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  • 1. Agarwal, Sahil
    et al.
    Del Sordo, Fabio
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Yale University, USA.
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Yale University, USA; University of Oxford, UK.
    EXOPLANETARY DETECTION BY MULTIFRACTAL SPECTRAL ANALYSIS2017In: Astronomical Journal, ISSN 0004-6256, E-ISSN 1538-3881, Vol. 153, no 1, article id 12Article in journal (Refereed)
    Abstract [en]

    Owing to technological advances, the number of exoplanets discovered has risen dramatically in the last few years. However, when trying to observe Earth analogs, it is often difficult to test the veracity of detection. We have developed a new approach to the analysis of exoplanetary spectral observations based on temporal multifractality, which identifies timescales that characterize planetary orbital motion around the host star and those that arise from stellar features such as spots. Without fitting stellar models to spectral data, we show how the planetary signal can be robustly detected from noisy data using noise amplitude as a source of information. For observation of transiting planets, combining this method with simple geometry allows us to relate the timescales obtained to primary and secondary eclipse of the exoplanets. Making use of data obtained with ground-based and space-based observations we have tested our approach on HD 189733b. Moreover, we have investigated the use of this technique in measuring planetary orbital motion via Doppler shift detection. Finally, we have analyzed synthetic spectra obtained using the SOAP 2.0 tool, which simulates a stellar spectrum and the influence of the presence of a planet or a spot on that spectrum over one orbital period. We have demonstrated that, so long as the signal-to-noise-ratio >= 75, our approach reconstructs the planetary orbital period, as well as the rotation period of a spot on the stellar surface.

  • 2. Agarwal, Sahil
    et al.
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Yale University, USA; University of Oxford, UK.
    Fluctuations in Arctic sea-ice extent: comparing observations and climate models2018In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 376, no 2129, article id 20170332Article in journal (Refereed)
    Abstract [en]

    The fluctuation statistics of the observed sea-ice extent during the satellite era are compared with model output from CMIP5 models using a multifractal time series method. The two robust features of the observations are that on annual to biannual time scales the ice extent exhibits white noise structure, and there is a decadal scale trend associated with the decay of the ice cover. It is shown that (i) there is a large inter-model variability in the time scales extracted from the models, (ii) none of the models exhibits the decadal time scales found in the satellite observations, (iii) five of the 21 models examined exhibit the observed white noise structure, and (iv) the multi-model ensemble mean exhibits neither the observed white noise structure nor the observed decadal trend. It is proposed that the observed fluctuation statistics produced by this method serve as an appropriate test bed for modelling studies. This article is part of the theme issue 'Modelling of sea-ice phenomena'.

  • 3. Agarwal, Sahil
    et al.
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Yale University, USA; University of Oxford, UK.
    Maximal stochastic transport in the Lorenz equations2016In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 380, no 1-2, p. 142-146Article in journal (Refereed)
    Abstract [en]

    We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh-Benard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected, the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering [1], but their variation with noise amplitude exhibits interesting behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity depends on the number of realizations in the ensemble; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits, the degree of which depends on the degree to which the ensemble represents the ergodic set. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations and the numerical convergence of the noise correlations. The numerical convergence of both the ensemble and time averages of the noise correlations is sufficiently slow that it is the limiting aspect of the realization of these bounds. Finally, we note that the full solutions of the stochastic equations demonstrate that the effect of noise is equivalent to the effect of chaos.

  • 4. Agarwal, Sahil
    et al.
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Yale University, USA; University of Oxford, United Kingdom.
    The Statistical Properties of Sea Ice Velocity Fields2017In: Journal of Climate, ISSN 0894-8755, E-ISSN 1520-0442, Vol. 30, no 13, p. 4873-4881Article in journal (Refereed)
    Abstract [en]

