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The need for organisms to regulate their volume and osmolarity when surrounded by freshwater is a basic physical challenge for many bacteria, protists and algae. Taking inspiration from the contractile vacuole complex found in many protists, we discuss how simple models of active membrane tubes can give insights into the fluid and active ionic transport properties of such systems. We show that a simple membrane tube with unidirectional ion pumps, and passive ion and water channels, forms a large vacuole due to osmotically-driven water flow and that this can be used to actively pump water out of the cell interior. We discuss the use of this system as a possible minimal method for osmoregulation., Comment: 12 pages, 8 figures

The reconstruction of electrical current densities from magnetic field measurements is an important technique with applications in materials science, circuit design, quality control, plasma physics, and biology. Analytic reconstruction methods exist for planar currents, but break down in the presence of high spatial frequency noise or large standoff distance, restricting the types of systems that can be studied. Here, we demonstrate the use of a deep convolutional neural network for current density reconstruction from two-dimensional (2D) images of vector magnetic fields acquired by a quantum diamond microscope (QDM) utilizing a surface layer of Nitrogen Vacancy (NV) centers in diamond. Trained network performance significantly exceeds analytic reconstruction for data with high noise or large standoff distances. This machine learning technique can perform quality inversions on lower SNR data, reducing the data collection time by a factor of about 400 and permitting reconstructions of weaker and three-dimensional current sources., Comment: 17 pages, 10 figures. Includes Supplemental Information

Faced with a dangerous epidemic humans will spontaneously social distance to reduce their risk of infection at a socio-economic cost. Compartmentalised epidemic models have been extended to include this endogenous decision making: Individuals choose their behaviour to optimise a utility function, self-consistently giving rise to population behaviour. Here we study the properties of the resulting Nash equilibria, in which no member of the population can gain an advantage by unilaterally adopting different behaviour. We leverage a new analytic solution to obtain, (1) a simple relationship between rational social distancing behaviour and the current number of infections; (2) new scaling results for how the infection peak and number of total cases depend on the cost of contracting the disease; (3) characteristic infection costs that divide regimes of strong and weak behavioural response and depend only on the basic reproduction number of the disease; (4) a closed form expression for the value of the utility. We discuss how these analytic results provide a deep and intuitive understanding into the disease dynamics, useful for both individuals and policymakers. In particular the relationship between social distancing and infections represents a heuristic that could be communicated to the population to encourage, or "bootstrap", rational behaviour.

With neural networks being used to control safety-critical systems, they increasingly have to be both accurate (in the sense of matching inputs to outputs) and robust. However, these two properties are often at odds with each other and a trade-off has to be navigated. To address this issue, this paper proposes a method to generate an approximation of a neural network which is certifiably more robust. Crucially, the method is fully convex and posed as a semi-definite programme. An application to robustifying model predictive control is used to demonstrate the results. The aim of this work is to introduce a method to navigate the neural network robustness/accuracy trade-off.

We elucidate the origin of the critical Stokes number $\mathrm{St}_\mathrm{c}$ for inertial particle capture by obstacles in flow fields, and explain the empirical observation made by Araujo et al. [Phys. Rev. Lett. 97, 138001 (2006)] that the capture efficiency grows as $(\mathrm{St}-\mathrm{St}_\mathrm{c})^\beta$ with $\beta=1/2$ for some critical Stokes number. This behaviour, which is inaccessible to classic perturbation theory, derives from the global structure of the phase space of particle trajectories from which viewpoint it is both generic and inevitable except in the limit of highly singular stagnation point flows which we example. In the context of airborne disease transmission, the phenomenon underlies the sharp decline in filtration efficiency of face coverings for micron-sized aerosol droplets., Comment: 8 pages + references + supporting material, 5 figures

