Soft matter physics of the ground beneath our feet.

The soft part of the Earth's surface - the ground beneath our feet - constitutes the basis for life and natural resources, yet a general physical understanding of the ground is still lacking. In this critical time of climate change, cross-pollination of scientific approaches is urgently needed to better understand the behavior of our planet's surface. The major topics in current research in this area cross different disciplines, spanning geosciences, and various aspects of engineering, material sciences, physics, chemistry, and biology.

Wrinkling composite sheets.

We examine the buckling shape and critical compression of confined inhomogeneous composite sheets lying on a liquid foundation. The buckling modes are controlled by the bending stiffness of the sheet, the density of the substrate, and the size and the spatially dependent elastic coefficients of the sheet. We solve the beam equation describing the mechanical equilibrium of a sheet when its bending stiffness varies parallel to the direction of confinement.

Stochastic paleoclimatology: Modeling the EPICA ice core climate records.

We analyze and model the stochastic behavior of paleoclimate time series and assess the implications for the coupling of climate variables during the Pleistocene glacial cycles. We examine 800 kiloyears of carbon dioxide, methane, nitrous oxide, and temperature proxy data from the European Project for Ice Coring in Antarctica (EPICA) Dome-C ice core, which are characterized by 100 ky glacial cycles overlain by fluctuations across a wide range of timescales. We quantify this behavior through multifractal time-weighted detrended fluctuation analysis, which distinguishes near-red-noise and white-noise behavior below and above the 100 ky glacial cycle, respectively, in all records.

Wavier jet streams driven by zonally asymmetric surface thermal forcing.

Recent studies have argued that global warming is responsible for a wavier jet stream, thereby driving midlatitude extreme flooding and drought. Polar amplification-the relative enhancement of high-latitude temperatures under global warming-is argued to be the principal climate state driving midlatitude extremes. Namely, the decreased meridional temperature gradient suppresses the mean zonal winds, leading to wavier midlatitude jets.

Premelting controlled active matter in ice.

Self-propelled particles can undergo complex dynamics due to a range of bulk and surface interactions. When a particle is embedded in a host solid near its bulk melting temperature, the latter may melt at the surface of the former in a process known as interfacial premelting. The thickness of the melt film depends on the temperature, impurities, material properties and geometry.

Analytical solution of stochastic resonance in the nonadiabatic regime.

We generalize stochastic resonance to the nonadiabatic limit by treating the double-well potential using two quadratic potentials. We use a singular perturbation method to determine an approximate analytical solution for the probability density function that asymptotically connects local solutions in boundary layers near the two minima with those in the region of the maximum that separates them. The validity of the analytical solution is confirmed numerically.

Predicting critical transitions in multiscale dynamical systems using reservoir computing.

We study the problem of predicting rare critical transition events for a class of slow-fast nonlinear dynamical systems. The state of the system of interest is described by a slow process, whereas a faster process drives its evolution and induces critical transitions. By taking advantage of recent advances in reservoir computing, we present a data-driven method to predict the future evolution of the state.

Impurity effects in thermal regelation.

When a particle is placed in a material with a lower bulk melting temperature, intermolecular forces can lead to the existence of a "premelted" liquid film of the lower melting temperature material. Despite the system being below the melting temperatures of both solids, the liquid film is a consequence of thermodynamic equilibrium, controlled by intermolecular, ionic and other interactions. An imposed temperature gradient drives the translation of the particle by a process of melting and refreezing known as "thermal regelation".

Coupling functions in climate.

We examine how coupling functions in the theory of dynamical systems provide a quantitative window into climate dynamics. Previously, we have shown that a one-dimensional periodic non-autonomous stochastic dynamical system can simulate the monthly statistics of surface air temperature data. Here, we expand this approach to two-dimensional dynamical systems to include interactions between two sub-systems of the climate.

Hydrodynamic interactions and the diffusivity of spheroidal particles.

It is intuitive that the diffusivity of an isolated particle differs from those in a monodisperse suspension, in which hydrodynamic interactions between the particles are operative. Batchelor [J. Fluid Mech.

Surface phase transitions in ice: from fundamental interactions to applications.

Interfaces divide all phases of matter and yet in most practical settings it is tempting to ignore their energies and the associated implications. There are many reasons for this, not the least of which is the introduction of a new pair of canonically conjugate variables-interfacial energy and its counterpart the surface area. A key set of questions surrounding the treatment of multiphase flows concerns how and when we must account for such effects.

Intrinsic Pink-Noise Multidecadal Global Climate Dynamics Mode.

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.

Fluctuations in Arctic sea-ice extent: comparing observations and climate models.

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.

Confinement effects in premelting dynamics.

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.

Fluctuation spectra and force generation in nonequilibrium systems.

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.

A unified nonlinear stochastic time series analysis for climate science.

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.

Roughness as a Route to the Ultimate Regime of Thermal Convection.

We use highly resolved numerical simulations to study turbulent Rayleigh-Bénard convection in a cell with sinusoidally rough upper and lower surfaces in two dimensions for Pr=1 and Ra=[4×10^{6},3×10^{9}]. By varying the wavelength λ at a fixed amplitude, we find an optimal wavelength λ_{opt} for which the Nusselt-Rayleigh scaling relation is (Nu-1∝Ra^{0.483}), maximizing the heat flux.

Surface tension and a self-consistent theory of soft composite solids with elastic inclusions.

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≡γ/E, where γ 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.

Statistical Mechanics and the Climatology of the Arctic Sea Ice Thickness Distribution.

We study the seasonal changes in the thickness distribution of Arctic sea ice, (), under climate forcing. Our analytical and numerical approach is based on a Fokker-Planck equation for () (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).

Surface tension and the Mori-Tanaka theory of non-dilute soft composite solids.

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.

Segregated Ice Growth in a Suspension of Colloidal Particles.

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.

Interfacial tension and a three-phase generalized self-consistent theory of non-dilute soft composite solids.

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≡γ/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.

Theory of the Sea Ice Thickness Distribution.

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.