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In this paper, we will explore Padmanabhan's mesoscopic, statistical approach to gravity [62] with a twist. The general picture of his approach is that spacetime is made of large numbers of localized quantum degrees of freedom. Padmanabhan assumed that the degrees of freedom of a given quantum state of geometry contribute, after averaging over fluctuations, a vector degree of freedom for space-time at a point. For null vectors, this can be regarded as corresponding to one single vector, i.e. a pure state, for the statistical ensemble on the light cone at every point. In the present paper, we consider instead the case where the states of the gravitational degrees of freedom are spread out and overlap, with only probabilistic information on which of them determines the actual spacetime at a point. In the continuum limit, this corresponds to a mixed state for the statistical ensemble on the light cone at every point. This change in assumptions leads to some interesting observations. When we define a statistical ensemble on the light cone, its variance "knows" about the interior of the light cone. As an intriguing consequence, we find that the cosmological constant can be related to the variance over the light cone. With a mixed state, we can no longer derive the gravitational field equations from an entropy functional. Here, instead, we show that a naive implementation of the measure of a mixed state on the light cone in the variation principle leads to modified measure theories (MMT) as the grand canonical ensemble and allows one to reframe unimodular gravity as the canonical ensemble of a statistical theory on the light cone.

Certain periodical cicadas exhibit life cycles with durations of 13 or 17 years, and it is now generally accepted that such large prime numbers arise evolutionarily to avoid synchrony with predators. Less well explored is the question of how, in the face of intrinsic biological and environmental noise, insects within a brood emerge together in large successive swarms from underground during springtime warming. Here we consider the decision-making process of underground cicada nymphs experiencing random but spatially-correlated thermal microclimates like those in nature. Introducing short-range communication between insects leads to a model of consensus building that maps on to the statistical physics of an Ising model with a quenched, spatially correlated random magnetic field and annealed site dilution, which displays the kinds of collective swarms seen in nature., Comment: 5 pages, 4 figures

Most of the existing proposals for laboratory tests of a quantum nature of gravity are based on the use of two delocalized masses or harmonically bound masses prepared in pure quantum states with large enough spatial extent. Here a setup is proposed that is based on a single delocalized mass coupled to a harmonically trapped test mass (undergoing first expansion and then compression) that moves under the action of gravity. We investigate the in-principle feasibility of such an experiment, which turns out to crucially depend on the ability to tame Casimir-Polder forces. We thus proceed with a design aimed at achieving this, trying at the same time to take advantage of these forces rather than only fighting them., Comment: 11 pages, 6 figures. v2: Final revision, corresponding to the published version

In a known gedanken experiment, a delocalized mass is recombined while the gravitational field sourced by it is probed by another (distant) particle; in it, this is used to explore a possible tension between complementarity and causality in case the gravitational field entangles with the superposed locations, a proposed resolution being graviton emission from quadrupole moments. Here, we focus on the delocalized particle (forgetting about the probe and the gedanken experiment) and explore the conditions (in terms of mass, separation, and recombination time) for graviton emission. Through this, we find that the variations of quadrupole moments in the recombination are generically greatly enhanced if the field is entangled compared to if it is sourced instead by the energy momentum expectation value on the delocalized state (moment variation $\sim m \, d^2$ in the latter case, with $m$ mass, $d$ separation). In addition, we obtain the (upper) limit recombination time for graviton emission growing as $m$ in place of the naive expectation $\sqrt{m}$. In this, the Planck mass acts as threshold mass (huge, for delocalized objects): no graviton emission is possible below it, however fast the recombination occurs. If this is compared with the decay times foreseen in the collapse models of Di\'osi and Penrose (in their basic form), one finds that no (quadrupole) graviton emission from recombination is possible in them. Indeed, right when $m$ becomes large enough to allow for emission, it also becomes too large for the superposition to survive collapse long enough to recombine., Comment: 12 pages, 1 figure; v3: some further comments, in particular on the role of the limit length; several references added; corresponds to the published version