Wide-field imaging of magnetic signals using ensembles of nitrogen-vacancy (NV) centers in diamond has garnered increasing interest due to its combination of micron-scale resolution, millimeter-scale field of view, and compatibility with diverse samples from across the physical and life sciences. Recently, wide-field NV magnetic imaging based on the Ramsey protocol has achieved uniform and enhanced sensitivity compared to conventional measurements. Here, we integrate the Ramsey-based protocol with spin-bath driving to extend the NV spin dephasing time and improve magnetic sensitivity. We also employ a high-speed camera to enable dynamic wide-field magnetic imaging. We benchmark the utility of this quantum diamond microscope (QDM) by imaging magnetic fields produced from a fabricated wire phantom. Over a $270\times270 \hspace{0.08333em} \mu\mathrm{m}$$^2$ field of view, a median per-pixel magnetic sensitivity of $4.1(1)\hspace{0.08333em}\mathrm{nT}$$/\sqrt{\mathrm{Hz}}$ is realized with a spatial resolution $\lesssim\hspace{0.08333em}10\hspace{0.08333em}\mu\mathrm{m}$ and sub-millisecond temporal resolution. Importantly, the spatial magnetic noise floor can be reduced to the picotesla scale by time-averaging and signal modulation, which enables imaging of a magnetic-field pattern with a peak-to-peak amplitude difference of about $300\hspace{0.08333em}\mathrm{pT}$. Finally, we discuss potential new applications of this dynamic QDM in studying biomineralization and electrically-active cells., Comment: 18 Pages, 13 figures

During epidemics people may reduce their social and economic activity to lower their risk of infection. Such social distancing strategies will depend on information about the course of the epidemic but also on when they expect the epidemic to end, for instance due to vaccination. Typically it is difficult to make optimal decisions, because the available information is incomplete and uncertain. Here, we show how optimal decision-making depends on information about vaccination timing in a differential game in which individual decision-making gives rise to Nash equilibria, and the arrival of the vaccine is described by a probability distribution. We predict stronger social distancing the earlier the vaccination is expected and also the more sharply peaked its probability distribution. In particular, equilibrium social distancing only meaningfully deviates from the no-vaccination equilibrium course if the vaccine is expected to arrive before the epidemic would have run its course. We demonstrate how the probability distribution of the vaccination time acts as a generalised form of discounting, with the special case of an exponential vaccination time distribution directly corresponding to regular exponential discounting.

Inspired by the swarming or flocking of animal systems we study groups of agents moving in unbounded 2D space. Individual trajectories derive from a ``bottom-up'' principle: individuals reorient to maximise their future path entropy over environmental states. This can be seen as a proxy for keeping options open, a principle that may confer evolutionary fitness in an uncertain world. We find an ordered (co-aligned) state naturally emerges, as well as disordered states or rotating clusters; similar phenotypes are observed in birds, insects and fish, respectively. The ordered state exhibits an order-disorder transition under two forms of noise: (i) standard additive orientational noise, applied to the post-decision orientations (ii) ``cognitive'' noise, overlaid onto each individual's model of the future paths of other agents. Unusually, the order increases at low noise, before later decreasing through the order-disorder transition as the noise increases further., Comment: Corrected bibliography (removing erroneous refs.), Published 19 April 2023 Phys. Rev. Lett

The hydrodynamic effects of macromolecular crowding inside cells is often studied in vitro by using polymers as crowding reagents. Confinement of polymers inside cell-sized droplets has been shown to affect the diffusion of small molecules. Here we develop a method, based on digital holographic microscopy, to measure the diffusion of polystyrene microspheres that are confined within lipid vesicles containing a high concentration of solute. We apply the method to three solutes of varying complexity: sucrose, dextran, and PEG, prepared at ~7 % (w/w). We find that diffusion inside and outside the vesicles is the same when the solute is sucrose or dextran that is prepared below the critical overlap concentration. For polyethylene glycol, which is present at a concentration higher than the critical overlap concentration, the diffusion of microspheres inside vesicles is slower, hinting at the potential effects of confinement on crowding agents., Comment: 4 figures, 6 pages

The Earth's atmosphere is an aerosol, it contains suspended particles. When air flows over an obstacle such as an aircraft wing or tree branch, these particles may not follow the same paths as the air flowing around the obstacle. Instead the particles in the air may deviate from the path of the air and so collide with the surface of the obstacle. It is known that particle inertia can drive this deposition, and that there is a critical value of this inertia, below which no point particles deposit. Particle inertia is measured by the Stokes number, St. We show that near the critical value of the Stokes number, St$_c$, the amount of deposition has the unusual scaling law of exp(-1/(St-St$_c$)$^{1/2}$). The scaling is controlled by the stagnation point of the flow. This scaling is determined by the time for the particle to reach the surface of the cylinder varying as 1/(St-St$_c$)$^{1/2}$, together with the distance away from the stagnation point (perpendicular to the flow direction) increasing exponentially with time. The scaling law applies to inviscid flow, a model for flow at high Reynolds numbers. The unusual scaling means that the amount of particles deposited increases only very slowly above the critical Stokes number. This has consequences for applications ranging from rime formation and fog harvesting to pollination., Comment: 10 pages, 8 figures