    By arguing that the surface pressure field over the Arctic Ocean can be treated as an isotropic, stationary, homogeneous, Gaussian random field, Thorndike estimated a number of covariance functions from two years of data (1979 and 1980). Given the active interest in changes of general circulation quantities and indices in the polar regions during the recent few decades, the spatial correlations in sea ice velocity fields are of particular interest. It is thus natural to ask, How persistent are these correlations?'' To this end, a multifractal stochastic treatment is developed to analyze observed Arctic sea ice velocity fields from satellites and buoys for the period 1978-2015. Since it was previously found that the Arctic equivalent ice extent (EIE) has a white noise structure on annual to biannual time scales, the connection between EIE and ice motion is assessed. The long-term stationarity of the spatial correlation structure of the velocity fields and the robustness of their white noise structure on multiple time scales is demonstrated; these factors (i) combine to explain the white noise characteristics of the EIE on annual to biannual time scales and (ii) explain why the fluctuations in the ice velocity are proportional to fluctuations in the geostrophic winds on time scales of days to months. Moreover, it is shown that the statistical structure of these two quantities is commensurate from days to years, which may be related to the increasing prevalence of free drift in the ice pack.

  • 5. Bar-Dolev, Maya
    et al.
    Celik, Yeliz
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Davies, Peter L.
    Braslavsky, Ido
    New insights into ice growth and melting modifications by antifreeze proteins2012In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 9, no 77, p. 3249-3259Article in journal (Refereed)
    Abstract [en]

    Antifreeze proteins (AFPs) evolved in many organisms, allowing them to survive in cold climates by controlling ice crystal growth. The specific interactions of AFPs with ice determine their potential applications in agriculture, food preservation and medicine. AFPs control the shapes of ice crystals in a manner characteristic of the particular AFP type. Moderately active AFPs cause the formation of elongated bipyramidal crystals, often with seemingly defined facets, while hyperactive AFPs produce more varied crystal shapes. These different morphologies are generally considered to be growth shapes. In a series of bright light and fluorescent microscopy observations of ice crystals in solutions containing different AFPs, we show that crystal shaping also occurs during melting. In particular, the characteristic ice shapes observed in solutions of most hyperactive AFPs are formed during melting. We relate these findings to the affinities of the hyperactive AFPs for the basal plane of ice. Our results demonstrate the relation between basal plane affinity and hyperactivity and show a clear difference in the ice-shaping mechanisms of most moderate and hyperactive AFPs. This study provides key aspects associated with the identification of hyperactive AFPs.

  • 6. Lee, Alpha A.
    et al.
    Vella, Dominic
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Oxford, UK; Yale University, USA .
    Fluctuation spectra and force generation in nonequilibrium systems2017In: Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, E-ISSN 1091-6490, Vol. 114, no 35, p. 9255-9260Article in journal (Refereed)
    Abstract [en]

    Many biological systems are appropriately viewed as passive inclusions immersed in an active bath: from proteins on active membranes to microscopic swimmers confined by boundaries. The nonequilibrium forces exerted by the active bath on the inclusions or boundaries often regulate function, and such forces may also be exploited in artificial active materials. Nonetheless, the general phenomenology of these active forces remains elusive. We show that the fluctuation spectrum of the active medium, the partitioning of energy as a function of wavenumber, controls the phenomenology of force generation. We find that, for a narrow, unimodal spectrum, the force exerted by a nonequilibrium system on two embedded walls depends on the width and the position of the peak in the fluctuation spectrum, and oscillates between repulsion and attraction as a function of wall separation. We examine two apparently disparate examples: the Maritime Casimir effect and recent simulations of active Brownian particles. A key implication of our work is that important nonequilibrium interactions are encoded within the fluctuation spectrum. In this sense, the noise becomes the signal.