In the vast amount of results linking gravity with thermodynamics, statistics, information, a path is described which tries to explore this connection from the point of view of (non)locality of the gravitational field. First the emphasis is put on that well-known thermodynamic results related to null hypersurfaces (i.e. to lightsheets and to generalized covariant entropy bound) can be interpreted as implying an irreducible intrinsic nonlocality of gravity. This nonlocality even if possibly concealed at ordinary scales(depending on which matter is source of the gravitational field, and which matter we use to probe the latter) unavoidably shows up at the smallest scales, read the Planck length $l_p$, whichever are the circumstances we are considering. Some consequences are then explored of this nonlocality when embodied in the fabric itself of spacetime by endowing the latter with a minimum length $L$, in particular the well-known and intriguing fact that this brings to get the field equations, and all of gravity with it, as a statistical-mechanical result. This is done here probing the neighborhood of a would-be (in ordinary spacetime) generic event through lightsheets (instead of spacelike or timelike geodesic congruences as in other accounts) from it. The tools for these derivations are nonlocal quantities, and among them the minimum-length Ricci scalar stands out both for providing micro degrees of freedom for gravity in the statistical account and for the fact that intriguingly the ordinary, or `classical', Ricci scalar can not be recovered from it in the $L\to 0$ limit. Emphasis is put on that classical gravity is generically obtained this way for $\hbar\ne 0$, but not in the $\hbar\to 0$ limit (the statistically derived field equations become singular in this limit), adding to previous results in this sense. (truncated Abstract; see the paper for full Abstract), Comment: 40 pages, 1 figure, contribution to the special issue of GERG dedicated to the memory of Prof. Thanu Padmanabhan

A fundamental issue in biology is the nature of evolutionary transitions from unicellular to multicellular organisms. Volvocine algae are models for this transition, as they span from the unicellular biflagellate Chlamydomonas to multicellular species of Volvox with up to 50,000 Chlamydomonas-like cells on the surface of a spherical extracellular matrix. The mechanism of phototaxis in these species is of particular interest since they lack a nervous system and intercellular connections; steering is a consequence of the response of individual cells to light. Studies of Volvox and Gonium, a 16-cell organism with a plate-like structure, have shown that the flagellar response to changing illumination of the cellular photosensor is adaptive, with a recovery time tuned to the rotation period of the colony around its primary axis. Here, combining high-resolution studies of the flagellar photoresponse with 3D tracking of freely-swimming cells, we show that such tuning also underlies phototaxis of Chlamydomonas. A mathematical model is developed based on the rotations around an axis perpendicular to the flagellar beat plane that occur through the adaptive response to oscillating light levels as the organism spins. Exploiting a separation of time scales between the flagellar photoresponse and phototurning, we develop an equation of motion that accurately describes the observed photoalignment. In showing that the adaptive time scale is tuned to the organisms' rotational period across three orders of magnitude in cell number, our results suggest a unified picture of phototaxis in green algae in which the asymmetry in torques that produce phototurns arise from the individual flagella of Chlamydomonas, the flagellated edges of Gonium and the flagellated hemispheres of Volvox., Comment: 24 pages, 21 figures, 3 supplementary videos (available from REG)

The collapse of a catenoidal soap film when the rings supporting it are moved beyond a critical separation is a classic problem in interface motion in which there is a balance between surface tension and the inertia of the surrounding air, with film viscosity playing only a minor role. Recently [Goldstein, et al., Phys. Rev. E 104, 035105 (2021)], we introduced a variant of this problem in which the catenoid is bisected by a glass plate located in a plane of symmetry perpendicular to the rings, producing two identical hemicatenoids, each with a surface Plateau border (SPB) on the glass plate. Beyond the critical ring separation, the hemicatenoids collapse in a manner qualitatively similar to the bulk problem, but their motion is governed by the frictional forces arising from viscous dissipation in the SPBs. Here we present numerical studies of a model that includes classical friction laws for SPB motion on wet surfaces and show consistency with our experimental measurements of the temporal evolution of this process. This study can help explain the fragmentation of bubbles inside very confined geometries such as porous materials or microfluidic devices., Comment: 9 pages, 9 figures, supplementary videos available at website of REG

Starting from some results regarding the form of the Ricci scalar at a point $P$ in a spacetime endowed with a minimum distance, we investigate how they might be accommodated, specifically for the case of null separations, in a as-simple-as-possible quantum structure for spacetime at $P$, and we try to accomplish this in terms of potentially operationally-defined concepts. In so doing, we provide a possible explicit form for the operator expressing the Ricci scalar as a quantum observable, and give quantum-informational support, thus regardless of or before field equations, to associating with a patch of horizon an entropy proportional to its area., Comment: v2: 14 pages, some editing/clarifications, references added

We present a general framework for the estimation of corporate default based on a firm's capital structure, when its assets are assumed to follow a pure jump L\'evy processes; this setup provides a natural extension to usual default metrics defined in diffusion (log-normal) models, and allows to capture extreme market events such as sudden drops in asset prices, which are closely linked to default occurrence. Within this framework, we introduce several pure jump processes featuring negative jumps only and derive practical closed formulas for equity prices, which enable us to use a moment-based algorithm to calibrate the parameters from real market data and to estimate the associated default metrics. A notable feature of these models is the redistribution of credit risk towards shorter maturity: this constitutes an interesting improvement to diffusion models, which are known to underestimate short term default probabilities. We also provide extensions to a model featuring both positive and negative jumps and discuss qualitative and quantitative features of the results. For readers convenience, practical tools for model implementation and GitHub links are also included., Comment: V3 (final version): correction of minor typos and bibliographical references

