Collapse Threshold Research Articles

Self-Bound Quantum Droplets of Atomic Mixtures in Free Space.

Self-bound quantum droplets are a newly discovered phase in the context of ultracold atoms. In this Letter, we report their experimental realization following the original proposal by Petrov [Phys. Rev. Lett. 115, 155302 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.155302], using an attractive bosonic mixture. In this system, spherical droplets form due to the balance of competing attractive and repulsive forces, provided by the mean-field energy close to the collapse threshold and the first-order correction due to quantum fluctuations. Thanks to an optical levitating potential with negligible residual confinement, we observe self-bound droplets in free space, and we characterize the conditions for their formation as well as their size and composition. This work sets the stage for future studies on quantum droplets, from the measurement of their peculiar excitation spectrum to the exploration of their superfluid nature.

Global warming transforms coral reef assemblages.

Global warming is rapidly emerging as a universal threat to ecological integrity and function, highlighting the urgent need for a better understanding of the impact of heat exposure on the resilience of ecosystems and the people who depend on them 1 . Here we show that in the aftermath of the record-breaking marine heatwave on the Great Barrier Reef in 2016 2 , corals began to die immediately on reefs where the accumulated heat exposure exceeded a critical threshold of degree heating weeks, which was 3-4 °C-weeks. After eight months, an exposure of 6 °C-weeks or more drove an unprecedented, regional-scale shift in the composition of coral assemblages, reflecting markedly divergent responses to heat stress by different taxa. Fast-growing staghorn and tabular corals suffered a catastrophic die-off, transforming the three-dimensionality and ecological functioning of 29% of the 3,863 reefs comprising the world's largest coral reef system. Our study bridges the gap between the theory and practice of assessing the risk of ecosystem collapse, under the emerging framework for the International Union for Conservation of Nature (IUCN) Red List of Ecosystems 3 , by rigorously defining both the initial and collapsed states, identifying the major driver of change, and establishing quantitative collapse thresholds. The increasing prevalence of post-bleaching mass mortality of corals represents a radical shift in the disturbance regimes of tropical reefs, both adding to and far exceeding the influence of recurrent cyclones and other local pulse events, presenting a fundamental challenge to the long-term future of these iconic ecosystems.

Improved procedure for determining the ductility of buildings under seismic loads

Displacement ductility is a parameter that characterizes the seismic response of structures. Moreover, displacement ductility can be used in order to determine whether a structural design, performed according to a specific seismic code or not, may achieve the main goal of the seismic design: to develop energy dissipation in a stable manner. Determination of displacement ductility is not an easy task, because the structural response usually does not show a clear location of the points that define yield and ultimate displacements. In this paper, some of the main procedures for ductility displacement are revised and compared, and then improvements are performed to such procedures in order to compute the displacement ductility. A new procedure is then introduced, leading to determine the ultimate displacement using the seismic collapse threshold and the yield displacement, achieving the balance of dissipated energy. The procedure has been used to calculate displacement ductility of reinforced concrete framed buildings.

Tidal shear and the consistency of microscopic Lagrangian halo approaches

We delineate the conditions under which the consistency relation for the non-Gaussian bias and the universality of the halo mass function hold in the context of microscopic Lagrangian descriptions of halos. The former is valid provided that the collapse barrier depends only on the physical fields (instead of fields normalized by their variance for example) and explicitly includes the effect of all physical fields such as the tidal shear. The latter holds provided that the response of the halo number density to a long-wavelength density fluctuation is equivalent to the response induced by shifting the spherical collapse threshold. Our results apply to any Lagrangian halo bias prescription. Effective “moving” barriers, which are ubiquitous in the literature, do not generally satisfy the consistency relation. Microscopic barriers including the tidal shear lead to two additional, second-order Lagrangian bias parameters which ensure that the consistency relation is satisfied. We provide analytic expressions for them.