Microswimmers can acquire information on the surrounding fluid by sensing mechanical queues. They can then navigate in response to these signals. We analyse this navigation by combining deep reinforcement learning with direct numerical simulations to resolve the hydrodynamics. We study how local and non-local information can be used to train a swimmer to achieve particular swimming tasks in a non-uniform flow field, in particular a zig-zag shear flow. The swimming tasks are (1) learning how to swim in the vorticity direction, (2) the shear-gradient direction, and (3) the shear flow direction. We find that access to lab frame information on the swimmer's instantaneous orientation is all that is required in order to reach the optimal policy for (1,2). However, information on both the translational and rotational velocities seem to be required to achieve (3). Inspired by biological microorganisms we also consider the case where the swimmers sense local information, i.e. surface hydrodynamic forces, together with a signal direction. This might correspond to gravity or, for micro-organisms with light sensors, a light source. In this case, we show that the swimmer can reach a comparable level of performance as a swimmer with access to lab frame variables. We also analyse the role of different swimming modes, i.e. pusher, puller, and neutral swimmers.

Transport of material across liquid interfaces is ubiquitous for living cells and is also a crucial step in drug delivery and in many industrial processes. The fluids that are present on either side of the interfaces will usually have different viscosities. We present a physical model for the dynamics of microswimmers near a soft and penetrable interface that we solve using computer simulations of Navier-Stokes flows. The literature contains studies of similar isoviscous fluid systems, where the two fluids have the same viscosity. Here we extend this to the more general case where they have different viscosities. We investigate the effect of the fluid viscosity ratio on the movement patterns of microswimmers. We find that swimmers systematically reorientate towards the region containing the lower viscosity fluid. Ultimately this is expected to drive the swimmers to behave as if they are more inclined to swim in low viscosity fluids. Furthermore, in addition to the types of swimming already reported in the isoviscous system, i.e. bouncing, sliding and penetrating, we observed a hovering motion, in which strong pullers swim parallel to the interface with a certain distance, which is consistent with the dynamics of such swimmers near the solid wall.

Few simulations exist for microswimmers near deformable interfaces. Here, we present numerical simulations of the hydrodynamic flows associated with a single microswimmer embedded in a binary fluid mixture. The two fluids demix, separated by a penetrable and deformable interface that we assume to be initially prepared in its planar ground-state. We find that the microswimmer can either penetrate the interface, move parallel to it or bounce back off it. We analyze how the trajectory depends on the swimmer type (pusher/puller) and the angle of incidence with respect to the interface. Our simulations are performed in a system with periodic boundary conditions, corresponding to an infinite array of fluid interfaces. A puller reaches a steady state in which it either swims parallel to the interface or selects a perpendicular orientation, repeatedly penetrating through the interface. In contrast, a pusher follows a bouncing trajectory between two interfaces. We discuss several examples in biology in which swimmers penetrate soft interfaces. Our work can be seen as a highly simplified model of such processes.

A Quincke roller is a unique active particle that can run and tumble freely on a flat plate due to the torque generated by a uniform DC electric field applied perpendicular to the plate. A system involving many such particles exhibits a variety of collective dynamics, such as the disordered gas, polar liquid, and active crystal states. We performed direct numerical simulations of a three-dimensional system containing many self-rotating particles to explicitly resolve the hydrodynamic interactions among rotating particles. The collective motion depends on the magnitude of the dipole moments induced on the dielectric particles, the area fraction of particles, and the strength of interparticle attraction. We find that the highly ordered polar liquid state is destabilized by the hydrodynamic interaction between rotating particles at high densities: the near-field lubrication interaction becomes dominant over far-field effects as the interparticle separation becomes shorter., Comment: 16 pages, 11 figures

Nitrogen-vacancy (NV) spin ensembles in diamond provide an advanced magnetic sensing platform, with applications in both the physical and life sciences. The development of isotopically engineered $^{15}$NV diamond offers advantages over naturally occurring $^{14}$NV for magnetometry, due to its simpler hyperfine structure. However, for sensing modalities requiring a bias magnetic field not aligned with the sensing NV axis, the absence of a quadrupole moment in the $^{15}$N nuclear spin leads to pronounced envelope modulation effects in time-dependent measurements of $^{15}$NV spin evolution. While such behavior in spin echo experiments are well studied, analogous effects in Ramsey measurements and the implications for magnetometry remain under-explored. Here, we derive the modulated $^{15}$NV Ramsey response to a misaligned bias field, using a simple vector description of the effective magnetic field on the nuclear spin. The predicted modulation properties are then compared to experimental results, revealing significant magnetic sensitivity loss if unaddressed. We demonstrate that double-quantum coherences of the NV $S=1$ electronic spin states dramatically suppress these envelope modulations, while additionally proving resilient to other parasitic effects such as strain heterogeneity and temperature shifts., Comment: Main text: 9 pages, 5 figures