In this paper, we consider a specific model, implementing the existence of a fundamental limit distance $L_0$ between (space or time separated) points in spacetime, which in the recent past has exhibited the intriguing feature of having a minimum-length Ricci scalar $R_{(q)}$ that does not approach the ordinary Ricci scalar $R$ in the limit of vanishing $L_0$. $R_{(q)}$ at a point has been found to depend on the direction along which the existence of minimum distance is implemented. Here, we point out that the convergence $R_{(q)}\to R$ in the $L_0\to 0$ limit is anyway recovered in a relaxed or generalized sense, which is when we average over directions, this suggesting we might be taking the expectation value of $R_{(q)}$ promoted to be a quantum variable. It remains as intriguing as before the fact that we cannot identify (meaning this is much more than simply equating in the generalised sense above) $R_{(q)}$ with $R$ in the $L_0\to 0$ limit, namely when we get ordinary spacetime. Thing is like if, even when $L_0$ (read here the Planck length) is far too small to have any direct detection of it feasible, the intrinsic quantum nature of spacetime might anyway be experimentally at reach, witnessed by the mentioned special feature of Ricci, not fading away with $L_0$ (i.e. persisting when taking the $\hbar \to 0$ limit)., Comment: v2: 9 pages; clarification of a point in the discussion of the Lorentz case; added a possible connection with other approaches; it corresponds to the published version; in memory of Prof. Thanu Padmanabhan

We study the recently reported qmetric (or zero-point-length) expressions of the Ricci (bi)scalar $R_{(q)}$ (namely, expressions of the Ricci scalar in a spacetime with a limit length $L_0$ built in), focusing specifically on the case of null separated events. A feature of these expressions is that, when considered in the coincidence limit $p \to P$, they generically exhibit a dependence on the geodesic along which the varying point $p$ approached $P$, sort of memory of how $p$ went to $P$. This fact demands a deeper understanding of the meaning of the quantity $R_{(q)}$, for this latter tells about curvature of spacetime as a whole at $P$ and would not be supposed to depend on whichever vector we might happen to consider at $P$. Here, we try to search for a framework in which these two apparently conflicting aspects might be consistently reconciled. We find a tentative sense in which this could be achieved by endowing spacetime of a specific operational meaning. This comes, however, at the price (or with the benefit) of having a spacetime no longer arbitrary but, in a specific sense, constrained. The constraint turns out to be in the form of a relation between spacetime geometry in the large scale (as compared to $L_0$) and the matter content, namely as sort of field equations. This comes thanks to something which happens to coincide with the expression of balance of (matter and spacetime) exchanged heats, i.e. the thermodynamic variational principle from which the field equations have been reported to be derivable. This establishes a link between (this specific, operational understanding of) the meaning of the limit expression of $R_{(q)}$ on one side and the (large-scale) field equations on the other, this way reconnecting (once more) the latter to a quantum feature., Comment: 17 pages; v2: some corrections/editing/clarifications, reference added, it corresponds to the published version

The growing concerns over desertification have spurred research into technologies aimed at acquiring water from non-traditional sources such as dew, fog, and water vapor. Some of the most promising developments have focused on improving designs to collect water from fog. However, the absence of a shared framework to predict, measure and compare the water collection efficiencies of new prototypes is becoming a major obstacle to progress in the field. We address this problem by providing a general theory to design efficient fog collectors as well as a concrete experimental protocol to furnish our theory with all the necessary parameters to quantify the effective water collection efficiency. We show in particular that multi-layer collectors are required for high fog collection efficiency and that all efficient designs are found within a narrow range of mesh porosity. We support our conclusions with measurements on simple multi-layer harp collectors., Comment: 33 pages, 8 figures (including supplemental material); in press at ACS Applied Materials & Interfaces

