyancy forces on a bubble passing through a PBR. This analysis leads us to define new dimensionless Weber-like numbers that delineate bubble entrapment from bubble displacement., Comment: 12 pages, 9 figures; v2: minor updates, to appear in the AIChE Journal

The quantum entanglement entropy of the electrons in one-dimensional hydrogen molecule is quantified locally using an appropriate partitioning of the two-dimensional configuration space. Both the global and the local entanglement entropy exhibit a monotonic increase when increasing the inter-nuclear distance, while the local entropy remains peaked at the middle between the nuclei with its width decreasing. Our findings show that at the inter-nuclear distance where stable hydrogen molecule is formed, the quantum entropy shows no peculiarity thus indicating that the entropy and the energy measures display different sensitivity with respect to the interaction between the two identical electrons involved. One possible explanation is that the calculation of the quantum entropy does not account explicitly for the distance between the nuclei, which contrasts to the total energy calculation where the energy minimum depends decisively on that distance. The numerically exact and the time-dependent quantum Monte Carlo calculations show close results.

Sixth-order boundary value problems (BVPs) arise in thin-film flows with a surface that has elastic bending resistance. To solve such problems, we first derive a complete set of odd and even orthonormal eigenfunctions -- resembling trigonometric sines and cosines, as well as the so-called ``beam'' functions. These functions intrinsically satisfy boundary conditions (BCs) of relevance to thin-film flows, since they are the solutions of a self-adjoint sixth-order Sturm--Liouville BVP with the same BCs. Next, we propose a Galerkin spectral approach for sixth-order problems; namely the sought function as well as all its derivatives and terms appearing in the differential equation are expanded into an infinite series with respect to the derived complete orthonormal (CON) set of eigenfunctions. The unknown coefficients in the series expansion are determined by solving the algebraic system derived by taking successive inner products with each member of the CON set of eigenfunctions. The proposed method and its convergence are demonstrated by solving two model sixth-order BVPs., Comment: 18 pages, 5 figures, IoP jpconf style; v2: correct minor typos, to appear in the proceedings of the Fifteenth Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences (AMiTaNS'23)

The Single-Mirror Small-Sized Telescope, or SST-1M, was originally developed as a prototype of a small-sized telescope for CTA, designed to form an array for observations of gamma-ray-induced atmospheric showers for energies above 3 TeV. A pair of SST-1M telescopes is currently being commissioned at the Ondrejov Observatory in the Czech Republic, and the telescope capabilities for mono and stereo observations are being tested in better astronomical conditions. The final location for the telescopes will be decided based on these tests. In this contribution, we present a data analysis pipeline called sst1mpipe, and the performance of the telescopes when working independently and in a stereo regime., Comment: Submitted as proceeding for the 38th International Cosmic Ray Conference (ICRC2023), 8 pages, 6 figures

We develop a method for modeling and simulating a class of two-phase flows consisting of two immiscible incompressible dielectric fluids and their interactions with imposed external electric fields in two and three dimensions. We first present a thermodynamically-consistent and reduction-consistent phase field model for two-phase dielectric fluids. The model honors the conservation laws and thermodynamic principles, and has the property that, if only one fluid component is present in the system, the two-phase formulation will exactly reduce to that of the corresponding single-phase system. In particular, this model accommodates an equilibrium solution that is compatible with the zero-velocity requirement based on physics. This property provides a simpler method for simulating the equilibrium state of two-phase dielectric systems. We further present an efficient numerical algorithm, together with a spectral-element (for two dimensions) or a hybrid Fourier-spectral/spectral-element (for three dimensions) discretization in space, for simulating this class of problems. This algorithm computes different dynamic variables successively in an un-coupled fashion, and involves only coefficient matrices that are time-independent in the resultant linear algebraic systems upon discretization, even when the physical properties (e.g. permittivity, density, viscosity) of the two dielectric fluids are different. This property is crucial and enables us to employ fast Fourier transforms for three-dimensional problems. Ample numerical simulations of two-phase dielectric flows under imposed voltage are presented to demonstrate the performance of the method herein and to compare the simulation results with theoretical models and experimental data., Comment: 38 pages, 19 figures, 2 tables