Epidemics of infectious diseases posing a serious risk to human health have occurred throughout history. During recent epidemics there has been much debate about policy, including how and when to impose restrictions on behaviour. Policymakers must balance a complex spectrum of objectives, suggesting a need for quantitative tools. Whether health services might be `overwhelmed' has emerged as a key consideration. Here we show how costly interventions, such as taxes or subsidies on behaviour, can be used to exactly align individuals' decision making with government preferences even when these are not aligned. In order to achieve this, we develop a nested optimisation algorithm of both the government intervention strategy and the resulting equilibrium behaviour of individuals. We focus on a situation in which the capacity of the healthcare system to treat patients is limited and identify conditions under which the disease dynamics respect the capacity limit. We find an extremely sharp drop in peak infections at a critical maximum infection cost in the government's objective function. This is in marked contrast to the gradual reduction of infections if individuals make decisions without government intervention. We find optimal interventions vary less strongly in time when interventions are costly to the government and that the critical cost of the policy switch depends on how costly interventions are.

This paper presents a method for hardware trojan detection in integrated circuits. Unsupervised deep learning is used to classify wide field-of-view (4x4 mm$^2$), high spatial resolution magnetic field images taken using a Quantum Diamond Microscope (QDM). QDM magnetic imaging is enhanced using quantum control techniques and improved diamond material to increase magnetic field sensitivity by a factor of 4 and measurement speed by a factor of 16 over previous demonstrations. These upgrades facilitate the first demonstration of QDM magnetic field measurement for hardware trojan detection. Unsupervised convolutional neural networks and clustering are used to infer trojan presence from unlabeled data sets of 600x600 pixel magnetic field images without human bias. This analysis is shown to be more accurate than principal component analysis for distinguishing between field programmable gate arrays configured with trojan free and trojan inserted logic. This framework is tested on a set of scalable trojans that we developed and measured with the QDM. Scalable and TrustHub trojans are detectable down to a minimum trojan trigger size of 0.5% of the total logic. The trojan detection framework can be used for golden-chip free detection, since knowledge of the chips' identities is only used to evaluate detection accuracy, Comment: 25 pages, 17 figures

There is a growing debate on whether the future of feedback control systems will be dominated by data-driven or model-driven approaches. Each of these two approaches has their own complimentary set of advantages and disadvantages, however, only limited attempts have, so far, been developed to bridge the gap between them. To address this issue, this paper introduces a method to bound the worst-case error between feedback control policies based upon model predictive control (MPC) and neural networks (NNs). This result is leveraged into an approach to automatically synthesize MPC policies minimising the worst-case error with respect to a NN. Numerical examples highlight the application of the bounds, with the goal of the paper being to encourage a more quantitative understanding of the relationship between data-driven and model-driven control.

We report efforts to quantify the loading of cell-sized lipid vesicles using in-line digital holographic microscopy. This method does not require fluorescent reporters, fluorescent tracers, or radioactive tracers. A single-color LED light source takes the place of conventional illumination to generate holograms rather than bright field images. By modelling the vesicle's scattering in a microscope with a Lorenz-Mie light scattering model, and comparing the results to data holograms, we are able to measure the vesicle's refractive index and thus loading. Performing the same comparison for bulk light scattering measurements enables retrieval of vesicle loading for nanoscale vesicles., Comment: 7 figures

We propose Nash Neural Networks ($N^3$) as a new type of Physics Informed Neural Network that is able to infer the underlying utility from observations of how rational individuals behave in a differential game with a Nash equilibrium. We assume that the dynamics for both the population and the individual are known, but not the payoff function, which specifies the cost per unit time of being in any particular state. We construct our network in such a way that the Euler-Lagrange equations of the corresponding optimal control problem are satisfied and the optimal control is self-consistently determined. In this way, we are able to learn the unknown payoff function in an unsupervised manner. We have applied the $N^3$ to study the optimal behaviour during epidemics, in which individuals can choose to socially distance depending on the state of the pandemic and the cost of being infected. Training our network against synthetic data for a simple SIR model, we showed that it is possible to accurately reproduce the hidden payoff function, in such a way that the game dynamics are respected. Our approach will have far-reaching applications, as it allows one to infer utilities from behavioural data, and can thus be applied to study a wide array of problems in science, engineering, economics and government planning., Comment: 14 pages, 7 figures