We consider spacetime endowed with a zero-point length, i.e. with an effective metric structure which allows for a (quantum-mechanically arising) finite distance $L_0$ between events in the limit of their coincidence. Restricting attention to null separated events, we find an expression for the Ricci (bi)scalar in this zero-point-length metric; this is done for when geometric circumstances are such that the collection of all null geodesics emerging from a point $P$ has all the information needed to fix the value of scalar curvature at $P$. Taking then the coincidence and further $L_0 \to 0$ limits, we find that this expression does not reduce to the Ricci scalar $R$ of the ordinary metric but to $(D-1) R_{ab} l^a l^b$ in $D$-dimensional spacetime ($D \ge 4$), where $R_{ab}$ and $l^a$ are the ordinary Ricci tensor and tangent vector to the null geodesics. This adds nicely to the existing results for time and space separations. This finding seems to give further support to the view that the quantity $R_{ab} l^a l^b$, ubiquitous in horizon thermodynamics, embodies something which remains as a relic/remnant/memory of a quantum underlying structure for spacetime in the limit of (actual detectability of) this quantumness fading away, and which as such should enter the scene when aiming to derive/motivate the field equations. Further, it turns out to be the same quantity used in an existing derivation of field equations from a thermodynamic variational principle, thus adding further evidence of an origin as quantum-spacetime relic for the latter., Comment: 24 pages; v3: some clarifications, it corresponds to the published version

The Raychaudhuri equation for a geodesic congruence in the presence of a zero-point length has been investigated. This is directly related to the small-scale structure of spacetime and possibly captures some quantum gravity effects. The existence of such a minimum distance between spacetime events modifies the associated metric structure and hence the expansion as well as its rate of change deviates from standard expectations. This holds true for any kind of geodesic congruences, including time-like and null geodesics. Interestingly, this construction works with generic spacetime geometry without any need of invoking any particular symmetry. In particular, inclusion of a zero-point length results into a non-vanishing cross-sectional area for the geodesic congruences even in the coincidence limit, thus avoiding formation of caustics. This will have implications for both time-like and null geodesic congruences, which may lead to avoidance of singularity formation in the quantum spacetime., Comment: Revised Version, Published, 16 pages, no figures

Recently, a proposal has been made to figure out the expected discrete nature of spacetime at the smallest scales in terms of atoms of spacetime, capturing their effects through a scalar $\rho$, related to their density, function of the point $P$ and vector $v^a$ at $P$. This has been done in the Euclideanized space one obtains through analytic continuation from Lorentzian sector at $P$. $\rho$ has been defined in terms of a peculiar `effective' metric $q_{ab}$, of quantum origin, introduced for spacelike/timelike separated events. This metric stems from requiring that $q_{ab}$ coincides with $g_{ab}$ at large (space/time) distances, but gives finite distance in the coincidence limit, and implements directly this way one single, very basic aspect associated to any quantum description of spacetime: length quantization. Since the latter appears a quite common feature in the available quantum descriptions of gravity, this quantum metric $q_{ab}$ can be suspected to have a rather general scope and to be re-derivable (and cross-checkable) in various specific quantum models of gravity, even markedly different one from the other. This work reports on an attempt to introduce a definition of $\rho$ not through the Euclidean but directly in the Lorentz sector. This turns out to be not a so trivial task, essentially because of the null case, meaning when $v^a$ is null, as in this case it seems we lack even a concept of $q_{ab}$. A notion for the quantum metric $q_{ab}$ for null separated events is then proposed and an expression for it is derived. From it, a formula for $\rho$ is deduced, which turns out to coincide with what obtained through analytic continuation. This virtually completes the task of having quantum expressions of any kind of spacetime intervals, with, moreover, $\rho$ defined directly in terms of them (not in the Euclideanized space)., Comment: v4: version amended according to a corrigendum (Class. Quantum Grav. 36 229501) concerning the derivation (not the end result) of equation (33). arXiv admin note: substantial text overlap with arXiv:1803.05726

In this article, we present experimental and numerical techniques to investigate the transfer, transport, and reaction of a chemical species in the vicinity of rising bubbles. In the experiment, single oxygen bubbles of diameter d b = 0.55 . . . 0.85 mm are released into a measurement cell filled with tap water. The oxygen dissolves and reacts with sulfite to sulfate. Laser-induced fluorescence is used to visualize the oxygen concentration in the bubble wake from which the global mass transfer coefficient can be calculated. The ruthenium-based fluorescent dye seems to be surface active, such that the rise velocity is reduced by up to 50 % compared to the experiment without fluorescent dye and a recirculation zone forms in the bubble wake. To access the local mass transfer at the interface, we perform complementary numerical simulations. Since the fluorescence tracer is essential for the experimental method, the effect of surface contamination is also considered in the simulation. We employ several improvements in the experimental and numerical procedures which allow for a quantitative comparison (locally and globally). Rise velocity and mass transfer coefficient agree within a few percents between experiment, simulation and literature results. Because the fluorescence tracer is frequently used in mass transfer experiments, we discuss its potential surface activity., Comment: 26 pages, 22 figures