Thermal greases, often used as thermal interface materials, are complex paste-like mixtures composed of a base polymer in which dense metallic (or ceramic) filler particles are dispersed to improve the heat transfer properties of the material. They have complex rheological properties that impact the performance of the thermal interface material over its lifetime. We perform rheological experiments on thermal greases and observe both stress relaxation and stress buildup regimes. This time-dependent rheological behavior of such complex fluid-like materials is not captured by steady shear-thinning models often used to describe these materials. We find that thixo-elasto-visco-plastic (TEVP) and nonlinear-elasto-visco-plastic (NEVP) constitutive models characterize the observed stress relaxation and buildup regimes respectively. Specifically, we use the models within a data-driven approach based on physics-informed neural networks (PINNs). PINNs are used to solve the inverse problem of determining the rheological model parameters from the dynamic response in experiments. This training data is generated by startup flow experiments at different (constant) shear rates using a shear rheometer. We validate the ``learned'' models by comparing their predicted shear stress evolution to experiments under shear rates not used in the training datasets. We further validate the learned TEVP model by solving a forward problem numerically to determine the shear stress evolution for an input step-strain profile. Meanwhile, the NEVP model is further validated by comparison to a steady Herschel--Bulkley fit of the material's flow curve., Comment: 13 pages, 10 figures; v2 included new validation appendices; to appear in J. Rheol

Discrete dynamical models of walking droplets ("walkers") have allowed swift numerical experiments revealing heretofore unobserved quantum statistics and related behaviors in a classical hydrodynamic system. We present evidence that one such model of walking droplets exhibits the empirically elusive $n$-bounce resonances that are traditionally seen in the scattering of solitary waves governed by covariant nonlinear field theories with polynomial self-interaction. A numerical investigation of the chosen model of interacting walking droplets reveals a fractal structure of resonances in the velocity in--velocity out diagram, much like the usual maps constructed for collisions of solitary waves. We suggest avenues for further theoretical analysis of walker collisions, which may connect this discrete model to the field-theoretic setting, as well as directions towards new experimental realizations $n$-bounce resonances., Comment: 13 pages, 5 figures. v2: minor updates, accepted for publication in a Special Issue of Mechanics Research Communications. This paper is dedicated to the memory of our friend, mentor, and colleague, Denis Blackmore. Sk\r{a}l

We develop a theory of fluid--structure interaction (FSI) between an oscillatory Newtonian fluid flow and a compliant conduit. We consider the canonical geometries of a 2D channel with a deformable top wall and an axisymmetric deformable tube. Focusing on the hydrodynamics, we employ a linear relationship between wall displacement and hydrodynamic pressure, which has been shown to be suitable for a leading-order-in-slenderness theory. The slenderness assumption also allows the use of lubrication theory, and the flow rate is related to the pressure gradient (and the tube/wall deformation) via the classical solutions for oscillatory flow in a channel and in a tube (attributed to Womersley). Then, by two-way coupling the oscillatory flow and the wall deformation via the continuity equation, a one-dimensional nonlinear partial differential equation (PDE) governing the instantaneous pressure distribution along the conduit is obtained, without \textit{a priori} assumptions on the magnitude of the oscillation frequency (\textit{i.e.}, at arbitrary Womersley number). We find that the cycle-averaged pressure (for harmonic pressure-controlled conditions) deviates from the expected steady pressure distribution, suggesting the presence of a streaming flow. An analytical perturbative solution for a weakly deformable conduit is obtained to rationalize how FSI induces such streaming. In the case of a compliant tube, the results obtained from the proposed reduced-order PDE and its perturbative solutions are validated against three-dimensional, two-way-coupled direct numerical simulations. We find good agreement between theory and simulations for a range of dimensionless parameters characterizing the oscillatory flow and the FSI, demonstrating the validity of the proposed theory of oscillatory flows in compliant conduits at arbitrary Womersley number., Comment: 18 pages, 4 figures; v2 makes some revisions to the presentation, introduces a Strouhal number, which is then fixed, and compares the model against new 3D simulations; v3 corrects minor typos, to appear in Phys. Rev. Fluids