A fundamental result of quantum mechanics is that the fluctuations of a bosonic field are given by its temperature $T$. An electromagnetic mode with frequency $\omega$ in the microwave band has a significant thermal photon occupation at room temperature according to the Bose-Einstein distribution $\bar{n} = k_BT / \hbar\omega$. The room temperature thermal state of a 3 GHz mode, for example, is characterized by a mean photon number $\bar{n} \sim 2000$ and variance $\Delta n^2 \approx \bar{n}^2$. This thermal variance sets the measurement noise floor in applications ranging from wireless communications to positioning, navigation, and timing to magnetic resonance imaging. We overcome this barrier in continuously cooling a ${\sim} 3$ GHz cavity mode by coupling it to an ensemble of optically spin-polarized nitrogen-vacancy (NV) centers in a room-temperature diamond. The NV spins are pumped into a low entropy state via a green laser and act as a heat sink to the microwave mode through their collective interaction with microwave photons. Using a simple detection circuit we report a peak noise reduction of $-2.3 \pm 0.1 \, \textrm{dB}$ and minimum cavity mode temperature of $150 \pm 5 \textrm{K}$. We present also a linearized model to identify the important features of the cooling, and demonstrate its validity through magnetically tuned, spectrally resolved measurements. The realization of efficient mode cooling at ambient temperature opens the door to applications in precision measurement and communication, with the potential to scale towards fundamental quantum limits.

The adoption of 3D packaging technology necessitates the development of new approaches to failure electronic device analysis. To that end, our team is developing a tool called the quantum diamond microscope (QDM) that leverages an ensemble of nitrogen vacancy (NV) centers in diamond, achieving vector magnetic imaging with a wide field-of-view and high spatial resolution under ambient conditions. Here, we present the QDM measurement of 2D current distributions in an 8-nm flip chip IC and 3D current distributions in a multi-layer PCB. Magnetic field emanations from the C4 bumps in the flip chip dominate the QDM measurements, but these prove to be useful for image registration and can be subtracted to resolve adjacent current traces in the die at the micron scale. Vias in 3D ICs display only Bx and By magnetic fields due to their vertical orientation and are difficult to detect with magnetometers that only measure the Bz component (orthogonal to the IC surface). Using the multi-layer PCB, we show that the QDM's ability to simultaneously measure Bx, By, and Bz is advantageous for resolving magnetic fields from vias as current passes between layers. We also show how spacing between conducting layers is determined by magnetic field images and how it agrees with the design specifications of the PCB. In our initial efforts to provide further z-depth information for current sources in complex 3D circuits, we show how magnetic field images of individual layers can be subtracted from the magnetic field image of the total structure. This allows for isolation of signal layers and can be used to map embedded current paths via solution of the 2D magnetic inverse. In addition, the paper also discusses the use of neural networks to identify 2D current distributions and its potential for analyzing 3D structures.

Crystal strain variation imposes significant limitations on many quantum sensing and information applications for solid-state defect qubits in diamond. Thus, precision measurement and control of diamond crystal strain is a key challenge. Here, we report diamond strain measurements with a unique set of capabilities, including micron-scale spatial resolution, millimeter-scale field-of-view, and a two order-of-magnitude improvement in volume-normalized sensitivity over previous work [1], reaching $5(2) \times 10^{-8}/\sqrt{\rm{Hz}\cdot\rm{\mu m}^3}$ (with spin-strain coupling coefficients representing the dominant systematic uncertainty). We use strain-sensitive spin-state interferometry on ensembles of nitrogen vacancy (NV) color centers in single-crystal CVD bulk diamond with low strain gradients. This quantum interferometry technique provides insensitivity to magnetic-field inhomogeneity from the electronic and nuclear spin bath, thereby enabling long NV ensemble electronic spin dephasing times and enhanced strain sensitivity. We demonstrate the strain-sensitive measurement protocol first on a scanning confocal laser microscope, providing quantitative measurement of sensitivity as well as three-dimensional strain mapping; and second on a wide-field imaging quantum diamond microscope (QDM). Our strain microscopy technique enables fast, sensitive characterization for diamond material engineering and nanofabrication; as well as diamond-based sensing of strains applied externally, as in diamond anvil cells or embedded diamond stress sensors, or internally, as by crystal damage due to particle-induced nuclear recoils., Comment: 14 pages, 8 figures