  • 7. MacMinn, Christopher W.
    et al.
    Dufresne, Eric R.
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Yale University, USA; University of Oxford, United Kingdom.
    Large Deformations of a Soft Porous Material2016In: Physical Review Applied, ISSN 2331-7019, Vol. 5, no 4, article id 044020Article in journal (Refereed)
    Abstract [en]

    Compressing a porous material will decrease the volume of the pore space, driving fluid out. Similarly, injecting fluid into a porous material can expand the pore space, distorting the solid skeleton. This poromechanical coupling has applications ranging from cell and tissue mechanics to geomechanics and hydrogeology. The classical theory of linear poroelasticity captures this coupling by combining Darcy's law with Terzaghi's effective stress and linear elasticity in a linearized kinematic framework. Linear poroelasticity is a good model for very small deformations, but it becomes increasingly inappropriate for moderate to large deformations, which are common in the context of phenomena such as swelling and damage, and for soft materials such as gels and tissues. The well-known theory of large-deformation poroelasticity combines Darcy's law with Terzaghi's effective stress and nonlinear elasticity in a rigorous kinematic framework. This theory has been used extensively in biomechanics to model large elastic deformations in soft tissues and in geomechanics to model large elastoplastic deformations in soils. Here, we first provide an overview and discussion of this theory with an emphasis on the physics of poromechanical coupling. We present the large-deformation theory in an Eulerian framework to minimize the mathematical complexity, and we show how this nonlinear theory simplifies to linear poroelasticity under the assumption of small strain. We then compare the predictions of linear poroelasticity with those of large-deformation poroelasticity in the context of two uniaxial model problems: fluid outflow driven by an applied mechanical load (the consolidation problem) and compression driven by a steady fluid throughflow. We explore the steady and dynamical errors associated with the linear model in both situations, as well as the impact of introducing a deformation-dependent permeability. We show that the error in linear poroelasticity is due primarily to kinematic nonlinearity and that this error (i) plays a surprisingly important role in the dynamics of the deformation and (ii) is amplified by nonlinear constitutive behavior, such as deformation-dependent permeability.

  • 8.
    Mancarella, Francesco
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Style, Robert W.
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Yale University, USA.
    Interfacial tension and a three-phase generalized self-consistent theory of non-dilute soft composite solids2016In: Soft Matter, ISSN 1744-683X, E-ISSN 1744-6848, Vol. 12, no 10, p. 2744-2750Article in journal (Refereed)
    Abstract [en]

    In the dilute limit Eshelby's inclusion theory captures the behavior of a wide range of systems and properties. However, because Eshelby's approach neglects interfacial stress, it breaks down in soft materials as the inclusion size approaches the elastocapillarity length L equivalent to gamma/E. Here, we use a three-phase generalized self-consistent method to calculate the elastic moduli of composites comprised of an isotropic, linear-elastic compliant solid hosting a spatially random monodisperse distribution of spherical liquid droplets. As opposed to similar approaches, we explicitly capture the liquid-solid interfacial stress when it is treated as an isotropic, strain-independent surface tension. Within this framework, the composite stiffness depends solely on the ratio of the elastocapillarity length L to the inclusion radius R. Independent of inclusion volume fraction, we find that the composite is stiffened by the inclusions whenever R < 3L/2. Over the same range of parameters, we compare our results with alternative approaches (dilute and Mori-Tanaka theories that include surface tension). Our framework can be easily extended to calculate the composite properties of more general soft materials where surface tension plays a role.

  • 9.
    Mancarella, Francesco
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Style, Robert W.
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Oxford, UK; Yale University, USA.
    Surface tension and the Mori-Tanaka theory of non-dilute soft composite solids2016In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 472, no 2189, article id 20150853Article in journal (Refereed)
    Abstract [en]

    Eshelby's theory is the foundation of composite mechanics, allowing calculation of the effective elastic moduli of composites from a knowledge of their microstructure. However, it ignores interfacial stress and only applies to very dilute composites-i.e. where any inclusions are widely spaced apart. Here, within the framework of the Mori-Tanaka multiphase approximation scheme, we extend Eshelby's theory to treat a composite with interfacial stress in the non-dilute limit. In particular, we calculate the elastic moduli of composites comprised of a compliant, elastic solid hosting a non-dilute distribution of identical liquid droplets. The composite stiffness depends strongly on the ratio of the droplet size, R, to an elastocapillary lengthscale, L. Interfacial tension substantially impacts the effective elastic moduli of the composite when R/L less than or similar to 100. When R < 3L/2 (R = 3L/2) liquid inclusions stiffen (cloak the far-field signature of) the solid.