A ferrofluid droplet confined in a Hele-Shaw cell can be deformed into a stably spinning ``gear,'' using crossed magnetic fields. Previously, fully nonlinear simulation revealed that the spinning gear emerges as a stable traveling wave along the droplet's interface bifurcates from the trivial (equilibrium) shape. In this work, a center manifold reduction is applied to show the geometrical equivalence between a two-harmonic-mode coupled system of ordinary differential equations arising from a weakly nonlinear analysis of the interface shape and a Hopf bifurcation. The rotating complex amplitude of the fundamental mode saturates to a limit circle as the periodic traveling wave solution is obtained. An amplitude equation is derived from a multiple-time-scale expansion as a reduced model of the dynamics. Then, inspired by the well-known delay behavior of time-dependent Hopf bifurcations, we design a slowly time-varying magnetic field such that the timing and emergence of the interfacial traveling wave can be controlled. The proposed theory allows us to determine the time-dependent saturated state resulting from the dynamic bifurcation and delayed onset of instability. The amplitude equation also reveals hysteresis-like behavior upon time reversal of the magnetic field. The state obtained upon time reversal differs from the state obtained during the initial (forward-time) period, yet it can still be predicted by the proposed reduced-order theory., Comment: 16 pages, 11 figures; v2: minor updates; v3: clarifications & new appendices

Cerebral aneurysm progression is a result of a complex interplay of the biomechanical and clinical risk factors that drive aneurysmal growth and rupture. Subjects with multiple aneurysms are unique cases wherein clinical risk factors are expected to affect each aneurysm equally, thus allowing for disentangling the effect of biomechanical factors on aneurysmal growth. Towards this end, we performed a comparative computational fluid--structure interaction analysis of aneurysmal biomechanics in image-based models of stable and growing aneurysms in the same subjects, using the cardiovascular simulation platform SimVascular. We observed that areas exposed to low shear and the median peak systolic arterial wall displacement were higher by factors of 2 or more and 1.5, respectively, in growing aneurysms as compared to stable aneurysms. Furthermore, we defined a novel metric, the oscillatory stress index (OStI), that indicates locations of oscillating arterial wall stresses. We observed that growing aneurysms were characterized by regions of combined low wall shear and high OStI, which we hypothesize to be associated with regions of collagen degradation and remodeling. Such regions were either absent or below 5% of the surface area in stable aneurysms. Our results lay the groundwork for future studies in larger cohorts of subjects, to evaluate the statistical significance of these biomechanical parameters in cerebral aneurysm growth., Comment: 21 pages (8 figures) + 6 pages of supplementary appendices (4 figures); v2: fix typos

We analyze the steady non-Newtonian fluid-structure interaction between the flow of an Oldroyd-B fluid and a deformable channel. Specifically, we provide a theoretical framework for calculating the leading-order effect of the fluid's viscoelasticity on the flow rate-pressure drop relation and on the deformation of the channel's elastic wall. We first identify the characteristic scales and dimensionless parameters governing the fluid-structure interaction in slender and shallow channels. Applying the lubrication approximation for the flow and employing a perturbation expansion in powers of the Deborah number $De$, we derive a closed-form expression for the pressure as a function of the non-uniform shape of the channel in the weakly viscoelastic limit up to $\mathrm{O}(De)$. Coupling the hydrodynamic pressure to the elastic deformation, we provide the leading-order effect of the interplay between the viscoelasticity of the fluid and the compliance of the channel on the pressure and deformation fields, as well as on the flow rate-pressure drop relation. For the flow-rate-controlled regime and in the weakly viscoelastic limit, we show analytically that both the compliance of the deforming top wall and the viscoelasticity of the fluid decrease the pressure drop. Furthermore, we reveal a trade-off between the influence of compliance of the channel and the fluid's viscoelasticity on the deformation. While the channel's compliance increases the deformation, the fluid's viscoelasticity decreases it., Comment: 5 figures

Using numerically exact solution of the time-dependent Schroedinger equation together with time-dependent quantum Monte Carlo (TDQMC) calculations we compare the effects of spatial nonlocality versus nonlocal causality for the ground state and for real-time evolution of two entangled electrons in parabolic potential in one spatial dimension. It was found that the spatial entanglement quantified by the linear quantum entropy is predicted with good accuracy using the spatial nonlocality, parameterized naturally within the TDQMC approach. At the same time, the nonlocal causality predicted by the exact solution leads to only small oscillations in the quantum trajectories which belong to the idler electron as the driven electron is subjected to a strong high frequency electric field, without interaction between the electrons.