Massive collapse of two glaciers in western Tibet in 2016 after surge-like instability

Surges and glacier avalanches are expressions of glacier instability, and among the most dramatic phenomena in the mountain cryosphere. Until now, the catastrophic collapse of a glacier, combining the large volume of surges and mobility of ice avalanches, has been reported only for the 2002 130 × 106 m3 detachment of Kolka Glacier (Caucasus Mountains), which has been considered a globally singular event. Here, we report on the similar detachment of the entire lower parts of two adjacent glaciers in western Tibet in July and September 2016, leading to an unprecedented pair of giant low-angle ice avalanches with volumes of 68 ± 2 × 106 m3 and 83 ± 2 × 106 m3. On the basis of satellite remote sensing, numerical modelling and field investigations, we find that the twin collapses were caused by climate- and weather-driven external forcing, acting on specific polythermal and soft-bed glacier properties. These factors converged to produce surge-like enhancement of driving stresses and massively reduced basal friction connected to subglacial water and fine-grained bed lithology, to eventually exceed collapse thresholds in resisting forces of the tongues frozen to their bed. Our findings show that large catastrophic instabilities of low-angle glaciers can happen under rare circumstances without historical precedent.

Developing a standardized definition of ecosystem collapse for risk assessment

The International Union for Conservation of Nature (IUCN) Red List of Ecosystems is a powerful tool for classifying threatened ecosystems, informing ecosystem management, and assessing the risk of ecosystem collapse (that is, the endpoint of ecosystem degradation). These risk assessments require explicit definitions of ecosystem collapse, which are currently challenging to implement. To bridge the gap between theory and practice, we systematically review evidence for ecosystem collapses reported in two contrasting biomes – marine pelagic ecosystems and terrestrial forests. Most studies define states of ecosystem collapse quantitatively, but few studies adequately describe initial ecosystem states or ecological transitions leading to collapse. On the basis of our review, we offer four recommendations for defining ecosystem collapse in risk assessments: (1) qualitatively defining initial and collapsed states, (2) describing collapse and recovery transitions, (3) identifying and selecting indicators of collapse, and (4) setting quantitative collapse thresholds.

Influence of temperature fluctuations on equilibrium ice sheet volume

Abstract. Forecasting the future sea level relies on accurate modeling of the response of the Greenland and Antarctic ice sheets to changing temperatures. The surface mass balance (SMB) of the Greenland Ice Sheet (GrIS) has a nonlinear response to warming. Cold and warm anomalies of equal size do not cancel out and it is therefore important to consider the effect of interannual fluctuations in temperature. We find that the steady-state volume of an ice sheet is biased toward larger size if interannual temperature fluctuations are not taken into account in numerical modeling of the ice sheet. We illustrate this in a simple ice sheet model and find that the equilibrium ice volume is approximately 1 m SLE (meters sea level equivalent) smaller when the simple model is forced with fluctuating temperatures as opposed to a stable climate. It is therefore important to consider the effect of interannual temperature fluctuations when designing long experiments such as paleo-spin-ups. We show how the magnitude of the potential bias can be quantified statistically. For recent simulations of the Greenland Ice Sheet, we estimate the bias to be 30 Gt yr−1 (24–59 Gt yr−1, 95 % credibility) for a warming of 3 °C above preindustrial values, or 13 % (10–25, 95 % credibility) of the present-day rate of ice loss. Models of the Greenland Ice Sheet show a collapse threshold beyond which the ice sheet becomes unsustainable. The proximity of the threshold will be underestimated if temperature fluctuations are not taken into account. We estimate the bias to be 0.12 °C (0.10–0.18 °C, 95 % credibility) for a recent estimate of the threshold. In light of our findings it is important to gauge the extent to which this increased variability will influence the mass balance of the ice sheets.

Force loading explains spatial sensing of ligands by cells.

Cells can sense the density and distribution of extracellular matrix (ECM) molecules by means of individual integrin proteins and larger, integrin-containing adhesion complexes within the cell membrane. This spatial sensing drives cellular activity in a variety of normal and pathological contexts. Previous studies of cells on rigid glass surfaces have shown that spatial sensing of ECM ligands takes place at the nanometre scale, with integrin clustering and subsequent formation of focal adhesions impaired when single integrin-ligand bonds are separated by more than a few tens of nanometres. It has thus been suggested that a crosslinking 'adaptor' protein of this size might connect integrins to the actin cytoskeleton, acting as a molecular ruler that senses ligand spacing directly. Here, we develop gels whose rigidity and nanometre-scale distribution of ECM ligands can be controlled and altered. We find that increasing the spacing between ligands promotes the growth of focal adhesions on low-rigidity substrates, but leads to adhesion collapse on more-rigid substrates. Furthermore, disordering the ligand distribution drastically increases adhesion growth, but reduces the rigidity threshold for adhesion collapse. The growth and collapse of focal adhesions are mirrored by, respectively, the nuclear or cytosolic localization of the transcriptional regulator protein YAP. We explain these findings not through direct sensing of ligand spacing, but by using an expanded computational molecular-clutch model, in which individual integrin-ECM bonds-the molecular clutches-respond to force loading by recruiting extra integrins, up to a maximum value. This generates more clutches, redistributing the overall force among them, and reducing the force loading per clutch. At high rigidity and high ligand spacing, maximum recruitment is reached, preventing further force redistribution and leading to adhesion collapse. Measurements of cellular traction forces and actin flow speeds support our model. Our results provide a general framework for how cells sense spatial and physical information at the nanoscale, precisely tuning the range of conditions at which they form adhesions and activate transcriptional regulation.