  • 10.
    Mancarella, Francesco
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Yale University, USA; University of Oxford, UK.
    Surface tension and a self-consistent theory of soft composite solids with elastic inclusions2017In: Soft Matter, ISSN 1744-683X, E-ISSN 1744-6848, Vol. 13, no 5, p. 945-955Article in journal (Refereed)
    Abstract [en]

    The importance of surface tension effects is being recognized in the context of soft composite solids, where they are found to significantly affect the mechanical properties, such as the elastic response to an external stress. It has recently been discovered that Eshelby's inclusion theory breaks down when the inclusion size approaches the elastocapillary length L = gamma/E, where gamma is the inclusion/host surface tension and E is the host Young's modulus. Extending our recent results for liquid inclusions, here we model the elastic behavior of a non-dilute distribution of isotropic elastic spherical inclusions in a soft isotropic elastic matrix, subject to a prescribed infinitesimal far-field loading. Within our framework, the composite stiffness is uniquely determined by the elastocapillary length L, the spherical inclusion radius R, and the stiffness contrast parameter C, which is the ratio of the inclusion to the matrix stiffness. We compare the results with those from the case of liquid inclusions, and we derive an analytical expression for elastic cloaking of the composite by the inclusions. Remarkably, we find that the composite stiffness is influenced significantly by surface tension even for inclusions two orders of magnitude more stiff than the host matrix. Finally, we show how to simultaneously determine the surface tension and the inclusion stiffness using two independent constraints provided by global and local measurements.

  • 11.
    Moon, Woosok
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Agarwal, Sahil
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Yale University, USA; University of Oxford, United Kingdom.
    Intrinsic Pink-Noise Multidecadal Global Climate Dynamics Mode2018In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 121, no 10, article id 108701Article in journal (Refereed)
    Abstract [en]

    Understanding multidecadal variability is an essential goal of climate dynamics. For example, the recent phenomenon referred to as the global warming hiatus may reflect a coupling to an intrinsic, preindustrial, multidecadal variability process. Here, using a multifractal time-series method, we demonstrate that 42 data sets of 79 proxies with global coverage exhibit pink-noise characteristics on multidecadal timescales. To quantify the persistence of this behavior, we examine high-resolution ice core and speleothem data to find pink noise in both pre- and postindustrial periods. We examine the spatial structure with an empirical orthogonal function analysis of the monthly averaged surface temperature from 1901 to 2012. The first mode clearly shows the distribution of ocean heat flux sinks located in the eastern Pacific and the Southern Ocean and has pink-noise characteristics on a multidecadal timescale. We hypothesize that this pink-noise multidecadal spatial mode may resonate with externally driven greenhouse gas forcing, driving large-scale climate processes.

  • 12. Moon, Woosok
    et al.
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Yale University, USA; University of Oxford, United Kingdom.
    A Stochastic Dynamical Model of Arctic Sea Ice2017In: Journal of Climate, ISSN 0894-8755, E-ISSN 1520-0442, Vol. 30, no 13, p. 5119-5140Article in journal (Refereed)
    Abstract [en]

    The noise forcing underlying the variability in the Arctic ice cover has a wide range of principally unknown origins. For this reason, the analytical and numerical solutions of a stochastic Arctic sea ice model are analyzed with both additive and multiplicative noise over a wide range of external heat fluxes Delta F-0, corresponding to greenhouse gas forcing. The stochastic variability fundamentally influences the nature of the deterministic steady-state solutions corresponding to perennial and seasonal ice and ice-free states. Thus, the results are particularly relevant for the interpretation of the state of the system as the ice cover thins with Delta F-0, allowing a thorough examination of the differing effects of additive versusmultiplicative noise. In the perennial ice regime, the principal stochastic moments are calculated and compared to those determined from a stochastic perturbation theory described previously. As Delta F-0 increases, the competing contributions to the variability of the destabilizing sea ice-albedo feedback and the stabilizing longwave radiative loss are examined in detail. At the end of summer the variability of the stochastic paths shows a clear maximum, which is due to the combination of the increasing influence of the albedo feedback and an associated memory effect,'' in which fluctuations accumulate from early spring to late summer. This is counterbalanced by the stabilization of the ice cover resulting from the longwave loss of energy from the ice surface, which is enhanced during winter, thereby focusing the stochastic paths and decreasing the variability. Finally, common examples in stochastic dynamics with multiplicative noise are discussed wherein the choice of the stochastic calculus (Ito or Stratonovich) is not necessarily determinable a priori from observations alone, which is why both calculi are treated on equal footing herein.