We investigate the steady-state fluid--structure interaction between a Newtonian fluid flow and a deformable microtube in two novel geometric configurations arising in recent microfluidics experiments. The first configuration is a cylindrical fluidic channel surrounded by an annulus of soft material with a rigid outer wall, while the second one is a cylindrical fluidic channel extruded from a soft rectangular slab of material. In each configuration, we derive a mathematical theory for the nonlinear flow rate--pressure drop relation by coupling lubrication theory for the flow with linear elasticity for the inner tube wall's deformation. Using the flow conduit's axial slenderness and its axisymmetry, we obtain an analytical expression for the radial displacement in each configuration from a plane-strain configuration. The predicted displacement field, and the resulting closed-form flow rate--pressure drop relation, are each validated against three-dimensional direct numerical simulations via SimVascular's two-way-coupled fluid--structure interaction solver, svFSI, showing good agreement. We also show that weak flow inertia can be easily incorporated in the derivation, further improving the agreement between theory and simulations for larger imposed flow rates., Comment: 8 pages, 4 figures; v2: minor revisions; to appear in Brian Straughan 75th Birthday Celebratory Issue of Mechanics Research Communications

Viscous flows through configurations manufactured from soft materials apply both pressure and shear stress at the solid-liquid interface, leading to deformation of the cross-section, which affects the flow rate-pressure drop relation. Conventionally, calculating this flow rate-pressure drop relation requires solving the complete elastohydrodynamic problem, which couples the fluid flow and elastic deformation. In this work, we use the reciprocal theorems for Stokes flow and linear elasticity to derive a closed-form expression for the flow rate-pressure drop relation in deformable channels, bypassing the detailed calculation of the solution to the fluid-structure-interaction problem. For small deformations (under a domain perturbation scheme), our theory provides the leading-order effect, of the interplay between the fluid stresses and the compliance of the channel, on the flow rate-pressure drop relation. Our approach uses solely the fluid flow solution and the elastic deformation due to the fluid stress distribution in an undeformed channel, eliminating the need to solve the coupled elastohydrodynamic problem. Unlike previous theoretical studies that neglected the presence of lateral sidewalls and considered shallow geometries of effectively infinite width, our approach allows to determine the influence of confining sidewalls on the flow rate-pressure drop relation. For the flow-rate-controlled situation and the plate-bending theory for the elastic deformation, we show a trade-off between the effect of compliance of the deforming top wall and the drag due to sidewalls on the pressure drop. While increased compliance decreases the pressure drop, the effect of the sidewalls increases it. Our theoretical framework may provide insight into existing experimental data and pave the way for the design of novel optimized soft microfluidic configurations of different cross-sectional shapes., Comment: 9 pages, 2 figures

Experiments have shown that flow in compliant microchannels can become unstable at a much lower Reynolds number than the corresponding flow in a rigid conduit. Therefore, it has been suggested that the wall's elastic compliance can be exploited towards new modalities of microscale mixing. While previous studies mainly focused on the local instability induced by the fluid--structure interactions (FSIs) in the system, we derive a one-dimensional (1D) model to study the FSI's effect on the global instability. The proposed 1D FSI model is tailored to long, shallow rectangular microchannels with a deformable top wall, similar to the experiments. Going beyond the usual lubrication flows analyzed in these geometries, we include finite fluid inertia and couple the reduced flow equations to a novel reduced 1D wall deformation equation. Although a quantitative comparison to previous experiments is difficult, the behaviors of the proposed model show qualitative agreement with the experimental observations, and capture several key effects. Specifically, we find the critical conditions under which the inflated base state of the 1D FSI model is linearly unstable to infinitesimal perturbations. The critical Reynolds numbers predicted are in agreement with experimental observations. The unstable modes are highly oscillatory, with frequencies close to the natural frequency of the wall, suggesting that the observed instabilities are resonance phenomena. Furthermore, during the start-up from an undeformed initial state, self-sustained oscillations can be triggered by FSI. Our modeling framework can be applied to other microfluidic systems with similar geometric scale separation under different operating conditions., Comment: 34 pages, 15 figures + supplementary materials attached; v2: minor revisions

We harness the physics-informed neural network (PINN) approach to extend the utility of phenomenological models for particle migration in shear flow. Specifically, we propose to constrain the neural network training via a model for the physics of shear-induced particle migration in suspensions. Then, we train the PINN against experimental data from the literature, showing that this approach provides both better fidelity to the experiments, and a novel understanding of the relative roles of the hypothesized migration fluxes. We first verify the PINN approach for solving the inverse problem of radial particle migration in a non-Brownian suspension in an annular Couette flow. In this classical case, the PINN yields the same value (as reported in the literature) for the ratio of the two parameters of the empirical model. Next, we apply the PINN approach to analyze experiments on particle migration in both non-Brownian and Brownian suspensions in Poiseuille slot flow, for which a definitive calibration of the phenomenological migration model has been lacking. Using the PINN approach, we identify the unknown/empirical parameters in the physical model through the inverse solver capability of PINNs. Specifically, the values are significantly different from those for the Couette cell, highlighting an inconsistency in the literature that uses the latter value for Poiseuille flow. Importantly, the PINN results also show that the inferred values of the empirical model's parameters vary with the shear P\'eclet number and the particle bulk volume fraction of the suspension, instead of being constant as assumed in some previous literature., Comment: 19 pages, 9 figures; v2: minor updates & provided data accessibility statement; v3: accepted for publication in International Journal of Multiphase Flow