Clustering dark energy and halo abundances

Within the standard paradigm, dark energy is taken as a homogeneous fluid that drives the accelerated expansion of the universe and does not contribute to the mass of collapsed objects such as galaxies and galaxy clusters. The abundance of galaxy clusters—measured through a variety of channels—has been extensively used to constrain the normalization of the power spectrum: it is an important probe as it allows us to test if the standard ΛCDM model can indeed accurately describe the evolution of structures across billions of years. It is then quite significant that the Planck satellite has detected, via the Sunyaev-Zel'dovich effect, less clusters than expected according to the primary CMB anisotropies. One of the simplest generalizations that could reconcile these observations is to consider models in which dark energy is allowed to cluster, i.e., allowing its sound speed to vary. In this case, however, the standard methods to compute the abundance of galaxy clusters need to be adapted to account for the contributions of dark energy. In particular, we examine the case of clustering dark energy—a dark energy fluid with negligible sound speed—with a redshift-dependent equation of state. We carefully study how the halo mass function is modified in this scenario, highlighting corrections that have not been considered before in the literature. We address modifications in the growth function, collapse threshold, virialization densities and also changes in the comoving scale of collapse and mass function normalization. Our results show that clustering dark energy can impact halo abundances at the level of 10%–30%, depending on the halo mass, and that cluster counts are modified by about 30% at a redshift of unity.

Two-dimensional solitons and quantum droplets supported by competing self- and cross-interactions in spin-orbit-coupled condensates

We study two-dimensional (2D) matter-wave solitons in spinor Bose–Einstein condensates under the action of the spin–orbit coupling and opposite signs of the self- and cross-interactions. Stable 2D two-component solitons of the mixed-mode type are found if the cross-interaction between the components is attractive, while the self-interaction is repulsive in each component. Stable solitons of the semi-vortex type are formed in the opposite case, under the action of competing self-attraction and cross-repulsion. The solitons exist with the total norm taking values below a collapse threshold. Further, in the case of the repulsive self-interaction and inter-component attraction, stable 2D self-trapped modes, which may be considered as quantum droplets (QDs), are created if the beyond-mean-field Lee–Huang–Yang terms are added to the self-repulsion in the underlying system of coupled Gross–Pitaevskii equations. Stable QDs of the mixed-mode type, of a large size with an anisotropic density profile, exist with arbitrarily large values of the norm, as the Lee–Huang–Yang terms eliminate the collapse. The effect of the spin–orbit coupling term on characteristics of the QDs is systematically studied. We also address the existence and stability of QDs in the case of SOC with mixed Rashba and Dresselhaus terms, which makes the density profile of the QD more isotropic. Thus, QDs in the spin-orbit-coupled binary Bose–Einstein condensate are for the first time studied in the present work.

Cold dark energy constraints from the abundance of galaxy clusters

We constrain cold dark energy of negligible sound speed using galaxy cluster abundance observations. In contrast to standard quasi-homogeneous dark energy, negligible sound speed implies clustering of the dark energy fluid at all scales, allowing us to measure the effects of dark energy perturbations at cluster scales. We compare those models and set the stage for using non-linear information from semi-analytical modelling in cluster growth data analyses. For this, we recalibrate the halo mass function with non-linear characteristic quantities, the spherical collapse threshold and virial overdensity, that account for model and redshift dependent behaviours, as well as an additional mass contribution for cold dark energy. We present the first constraints from this cold dark matter plus cold dark energy mass function using our cluster abundance likelihood, which self-consistently accounts for selection effects, covariances and systematic uncertainties. We combine cluster growth data with CMB, SNe Ia and BAO data, and find a shift between cold versus quasi-homogeneous dark energy of up to $1\sigma$. We make a Fisher matrix forecast of constraints attainable with cluster growth data from the on-going Dark Energy Survey (DES). For DES, we predict $\sim$50$\%$ tighter constraints on $\left(\Omega_\mathrm{m},w \right)$ for cold dark energy versus $w$CDM models, with the same free parameters. Overall, we show that cluster abundance analyses are sensitive to cold dark energy, an alternative, viable model that should be routinely investigated alongside the standard dark energy scenario.