  • 13. Moon, Woosok
    et al.
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Yale University, USA; University of Oxford, UK.
    A unified nonlinear stochastic time series analysis for climate science2017In: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 7, article id 44228Article in journal (Refereed)
    Abstract [en]

    Earth's orbit and axial tilt imprint a strong seasonal cycle on climatological data. Climate variability is typically viewed in terms of fluctuations in the seasonal cycle induced by higher frequency processes. We can interpret this as a competition between the orbitally enforced monthly stability and the fluctuations/noise induced by weather. Here we introduce a new time-series method that determines these contributions from monthly-averaged data. We find that the spatio-temporal distribution of the monthly stability and the magnitude of the noise reveal key fingerprints of several important climate phenomena, including the evolution of the Arctic sea ice cover, the El Nino Southern Oscillation (ENSO), the Atlantic Nino and the Indian Dipole Mode. In analogy with the classical destabilising influence of the ice-albedo feedback on summertime sea ice, we find that during some time interval of the season a destabilising process operates in all of these climate phenomena. The interaction between the destabilisation and the accumulation of noise, which we term the memory effect, underlies phase locking to the seasonal cycle and the statistical nature of seasonal predictability.

  • 14. O'Rourke, J. G.
    et al.
    Riggs, A. J. E.
    Guertler, C. A.
    Miller, P. W.
    Padhi, C. M.
    Popelka, M. M.
    Wells, A. J.
    West, A. C.
    Zhong, J. -Q
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Mushy-layer dynamics in micro and hyper gravity2012In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 24, no 10, p. 103305-Article in journal (Refereed)
    Abstract [en]

    We describe the results of experiments on mushy layers grown from aqueous ammonium chloride solution in normal, micro, and hyper gravity environments. In the fully developed chimney state, the chimney plume dynamics differ strikingly when conditions change from micro to hyper gravity. In microgravity, we find fully arrested plume motion and suppressed convection. As gravity exceeds Earth conditions, we observe a host of phenomena, ranging from arched plumes that undergo forced Rayleigh-Taylor instabilities to in-phase multiple plume oscillatory behavior. For the same initial solute concentrations and fixed boundary cooling temperatures, we find that, in runs of over two hours, the averaged effects of microgravity and hypergravity result in suppressed growth of the mushy layers, a phenomenon caused by a net enhancement of convective heat and solute transport from the liquid to the mushy layers. These behaviors are placed in the context of the theory of convecting mushy layers as studied under normal laboratory conditions.

  • 15.
    Pramanik, Satyajit
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Wettlaufer, John S.
    Yale University, USA; University of Oxford, UK.
    Confinement effects in premelting dynamics2017In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 96, no 5, article id 052801Article in journal (Refereed)
    Abstract [en]

    We examine the effects of confinement on the dynamics of premelted films driven by thermomolecular pressure gradients. Our approach is to modify a well-studied setting in which the thermomolecular pressure gradient is driven by a temperature gradient parallel to an interfacially premelted elastic wall. The modification treats the increase in viscosity associated with the thinning of films, studied in a wide variety of materials, using a power law and we examine the consequent evolution of the confining elastic wall. We treat (1) a range of interactions that are known to underlie interfacial premelting and (2) a constant temperature gradient wherein the thermomolecular pressure gradient is a constant. The difference between the cases with and without the proximity effect arises in the volume flux of premelted liquid. The proximity effect increases the viscosity as the film thickness decreases thereby requiring the thermomolecular pressure driven flux to be accommodated at higher temperatures where the premelted film thickness is the largest. Implications for experiment and observations of frost heave are discussed.

