Abstract:
The formation of a solar system is believed to have followed a multi-stage process around a protostar. Whipple first noted that planetesimal growth by particle agglomeration is strongly influenced by gas drag; there is a "bottleneck" at the meter scale with such bodies rapidly spiraling into the central star, whereas much smaller or larger particles do not. Thus, successful planetary accretion requires rapid planetesimal growth to km scale. A commonly accepted picture is that for collisional velocities $V_c$ above a certain threshold collisional velocity, ${V_{th}} \sim$ 0.1-10 cm s$^{-1}$, particle agglomeration is not possible; elastic rebound overcomes attractive surface and intermolecular forces. However, if perfect sticking is assumed for all collisions the bottleneck can be overcome by rapid planetesimal growth. While previous work has dealt explicitly with the influences of collisional pressures and the possibility of particle fracture or penetration, the basic role of the phase behavior of matter--phase diagrams, amorphs and polymorphs--has been neglected. Here it is demonstrated that novel aspects of surface phase transitions provide a physical basis for efficient sticking through collisional melting or amphorph-/polymorphization and fusion to extend the collisional velocity range of primary accretion to $\Delta V_c \sim$ 1-100 m s$^{-1}$, which bound both turbulent RMS speeds and the velocity differences between boulder sized and small grains $\sim$ 1-50 m s$^{-1}$. Thus, as inspiraling meter sized bodies collide with smaller particles in this high velocity collisional fusion regime they grow rapidly to km scales and hence settle into stable Keplerian orbits in $\sim$ 10$^5$ years before photoevaporative wind clears the disk of source material.

Abstract:
In light of the rapid recent retreat of Arctic sea ice, a number of studies have discussed the possibility of a critical threshold (or "tipping point") beyond which the ice-albedo feedback causes the ice cover to melt away in an irreversible process. The focus has typically been centered on the annual minimum (September) ice cover, which is often seen as particularly susceptible to destabilization by the ice-albedo feedback. Here we examine the central physical processes associated with the transition from ice-covered to ice-free Arctic Ocean conditions. We show that while the ice-albedo feedback promotes the existence of multiple ice cover states, the stabilizing thermodynamic effects of sea ice mitigate this when the Arctic Ocean is ice-covered during a sufficiently large fraction of the year. These results suggest that critical threshold behavior is unlikely during the approach from current perennial sea ice conditions to seasonally ice-free conditions. In a further warmed climate, however, we find that a critical threshold associated with the sudden loss of the remaining wintertime-only sea ice cover may be likely.

Abstract:
We analyze the stability of a low-order coupled sea ice and climate model and extract the essential physics governing the time scales of response as a function of greenhouse gas forcing. Under present climate conditions the stability is controlled by longwave radiation driven heat conduction. However, as greenhouse gas forcing increases and the ice cover decays, the destabilizing influence of ice-albedo feedback acts on equal footing with longwave stabilization. Both are seasonally out of phase and as the system warms towards a seasonal ice state these effects, which underlie the bifurcations between climate states, combine exhibiting a "slowing down" to extend the intrinsic relaxation time scale from ~ 2 yr to 5 yr.

Abstract:
The Ito-Stratonovich dilemma is revisited from the perspective of the interpretation of Stratonovich calculus using shot noise. Over the long time scales of the displacement of an observable, the principal issue is how to deal with finite/zero autocorrelation of the stochastic noise. The former (non-zero) noise autocorrelation structure preserves the normal chain rule using a mid-point selection scheme, which is the basis Stratonovich calculus, whereas the instantaneous autocorrelation structure of Ito's approach does not. By considering the finite decay of the noise correlations on time scales very short relative to the overall displacement times of the observable, we suggest a generalization of the integral Taylor expansion criterion of Wong and Zakai (1965) for the validity of the Stratonovich approach.

Abstract:
Within the framework of lower order thermodynamic theories for the climatic evolution of Arctic sea ice we isolate the conditions required for the existence of stable seasonally-varying solutions, in which ice forms each winter and melts away each summer. This is done by constructing a two-season model from the continuously evolving theory of Eisenman and Wettlaufer (2009) and showing that seasonally-varying states are unstable under constant annual average short-wave radiative forcing. However, dividing the summer season into two intervals (ice covered and ice free) provides sufficient freedom to stabilize seasonal ice. Simple perturbation theory shows that the condition for stability is determined by when the ice vanishes in summer and hence the relative magnitudes of the summer heat flux over the ocean versus over the ice. This scenario is examined within the context of greenhouse gas warming, as a function of which stability conditions are discerned.

Abstract:
The effect of impurities on the grain boundary melting of ice is investigated through an extension of Derjaguin-Landau-Verwey-Overbeek theory, in which we include retarded potential effects in a calculation of the full frequency dependent van der Waals and Coulombic interactions within a grain boundary. At high dopant concentrations the classical solutal effect dominates the melting behavior. However, depending on the amount of impurity and the surface charge density, as temperature decreases, the attractive tail of the dispersion force interaction begins to compete effectively with the repulsive screened Coulomb interaction. This leads to a film-thickness/temperature curve that changes depending on the relative strengths of these interactions and exhibits a decrease in the film thickness with increasing impurity level. More striking is the fact that at very large film thicknesses, the repulsive Coulomb interaction can be effectively screened leading to an abrupt reduction to zero film thickness.

Abstract:
We use concepts from statistical physics to transform the original evolution equation for the sea ice thickness distribution $g(h)$ due to Thorndike et al., (1975) into a Fokker-Planck like conservation law. The steady solution is $g(h) = {\cal N}(q) h^q \mathrm{e}^{-~ h/H}$, 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 $h \ll 1$, $g(h)$ is controlled by both thermodynamics and mechanics, whereas for $h \gg 1$ 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.

Abstract:
We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh-B\'enard 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 \citet{Doering15}, 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.

Abstract:
The observation of reduced rotational inertia in a cell containing solid helium 4 has been interpreted as evidence for superfluidity of the solid. An alternative explanation is slippage of the solid at the container wall due to grain boundary premelting between the solid and dense adsorbed layers at the container wall. We calculate the range of film thickness and the viscous drag, and find that the slippage can account for the observations.

Abstract:
A controlling factor in the seasonal and climatological evolution of the sea ice cover is its albedo $\alpha$. Here we analyze Arctic data from the Advanced Very High Resolution Radiometer (AVHRR) Polar Pathfinder and assess the seasonality and variability of broadband albedo from a 23 year daily record. We produce a histogram of daily albedo over ice covered regions in which the principal albedo transitions are seen; high albedo in late winter and spring, the onset of snow melt and melt pond formation in the summer, and fall freeze up. The bimodal late summer distribution demonstrates the combination of the poleward progression of the onset of melt with the coexistence of perennial bare ice with melt ponds and open water, which then merge to a broad peak at $\alpha \gtrsim $ 0.5. We find the interannual variability to be dominated by the low end of the $\alpha$ distribution, highlighting the controlling influence of the ice thickness distribution and large-scale ice edge dynamics. The statistics obtained provide a simple framework for model studies of albedo parameterizations and sensitivities.