A sharp threshold for collapse of the random triangular group

The random triangular group \Gamma (n,p) is the group given by a random group presentation with n generators in which every relator of length three is present independently with probability p . We show that in the evolution of € \Gamma (n,p) the property of collapsing to the trivial group admits a very sharp threshold.

Gas vesicles: Acoustic biomolecules for ultrasound imaging

Expanding the capabilities of ultrasound for biological and diagnostic imaging requires the development of contrast agents linked to cellular and molecular processes in vivo. In optical imaging this is commonly accomplished using fluorescent biomolecules such as the green fluorescent protein. Analogously, we recently introduced gas vesicles (GVs) as the first acoustic biomolecules for ultrasound. GVs are physically stable gas-filled protein nanostructures (~250 nm) naturally expressed in aquatic photosynthetic microbes as a means to regulate buoyancy. Purified GVs produce robust ultrasound contrast across a range of frequencies at picomolar concentrations, exhibit nonlinear scattering to enable enhanced detection versus background in vivo, and have species-dependent thresholds for pressure-induced collapse to enable multiplexed imaging. Here, I will present our recent progress on understanding the biophysical and acoustic properties of these biomolecular contrast agents, engineering their mechanics and targeting at the genetic level, developing ultrasound pulse sequences to enhance their detection in vivo and expressing them heterologously as acoustic reporter genes. 1. Shapiro, M.G. et al. Nat. Nanotechnol. 9, 311-316 (2014). 2. Cherin, M. et al. U.M.B. (In press). 3. Lakshmanan, A. et al. ACS Nano 10, 7314-7322 (2016). 4. Maresca, D. et al. In revision. 5. Bourdeau, R.W. et al. Submitted. More information at http://shapirolab.caltech.edu.

Critical collapse of a rotating scalar field in 2+1 dimensions

We carry out numerical simulations of the collapse of a complex rotating scalar field of the form $\Psi(t,r,\theta)=e^{im\theta}\Phi(t,r)$, giving rise to an axisymmetric metric, in 2+1 spacetime dimensions with cosmological constant $\Lambda<0$, for $m=0,1,2$, for four 1-parameter families of initial data. We look for the familiar scaling of black hole mass and maximal Ricci curvature as a power of $|p-p_*|$, where $p$ is the amplitude of our initial data and $p_*$ some threshold. We find evidence of Ricci scaling for all families, and tentative evidence of mass scaling for most families, but the case $m>0$ is very different from the case $m=0$ we have considered before: the thresholds for mass scaling and Ricci scaling are significantly different (for the same family), scaling stops well above the scale set by $\Lambda$, and the exponents depend strongly on the family. Hence, in contrast to the $m=0$ case, and to many other self-gravitating systems, there is only weak evidence for the collapse threshold being controlled by a self-similar critical solution and no evidence for it being universal.

Delayed collapses of Bose-Einstein condensates in relation to anti-de Sitter gravity.

We numerically investigate spherically symmetric collapses in the Gross-Pitaevskii equation with attractive nonlinearity in a harmonic potential. Even below threshold for direct collapse, the wave function bounces off from the origin and may eventually become singular after a number of oscillations in the trapping potential. This is reminiscent of the evolution of Einstein gravity sourced by a scalar field in anti de Sitter space where collapse corresponds to black-hole formation. We carefully examine the long time evolution of the wave function for continuous families of initial states in order to sharpen out this qualitative coincidence which may bring new insights in both directions. On the one hand, we comment on possible implications for the so-called Bosenova collapses in cold atom Bose-Einstein condensates. On the other hand, Gross-Pitaevskii provides a toy model to study the relevance of either the resonance conditions or the nonlinearity for the problem of anti de Sitter instability.

Creating a safe operating space for wetlands in a changing climate

Many of the world's wetlands may be profoundly affected by climate change over the coming decades. Although wetland managers may have little control over the causes of climate change, they can help to counteract its effects through local measures. This is because direct anthropogenic impacts, such as water extraction and nutrient loading, work in concert with climate change to damage wetlands. Control of these local stressors may therefore ameliorate undesired effects of climate change, such as a shift towards dominance by invasive floating plants, increasingly frequent cyanobacteria blooms, or extinction of key species. Using the iconic Doñana wetlands in Spain as a case study, we illustrate how the concept of creating a “safe operating space” may be implemented to better ensure that ecosystems do not surpass thresholds for collapse during an era of global change.