  • 16. Schollick, Julia M. H.
    et al.
    Style, Robert W.
    Curran, Arran
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Oxford, United Kingdom; Yale University, United States.
    Dufresne, Eric R.
    Warren, Patrick B.
    Velikov, Krassimir P.
    Dullens, Roel P. A.
    Aarts, Dirk G. A. L.
    Segregated Ice Growth in a Suspension of Colloidal Particles2016In: Journal of Physical Chemistry B, ISSN 1520-6106, E-ISSN 1520-5207, Vol. 120, no 16, p. 3941-3949Article in journal (Refereed)
    Abstract [en]

    We study the freezing of a dispersion of colloidal silica particles in water, focusing on the formation of segregated ice in the form of ice lenses. Local temperature measurements in combination with video microscopy give insight into the rich variety of factors that control ice lens formation. We observe the initiation of the lenses, their growth morphology, and their final thickness and spacing over a range of conditions, in particular the effect of the particle packing and the cooling rate. We find that increasing the particle density drastically reduces the thickness of lenses but has little effect on the lens spacing. Therefore, the fraction of segregated ice formed reduces. The effect of the cooling rate, which is the product of the temperature gradient and the pulling speed across the temperature gradient, depends on which parameter is varied. A larger temperature gradient causes ice lenses to be initiated more frequently, while a lower pulling speed allows for more time for ice lenses to grow: both increase the fraction of segregated ice. Surprisingly, we find that the growth rate of a lens does not depend on its undercooling. Finally, we have indications of pore ice in front of the warmest ice lens, which has important consequences for the interpretation of the measured trends. Our findings are relevant for ice segregation occurring in a wide range of situations, ranging from model lab experiments and theories to geological and industrial processes, like frost heave and frozen food production.

  • 17. Style, Robert W.
    et al.
    Boltyanskiy, Rostislav
    Che, Yonglu
    Wettlaufer, J. S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Yale Univ, New Haven, CT 06520 USA.
    Wilen, Larry A.
    Dufresne, Eric R.
    Universal Deformation of Soft Substrates Near a Contact Line and the Direct Measurement of Solid Surface Stresses2013In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 110, no 6, p. 066103-Article in journal (Refereed)
    Abstract [en]

    Droplets deform soft substrates near their contact lines. Using confocal microscopy, we measure the deformation of silicone gel substrates due to glycerol and fluorinated-oil droplets for a range of droplet radii and substrate thicknesses. For all droplets, the substrate deformation takes a universal shape close to the contact line that depends on liquid composition, but is independent of droplet size and substrate thickness. This shape is determined by a balance of interfacial tensions at the contact line and provides a novel method for direct determination of the surface stresses of soft substrates. Moreover, we measure the change in contact angle with droplet radius and show that Young's law fails for small droplets when their radii approach an elastocapillary length scale. For larger droplets the macroscopic contact angle is constant, consistent with Young's law. DOI: 10.1103/PhysRevLett.110.066103

  • 18. Style, Robert W.
    et al.
    Che, Yonglu
    Park, Su Ji
    Weon, Byung Mook
    Je, Jung Ho
    Hyland, Callen
    German, Guy K.
    Power, Michael P.
    Wilen, Larry A.
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Yale Univversity, USA.
    Dufresne, Eric R.
    Patterning droplets with durotaxis2013In: Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, E-ISSN 1091-6490, Vol. 110, no 31, p. 12541-12544Article in journal (Refereed)
    Abstract [en]

    Numerous cell types have shown a remarkable ability to detect and move along gradients in stiffness of an underlying substrate-a process known as durotaxis. The mechanisms underlying durotaxis are still unresolved, but generally believed to involve active sensing and locomotion. Here, we show that simple liquid droplets also undergo durotaxis. By modulating substrate stiffness, we obtain fine control of droplet position on soft, flat substrates. Unlike other control mechanisms, droplet durotaxis works without imposing chemical, thermal, electrical, or topographical gradients. We show that droplet durotaxis can be used to create large-scale droplet patterns and is potentially useful for many applications, such as microfluidics, thermal control, and microfabrication.