The effects on Raychaudhuri's equation of an intrinsically-discrete or particle nature of spacetime are investigated. This is done through the consideration of null congruences emerging from, or converging to, a generic point of spacetime, i.e. in geometric circumstances somehow prototypical of singularity issues. We do this from an effective point of view, that is through a (continuous) description of spacetime modified to embody the existence of an intrinsic discreteness on the small scale, this adding to previous results for non-null congruences. Various expressions for the effective rate of change of expansion are derived. They in particular provide finite values for the limiting effective expansion and its rate of variation when approaching the focal point. Further, this results in a non-vanishing of the limiting cross-sectional area itself of the congruence., Comment: 7 pages; v2: some comparisons with other approaches added

Recently, a proposal has been made to figure out the expected discrete nature of spacetime at the smallest scales in terms of atoms of spacetime, capturing their effects through a scalar $\rho$, function of the point $P$ and the vector $v^a$ at $P$, expressing their density. This has been done in the Euclideanized space one obtains through analytic continuation from Lorentzian sector at $P$. $\rho$ is defined in terms of a peculiar `effective' metric $q_{ab}$, also recently introduced, which stems from a careful request that $q_{ab}$ coincides with $g_{ab}$ at large (space/time) distances, but gives finite distance in the coincidence limit. This work reports on an attempt to introduce a definition of $\rho$ directly in the Lorentz sector. This turns out to be not a so trivial task, essentially because of the null case, i.e. when $v^a$ is null, as in this case we lack even a concept of $q_{ab}$. A notion for $q_{ab}$ in the null case is here proposed and an expression for it is derived. In terms of it, an expression for $\rho$ can be derived, which turns out to coincide with what obtained from analytic continuation. This, joined with the consideration of timelike/spacelike cases, potentially completes a description of $q_{ab}$ and $\rho$ within Lorentz spacetimes., Comment: 11 pages; arXiv admin note: partial overlap with arXiv:1511.08665

This paper presents novel insights about the influence of soluble surfactants on bubble flows obtained by Direct Numerical Simulation (DNS). Surfactants are amphiphilic compounds which accumulate at fluid interfaces and significantly modify the respective interfacial properties, influencing also the overall dynamics of the flow. With the aid of DNS local quantities like the surfactant distribution on the bubble surface can be accessed for a better understanding of the physical phenomena occurring close to the interface. The core part of the physical model consists in the description of the surfactant transport in the bulk and on the deformable interface. The solution procedure is based on an Arbitrary Lagrangian-Eulerian (ALE) Interface-Tracking method. The existing methodology was enhanced to describe a wider range of physical phenomena. A subgrid-scale (SGS) model is employed in the cases where a fully resolved DNS for the species transport is not feasible due to high mesh resolution requirements and, therefore, high computational costs. After an exhaustive validation of the latest numerical developments, the DNS of single rising bubbles in contaminated solutions is compared to experimental results. The full velocity transients of the rising bubbles, especially the contaminated ones, are correctly reproduced by the DNS. The simulation results are then studied to gain a better understanding of the local bubble dynamics under the effect of soluble surfactant. One of the main insights is that the quasi-steady state of the rise velocity is reached without ad- and desorption being necessarily in local equilibrium.

A classical problem in fluid mechanics is the motion of an axisymmetric vortex sheet evolving under the action of surface tension, surrounded by an inviscid fluid. Lagrangian descriptions of these dynamics are well-known, involving complex nonlocal expressions for the radial and longitudinal velocities in terms of elliptic integrals. Here we use these prior results to arrive at a remarkably compact and exact Eulerian evolution equation for the sheet radius $r(z,t)$ in an explicit flux form associated with the conservation of enclosed volume. The flux appears as an integral involving the pairwise mutual induction formula for vortex loop pairs first derived by Helmholtz and Maxwell. We show how the well-known linear stability results for cylindrical vortex sheets in the presence of surface tension and streaming flows [A.M. Sterling and C.A. Sleicher, $J.~Fluid~Mech.$ ${\bf 68}$, 477 (1975)] can be obtained directly from this formulation. Furthermore, the inviscid limit of the empirical model of Eggers and Dupont [$J.~Fluid~Mech.$ $\textbf{262}$ 205 (1994); $SIAM~J.~Appl.~Math.$ ${\bf 60}$, 1997 (2000)], which has served as the basis for understanding singularity formation in droplet pinchoff, is derived within the present formalism as the leading order term in an asymptotic analysis for long slender axisymmetric vortex sheets, and should provide the starting point for a rigorous analysis of singularity formation., Comment: 12 pages, 2 figures