Harmonically trapped attractive and repulsive spin–orbit and Rabi coupled Bose–Einstein condensates

Numerically we investigate the ground state of effective one-dimensional spin–orbit (SO) and Rabi coupled two pseudo-spinor Bose–Einstein condensates (BECs) under the effect of harmonic traps. For both signs of the interaction, density profiles of SO and Rabi coupled BECs in harmonic potentials, which simulate a real experimental situation are obtained. The harmonic trap causes a strong reduction of the multi-peak nature of the condensate and it increases its density. For repulsive interactions, the increase of SO coupling results in an uncompressed less dense condensate and with increased multi-peak nature of the density. The increase of Rabi coupling leads to a density increase with an almost constant number of multi-peaks. For both signs of the interaction and negative values of Rabi coupling, the condensate develops a notch in the central point and it seems to a dark-in-bright soliton. In the case of the attractive nonlinearity, an interesting result is the increase of the collapse threshold under the action of the SO and Rabi couplings.

Einstein-Vlasov system in spherical symmetry: Reduction of the equations of motion and classification of single-shell static solutions in the limit of massless particles

We express the Einstein-Vlasov system in spherical symmetry in terms of a dimensionless momentum variable $z$ (radial over angular momentum). This regularises the limit of massless particles, and in that limit allows us to obtain a reduced system in independent variables $(t,r,z)$ only. Similarly, in this limit the Vlasov density function $f$ for static solutions depends on a single variable $Q$ (energy over angular momentum). This reduction allows us to show that any given static metric which has vanishing Ricci scalar, is vacuum at the centre and for $r>3M$ and obeys certain energy conditions uniquely determines a consistent $f=\bar k(Q)$ (in closed form). Vice versa, any $\bar k(Q)$ within a certain class uniquely determines a static metric (as the solution of a system of two first-order quasilinear ODEs). Hence the space of static spherically symmetric solutions of Einstein-Vlasov is locally a space of functions of one variable. For a simple 2-parameter family of functions $\bar k(Q)$, we construct the corresponding static spherically symmetric solutions, finding that their compactness is in the interval $0.7\lesssim \rm max_r(2M/r)\le 8/9$. This class of static solutions includes one that agrees with the approximately universal type-I critical solution recently found by Akbarian and Choptuik (AC) in numerical time evolutions. We speculate on what singles it out as the critical solution found by fine-tuning generic data to the collapse threshold, given that AC also found that {\em all} static solutions are one-parameter unstable and sit on the threshold of collapse.

Production of strongly bound K39 bright solitons

We report on the production of 39 K matter-wave bright solitons, i.e., 1D matter-waves that propagate without dispersion thanks to attractive interactions. The volume of the soliton is studied as a function of the scattering length through three-body losses, revealing peak densities as high as $\sim 5 \times 10^{20} m^{-3}$. Our solitons, close to the collapse threshold, are strongly bound and will find applications in fundamental physics and atom interferometry.

Early warning signals of regime shifts in coupled human–environment systems

In complex systems, a critical transition is a shift in a system’s dynamical regime from its current state to a strongly contrasting state as external conditions move beyond a tipping point. These transitions are often preceded by characteristic early warning signals such as increased system variability. However, early warning signals in complex, coupled human–environment systems (HESs) remain little studied. Here, we compare critical transitions and their early warning signals in a coupled HES model to an equivalent environment model uncoupled from the human system. We parameterize the HES model, using social and ecological data from old-growth forests in Oregon. We find that the coupled HES exhibits a richer variety of dynamics and regime shifts than the uncoupled environment system. Moreover, the early warning signals in the coupled HES can be ambiguous, heralding either an era of ecosystem conservationism or collapse of both forest ecosystems and conservationism. The presence of human feedback in the coupled HES can also mitigate the early warning signal, making it more difficult to detect the oncoming regime shift. We furthermore show how the coupled HES can be “doomed to criticality”: Strategic human interactions cause the system to remain perpetually in the vicinity of a collapse threshold, as humans become complacent when the resource seems protected but respond rapidly when it is under immediate threat. We conclude that the opportunities, benefits, and challenges of modeling regime shifts and early warning signals in coupled HESs merit further research.