  • 19. Toppaladoddi, Srikanth
    et al.
    Succi, Sauro
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Yale University, USA; University of Oxford, UK.
    Roughness as a Route to the Ultimate Regime of Thermal Convection2017In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 118, no 7, article id 074503Article in journal (Refereed)
    Abstract [en]

    We use highly resolved numerical simulations to study turbulent Rayleigh-Benard convection in a cell with sinusoidally rough upper and lower surfaces in two dimensions for Pr = 1 and Ra = [4 x 10(6), 3 x 10(9)]. By varying the wavelength. at a fixed amplitude, we find an optimal wavelength lambda(opt) for which the Nusselt-Rayleigh scaling relation is (Nu - 1 proportional to Ra-0.483), maximizing the heat flux. This is consistent with the upper bound of Goluskin and Doering [J. Fluid Mech. 804, 370 (2016)] who prove that Nu can grow no faster than O(Ra-1/2) as Ra -> infinity, and thus with the concept that roughness facilitates the attainment of the so-called ultimate regime. Our data nearly achieve the largest growth rate permitted by the bound. When lambda << lambda(opt) and lambda >> lambda(opt), the planar case is recovered, demonstrating how controlling the wall geometry manipulates the interaction between the boundary layers and the core flow. Finally, for each Ra, we choose the maximum Nu among all., thus optimizing over all lambda, to find Nu(opt) - 1 = 0.01xRa(0.444).

  • 20. Toppaladoddi, Srikanth
    et al.
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Yale University, USA; University of Oxford, United Kingdom.
    Penetrative convection at high Rayleigh numbers2018In: Physical review fluids, ISSN 2469-990X, Vol. 3, no 4, article id 043501Article in journal (Refereed)
    Abstract [en]

    We study penetrative convection of a fluid confined between two horizontal plates, the temperatures of which are such that a temperature of maximum density lies between them. The range of Rayleigh numbers studied is Ra = [10(6),10(8)] and the Prandtl numbers are Pr = 1 and 11.6. An evolution equation for the growth of the convecting region is obtained through an integral energy balance. We identify a new nondimensional parameter, Lambda, which is the ratio of temperature difference between the stable and unstable regions of the flow; larger values of Lambda denote increased stability of the upper stable layer. We study the effects of Lambda on the flow field using well-resolved lattice Boltzmann simulations and show that the characteristics of the flow depend sensitively upon it. For the range Lambda = [0.01,4], we find that for a fixed Ra the Nusselt number, Nu, increases with decreasing Lambda. We also investigate the effects of Lambda on the vertical variation of convective heat flux and the Brunt-Vaisala frequency. Our results clearly indicate that in the limit Lambda -> 0 the problem reduces to that of the classical Rayleigh-Benard convection.

  • 21. Toppaladoddi, Srikanth
    et al.
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Yale University, USA; University of Oxford, UK.
    Statistical Mechanics and the Climatology of the Arctic Sea Ice Thickness Distribution2017In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 167, no 3-4, p. 683-702Article in journal (Refereed)
    Abstract [en]

    We study the seasonal changes in the thickness distribution of Arctic sea ice, g(h), under climate forcing. Our analytical and numerical approach is based on a Fokker-Planck equation for g(h) (Toppaladoddi and Wettlaufer in Phys Rev Lett 115(14): 148501, 2015), in which the thermodynamic growth rates are determined using observed climatology. In particular, the Fokker-Planck equation is coupled to the observationally consistent thermodynamic model of Eisenman and Wettlaufer (Proc Natl Acad Sci USA 106: 28-32, 2009). We find that due to the combined effects of thermodynamics and mechanics, g(h) spreads during winter and contracts during summer. This behavior is in agreement with recent satellite observations from CryoSat-2 (Kwok and Cunningham in Philos Trans R Soc A 373(2045): 20140157, 2015). Because g(h) is a probability density function, we quantify all of the key moments (e. g., mean thickness, fraction of thin/thick ice, mean albedo, relaxation time scales) as greenhouse-gas radiative forcing, Delta F-0, increases. The mean ice thickness decays exponentially with Delta F-0, but much slower than do solely thermodynamic models. This exhibits the crucial role that ice mechanics plays in maintaining the ice cover, by redistributing thin ice to thick ice-far more rapidly than can thermal growth alone.