Zames-Falb multipliers are mathematical constructs which can be used to prove stability of so-called Lur'e systems: systems that consist of a feedback interconnection of a linear element and a static nonlinear element. The main advantage of Zames-Falb multipliers is that they enable "passivity"-like results to be obtained but with a level of conservatism much lower than \emph{pure} passivity results. However, some of the papers describing the development of the Zames-Falb multiplier machinery are somewhat abstruse and not entirely clear. This article attempts to provide a relatively simple construction of Zames and Falb's main results which will hopefully be understandable to most graduate-level control engineers., Comment: 18 pages, 5 figures

Nitrogen-Vacancy (NV) spin in diamond is a versatile quantum sensor, being able to measure physical quantities such as magnetic field, electric field, temperature, and pressure. In the present work, we demonstrate a multiplexed sensing of magnetic field and temperature. The dual frequency driving technique we employ here is based on frequency-division multiplexing, which enables sensing both measurables in real time. The pair of NV resonance frequencies for dual frequency driving must be selected to avoid coherent population trapping of NV spin states. With an enhanced optical collection efficiency higher than 50 $\%$ and a type 1b diamond crystal with natural abundance $^{13}$C spins, we achieve sensitivities of about 70 pT/$\sqrt{\mathrm{Hz}}$ and 25 $\mu$K/$\sqrt{\mathrm{Hz}}$ simultaneously. A high isolation factor of 34 dB in NV thermometry signal against magnetic field was obtained, and we provide a theoretical description for the isolation factor. This work paves the way for extending the application of NV quantum diamond sensors into more demanding conditions., Comment: 9 pages, 4 figures

Recent studies show the effectiveness of interview chatbots for information elicitation. However, designing an effective interview chatbot is non-trivial. Few tools exist to help designers design, evaluate, and improve an interview chatbot iteratively. Based on a formative study and literature reviews, we propose a computational framework for quantifying the performance of interview chatbots. Incorporating the framework, we have developed iChatProfile, an assistive chatbot design tool that can automatically generate a profile of an interview chatbot with quantified performance metrics and offer design suggestions for improving the chatbot based on such metrics. To validate the effectiveness of iChatProfile, we designed and conducted a between-subject study that compared the performance of 10 interview chatbots designed with or without using iChatProfile. Based on the live chats between the 10 chatbots and 1349 users, our results show that iChatProfile helped the designers build significantly more effective interview chatbots, improving both interview quality and user experience., Comment: 16 pages, 5 figures, accepted paper to CHI 2021 conference

We study the collective dynamics of groups of whirligig beetles Dineutus discolor (Coleoptera: Gyrinidae) swimming freely on the surface of water. We extract individual trajectories for each beetle, including positions and orientations, and use this to discover (i) a density dependent speed scaling like $v\sim\rho^{-\nu}$ with $\nu\approx0.4$ over two orders of magnitude in density (ii) an inertial delay for velocity alignment of $\sim 13$ ms and (iii) coexisting high and low density phases, consistent with motility induced phase separation (MIPS). We modify a standard active brownian particle (ABP) model to a Corralled ABP (CABP) model that functions in open space by incorporating a density-dependent reorientation of the beetles, towards the cluster. We use our new model to test our hypothesis that a MIPS (or a MIPS like effect) can explain the co-occurrence of high and low density phases we see in our data. The fitted model then successfully recovers a MIPS-like condensed phase for $N=200$ and the absence of such a phase for smaller group sizes $N=50,100$., Comment: To be published in the Journal of the Royal Society Interface on 14 April 2021 - Accepted 23 March 2021

Understanding nano- and micro-scale crystal strain in CVD diamond is crucial to the advancement of diamond quantum technologies. In particular, the presence of such strain and its characterization present a challenge to diamond-based quantum sensing and information applications -- as well as for future dark matter detectors where directional information of incoming particles is encoded in crystal strain. Here, we exploit nanofocused scanning X-ray diffraction microscopy to quantitatively measure crystal deformation from defects in diamond with high spatial and strain resolution. Combining information from multiple Bragg angles allows stereoscopic three-dimensional modeling of strain feature geometry; the diffraction results are validated via comparison to optical measurements of the strain tensor based on spin-state-dependent spectroscopy of ensembles of nitrogen vacancy (NV) centers in the diamond. Our results demonstrate both strain and spatial resolution sufficient for directional detection of dark matter via X-ray measurement of crystal strain, and provide a promising tool for diamond growth analysis and improvement of defect-based sensing.