Soft hydraulics, which addresses the interaction between an internal flow and a compliant conduit, is a central problem in microfluidics. We analyze Newtonian fluid flow in a rectangular duct with a soft top wall at steady state. The resulting fluid--structure interaction (FSI) is formulated for both vanishing and finite flow inertia. At the leading-order in the small aspect ratio, the lubrication approximation implies that the pressure only varies in the streamwise direction. Meanwhile, the compliant wall's slenderness makes the fluid--solid interface behave like a Winkler foundation, with the displacement fully determined by the local pressure. Coupling flow and deformation and averaging across the cross-section leads to a one-dimensional reduced model. In the case of vanishing flow inertia, an effective deformed channel height is defined rigorously to eliminate the spanwise dependence of the deformation. It is shown that a previously-used averaged height concept is an acceptable approximation. From the one-dimensional model, a friction factor and the corresponding Poiseuille number are derived. Unlike the rigid duct case, the Poiseuille number for a compliant duct is not constant but varies in the streamwise direction. Compliance can increase the Poiseuille number by a factor of up to four. The model for finite flow inertia is obtained by assuming a parabolic vertical variation of the streamwise velocity. To satisfy the displacement constraints along the edges of the channel, weak tension is introduced in the streamwise direction to regularize the Winkler-foundation-like model. Matched asymptotic solutions of the regularized model are derived., Comment: 17 pages, 6 figures; accepted for publication in Physics of Fluids as a contribution to the special issue "Tribute to Frank M. White on his 88th Anniversary"l v2: corrects a minor typos

In 1995, C. I. Christov and M. G. Velarde introduced the concept of a dissipative soliton in a long-wave thin-film equation [Physica D 86, 323--347]. In the 25 years since, the subject has blossomed to include many related phenomena. The focus of this short note is to survey the conceptual influence of the concept of a "production-dissipation (input-output) energy balance" that they identified. Our recent results on nonlinear periodic waves as dissipative solitons (in a model equation for a ferrofluid interface in a parallel-flow rectangular geometry subject to an inhomogeneous magnetic field) have shown that the classical concept also applies to nonlocalized (specifically, spatially periodic) nonlinear coherent structures. Thus, we revisit the so-called KdV-KSV equation studied by C. I. Christov and M. G. Velarde to demonstrate that it also possesses spatially periodic dissipative soliton solutions. These coherent structures arise when the linearly unstable flat film state evolves to sufficiently large amplitude. The linear instability is then arrested when the nonlinearity saturates, leading to permanent traveling waves. Although the two model equations considered in this short note feature the same prototypical linear long-wave instability mechanism, along with similar linear dispersion, their nonlinearities are fundamentally different. These nonlinear terms set the shape and eventual dynamics of the nonlinear periodic waves. Intriguingly, the nonintegrable equations discussed in this note also exhibit multiperiodic nonlinear wave solutions, akin to the polycnoidal waves discussed by J. P. Boyd in the context of the completely integrable KdV equation., Comment: 8 pages, 3 figures, REVTeX, submitted to the proceedings of the Thirteenth Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences

The time dependent quantum Monte Carlo method for fermions is introduced and applied for calculation of entanglement of electrons in one-dimensional quantum dots with several spin-polarized and spin-compensated electron configurations. The rich statistics of wave functions provided by the method allows one to build reduced density matrices for each electron and to quantify the spatial entanglement using measures such as quantum entropy by treating the electrons as identical or distinguishable particles. Our results indicate that the spatial entanglement in parallel-spin configurations is rather small and it is determined mostly by the quantum nonlocality introduced by the ground state. By contrast, in the spin-compensated case the outermost opposite-spin electrons interact like bosons which prevails their entanglement, while the inner shell electrons remain largely at their Hartree-Fock geometry. Our findings are in a close correspondence with the numerically exact results, wherever such comparison is possible.