  • 22. Toppaladoddi, Srikanth
    et al.
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Yale University, USA; University of Oxford, UK.
    Theory of the Sea Ice Thickness Distribution2015In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 115, no 14, article id 148501Article in journal (Refereed)
    Abstract [en]

    We use concepts from statistical physics to transform the original evolution equation for the sea ice thickness distribution g(h) from Thorndike et al. into a Fokker-Planck-like conservation law. The steady solution is g(h) = N(q)h(q)e(-h/H), where q and H are expressible in terms of moments over the transition probabilities between thickness categories. The solution exhibits the functional form used in observational fits and shows that for h << 1, g(h) is controlled by both thermodynamics and mechanics, whereas for h >> 1 only mechanics controls g(h). Finally, we derive the underlying Langevin equation governing the dynamics of the ice thickness h, from which we predict the observed g(h). The genericity of our approach provides a framework for studying the geophysical-scale structure of the ice pack using methods of broad relevance in statistical mechanics.

  • 23. Weady, Scott
    et al.
    Agarwal, Sahil
    Wilen, Larry
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Yale University, USA; University of Oxford, UK;.
    Circuit bounds on stochastic transport in the Lorenz equations2018In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 382, no 26, p. 1731-1737Article in journal (Refereed)
    Abstract [en]

    In turbulent Rayleigh-Benard convection one seeks the relationship between the heat transport, captured by the Nusselt number, and the temperature drop across the convecting layer, captured by the Rayleigh number. In experiments, one measures the Nusselt number for a given Rayleigh number, and the question of how close that value is to the maximal transport is a key prediction of variational fluid mechanics in the form of an upper bound. The Lorenz equations have traditionally been studied as a simplified model of turbulent Rayleigh-Benard convection, and hence it is natural to investigate their upper bounds, which has previously been done numerically and analytically, but they are not as easily accessible in an experimental context. Here we describe a specially built circuit that is the experimental analogue of the Lorenz equations and compare its output to the recently determined upper bounds of the stochastic Lorenz equations [1]. The circuit is substantially more efficient than computational solutions, and hence we can more easily examine the system. Because of offsets that appear naturally in the circuit, we are motivated to study unique bifurcation phenomena that arise as a result. Namely, for a given Rayleigh number, we find a reentrant behavior of the transport on noise amplitude and this varies with Rayleigh number passing from the homoclinic to the Hopf bifurcation.

  • 24. Wells, Andrew J.
    et al.
    Wettlaufer, J. S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Orszag, Steven A.
    Nonlinear mushy-layer convection with chimneys: stability and optimal solute fluxes2013In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 716, p. 203-227Article in journal (Refereed)
    Abstract [en]

    We model buoyancy-driven convection with chimneys - channels of zero solid fraction - in a mushy layer formed during directional solidification of a binary alloy in two dimensions. A large suite of numerical simulations is combined with scaling analysis in order to study the parametric dependence of the flow. Stability boundaries are calculated for states of finite-amplitude convection with chimneys, which for a narrow domain can be interpreted in terms of a modified Rayleigh number criterion based on the domain width and mushy-layer permeability. For solidification in a wide domain with multiple chimneys, it has previously been hypothesized that the chimney spacing will adjust to optimize the rate of removal of potential energy from the system. For a wide variety of initial liquid concentration conditions, we consider the detailed flow structure in this optimal state and derive scaling laws for how the flow evolves as the strength of convection increases. For moderate mushy-layer Rayleigh numbers these flow properties support a solute flux that increases linearly with Rayleigh number. This behaviour does not persist indefinitely, however, with porosity-dependent flow saturation resulting in sublinear growth of the solute flux for sufficiently large Rayleigh numbers. Finally, we consider the influence of the porosity dependence of permeability, with a cubic function and a Carman-Kozeny permeability yielding qualitatively similar system dynamics and flow profiles for the optimal states.

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