Cells coexist together in colonies or as tissues. Their behaviour is controlled by an interplay between intercellular forces and biochemical regulation. We develop a simple model of the cell cycle, the fundamental regulatory network controlling growth and division, and couple this to the physical forces arising within the cell collective. We analyse this model using both particle-based computer simulations and a continuum theory. We focus on 2D colonies confined in a channel. These develop moving growth fronts of dividing cells with quiescent cells in the interior. The profile and speed of these fronts are non-trivially related to the substrate friction and the cell cycle parameters, providing a possible approach to measure such parameters in experiments., Comment: Revised version, as accepted to appear in PRX

We introduce a double quantum (DQ) 4-Ramsey measurement protocol that enables wide-field magnetic imaging using nitrogen vacancy (NV) centers in diamond, with enhanced homogeneity of the magnetic sensitivity relative to conventional single quantum (SQ) techniques. The DQ 4-Ramsey protocol employs microwave-phase alternation across four consecutive Ramsey (4-Ramsey) measurements to isolate the desired DQ magnetic signal from any residual SQ signal induced by microwave pulse errors. In a demonstration experiment employing a 1-$\mu$m-thick NV layer in a macroscopic diamond chip, the DQ 4-Ramsey protocol provides volume-normalized DC magnetic sensitivity of $\eta^\text{V}=34\,$nTHz$^{-1/2} \mu$m$^{3/2}$ across a $125\,\mu$m$ \,\times\,125\,\mu $m field of view, with about 5$\times$ less spatial variation in sensitivity across the field of view compared to a SQ measurement. The improved robustness and magnetic sensitivity homogeneity of the DQ 4-Ramsey protocol enable imaging of dynamic, broadband magnetic sources such as integrated circuits and electrically-active cells., Comment: 20 pages, 10 figures

Searches for WIMP dark matter will in the near future be sensitive to solar neutrinos. Directional detection offers a method to reject solar neutrinos and improve WIMP searches, but reaching that sensitivity with existing directional detectors poses challenges. We propose a combined atomic/particle physics approach using a large-volume diamond detector. WIMP candidate events trigger a particle detector, after which spectroscopy of nitrogen vacancy centers reads out the direction of the incoming particle. We discuss the current state of technologies required to realize directional detection in diamond and present a path towards a detector with sensitivity below the neutrino floor., Comment: 25 pages, 8 figures

Utilising Onsager's variational formulation, we derive dynamical equations for the relaxation of a fluid membrane tube in the limit of small deformation, allowing for a contrast of solvent viscosity across the membrane and variations in surface tension due to membrane incompressibility. We compute the relaxation rates, recovering known results in the case of purely axis-symmetric perturbations and making new predictions for higher order (azimuthal) $m$-modes. We analyse the long and short wavelength limits of these modes by making use of various asymptotic arguments. We incorporate stochastic terms to our dynamical equations suitable to describe both passive thermal forces and non-equilibrium active forces. We derive expressions for the fluctuation amplitudes, an effective temperature associated with active fluctuations, and the power spectral density for both the thermal and active fluctuations. We discuss an experimental assay that might enable measurement of these fluctuations to infer the properties of the active noise. Finally we discuss our results in the context of active membranes more generally and give an overview of some open questions in the field., Comment: 14 pages, 9 figures

We use Brownian dynamics simulations and advanced topological profiling methods to characterize the out-of-equilibrium evolution of self-entanglement in linear polymers confined into nano-channels and under periodic compression. We distinguish two main forms of entanglement, geometrical and topological. The latter is measured by the number of (essential) crossings of the physical knot detected after a suitable bridging of the chain termini. The former is instead measured as the average number of times a linear chain appears to cross itself when viewed under all projections, and is irrespective of the physical knotted state. The key discovery of our work is that these two forms of entanglement are uncoupled and evolve with distinct dynamics. While geometrical entanglement is typically in phase with the compression-elongation cycles and it is primarily sensitive to its force f, the topological measure is mildly sensitive to cyclic modulation but strongly depends on both compression force f and duration k. The findings could assist the interpretation of experiments using fluorescence molecular tracers to track physical knots in polymers. Furthermore, we identify optimal regions in the experimentally-controllable parameter space in which to obtain more/less topological and geometrical entanglement; this may help designing polymers with targeted topology.

Optically-probed nitrogen-vacancy (NV) quantum defects in diamond can detect nuclear magnetic resonance (NMR) signals with high-spectral resolution from micron-scale sample volumes of about 10 picoliters. However, a key challenge for NV-NMR is detecting samples at millimolar concentrations. Here, we demonstrate an improvement in NV-NMR proton concentration sensitivity of about $10^5$ over thermal polarization by hyperpolarizing sample proton spins through signal amplification by reversible exchange (SABRE), enabling micron-scale NMR of small molecule sample concentrations as low as 1 millimolar in picoliter volumes. The SABRE-enhanced NV-NMR technique may enable detection and chemical analysis of low concentration molecules and their dynamics in complex micron-scale systems such as single-cells., Comment: 5 pages, 4 figures

The Gaussian (saddle splay) rigidity of fluid membranes controls their equilibrium topology but is notoriously difficult to measure. In lipid mixtures, typical of living cells, linear interfaces separate liquid ordered (LO) from liquid disordered (LD) bilayer phases at subcritical temperatures. Here we consider such membranes supported by curved supports that thereby control the membrane curvatures. We show how spectral analysis of the fluctuations of the LO-LD interface provides a novel way of measuring the difference in Gaussian rigidity between the two phases. We provide a number of conditions for such interface fluctuations to be both experimentally measurable and sufficiently sensitive to the value of the Gaussian rigidity, whilst remaining in the perturbative regime of our analysis., Comment: 5 pages, 3 figures. v2: version accepted for publication

Current density distributions in active integrated circuits (ICs) result in patterns of magnetic fields that contain structural and functional information about the IC. Magnetic fields pass through standard materials used by the semiconductor industry and provide a powerful means to fingerprint IC activity for security and failure analysis applications. Here, we demonstrate high spatial resolution, wide field-of-view, vector magnetic field imaging of static (DC) magnetic field emanations from an IC in different active states using a Quantum Diamond Microscope (QDM). The QDM employs a dense layer of fluorescent nitrogen-vacancy (NV) quantum defects near the surface of a transparent diamond substrate placed on the IC to image magnetic fields. We show that QDM imaging achieves simultaneous $\sim10$ $\mu$m resolution of all three vector magnetic field components over the 3.7 mm $\times$ 3.7 mm field-of-view of the diamond. We study activity arising from spatially-dependent current flow in both intact and decapsulated field-programmable gate arrays (FPGAs); and find that QDM images can determine pre-programmed IC active states with high fidelity using machine-learning classification methods., Comment: 12 pages, 5 figures, 1 table

Ensembles of nitrogen-vacancy (NV) centers in diamond are a leading platform for practical quantum sensors. Reproducible and scalable fabrication of NV-ensembles with desired properties is crucial. This work addresses these challenges by developing a chemical vapor deposition (CVD) synthesis process to produce diamond material at scale with improved NV-ensemble properties for a target NV density. The material reported in this work enables immediate sensitivity improvements for current devices. In addition, techniques established in this work for material and sensor characterization at different stages of the CVD synthesis process provide metrics for future efforts targeting other NV densities or sample geometries., Comment: 16 pages, 10 figures, 5 tables

This paper investigates the existence of localised axisymmetric (radial) patterns on the surface of a ferrofluid in the presence of a uniform vertical magnetic field. We formally investigate all possible small-amplitude solutions which remain bounded close to the pattern's centre (the core region) and decay exponentially away from the pattern's centre (the far-field region). The results are presented for a finite-depth, infinite expanse of ferrofluid equipped with a linear magnetisation law. These patterns bifurcate at the Rosensweig instability, where the applied magnetic field strength reaches a critical threshold. Techniques for finding localised solutions to a non-autonomous PDE system are established; solutions are decomposed onto a basis which is independent of the radius, reducing the problem to an infinite set of nonlinear, non-autonomous ODEs. Using radial centre manifold theory, local manifolds of small-amplitude solutions are constructed in the core and far-field regions, respectively. Finally, using geometric blow-up coordinates, we match the core and far-field manifolds; any solution that lies on this intersection is a localised radial pattern. Three distinct classes of stationary radial solutions are found: spot A and spot B solutions, which are equipped with two different amplitude scaling laws and achieve their maximum amplitudes at the core, and ring solutions, which achieve their maximum amplitudes away from the core. These solutions correspond exactly to the classes of localised radial solutions found for the Swift-Hohenberg equation. Different values of the linear magnetisation and depth of the ferrofluid are investigated and parameter regions in which the various localised radial solutions emerge are identified. The approach taken in this paper outlines a route to rigorously establishing the existence of axisymmetric localised patterns in the future., Comment: 74 pages, 23 figures