 Award ID(s):
 1740203
 NSFPAR ID:
 10326711
 Editor(s):
 USRA
 Date Published:
 Journal Name:
 53rd Lunar and Planetary Science Conference (2022)
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Origami structures with a large number of excess folds are capable of storing distinguishable geometric states that are energetically equivalent. As the number of excess folds is reduced, the system has fewer equivalent states and can eventually become rigid. We quantify this transition from a floppy to a rigid state as a function of the presence of folding constraints in a classic origami tessellation, Miuraori. We show that in a fully triangulated Miuraori that is maximally floppy, adding constraints via the elimination of diagonal folds in the quads decreases the number of degrees of freedom in the system, first linearly and then nonlinearly. In the nonlinear regime, mechanical cooperativity sets in via a redundancy in the assignment of constraints, and the degrees of freedom depend on constraint density in a scale invariant manner. A percolation transition in the redundancy in the constraints as a function of constraint density suggests how excess folds in an origami structure can be used to store geometric information in a scaleinvariant way.more » « less

Origami structures with a large number of excess folds are capable of storing distinguishable geometric states that are energetically equivalent. As the number of excess folds is reduced, the system has fewer equivalent states and can eventually become rigid. We quantify this transition from a floppy to a rigid state as a function of the presence of folding constraints in a classic origami tessellation, Miuraori. We show that in a fully triangulated Miuraori that is maximally floppy, adding constraints via the elimination of diagonal folds in the quads decreases the number of degrees of freedom in the system, first linearly and then nonlinearly. In the nonlinear regime, mechanical cooperativity sets in via a redundancy in the assignment of constraints, and the degrees of freedom depend on constraint density in a scaleinvariant manner. A percolation transition in the redundancy in the constraints as a function of constraint density suggests how excess folds in an origami structure can be used to store geometric information in a scaleinvariant way.

The Xcube model, a prototypical gapped fracton model, was shown in Ref. [1] to have a foliation structure. That is, inside the 3+1 D model, there are hidden layers of 2+1 D gapped topological states. A screw dislocation in a 3+1 D lattice can often reveal nontrivial features associated with a layered structure. In this paper, we study the Xcube model on lattices with screw dislocations. In particular, we find that a screw dislocation results in a finite change in the logarithm of the ground state degeneracy of the model. Part of the change can be traced back to the effect of screw dislocations in a simple stack of 2+1 D topological states, hence corroborating the foliation structure in the model. The other part of the change comes from the induced motion of fractons or subdimensional excitations along the dislocation, a feature absent in the stack of 2+1D layers.more » « less

Abstract Manybody dynamical models in which Boltzmann statistics can be derived directly from the underlying dynamical laws without invoking the fundamental postulates of statistical mechanics are scarce. Interestingly, one such model is found in econophysics and in chemistry classrooms: the money game, in which players exchange money randomly in a process that resembles elastic intermolecular collisions in a gas, giving rise to the Boltzmann distribution of money owned by each player. Although this model offers a pedagogical example that demonstrates the origins of Boltzmann statistics, such demonstrations usually rely on computer simulations. In fact, a proof of the exponential steadystate distribution in this model has only become available in recent years. Here, we study this random money/energy exchange model and its extensions using a simple meanfieldtype approach that examines the properties of the onedimensional random walk performed by one of its participants. We give a simple derivation of the Boltzmann steadystate distribution in this model. Breaking the timereversal symmetry of the game by modifying its rules results in nonBoltzmann steadystate statistics. In particular, introducing ‘unfair’ exchange rules in which a poorer player is more likely to give money to a richer player than to receive money from that richer player, results in an analytically provable Paretotype powerlaw distribution of the money in the limit where the number of players is infinite, with a finite fraction of players in the ‘ground state’ (i.e. with zero money). For a finite number of players, however, the game may give rise to a bimodal distribution of money and to bistable dynamics, in which a participant’s wealth jumps between poor and rich states. The latter corresponds to a scenario where the player accumulates nearly all the available money in the game. The time evolution of a player’s wealth in this case can be thought of as a ‘chemical reaction’, where a transition between ‘reactants’ (rich state) and ‘products’ (poor state) involves crossing a large free energy barrier. We thus analyze the trajectories generated from the game using ideas from the theory of transition paths and highlight nonMarkovian effects in the barrier crossing dynamics.

Abstract The diurnal cycle (DC) in the cirrus canopy of tropical cyclones (TCs) is a welldocumented phenomenon. While early studies linked the DC in the area of the cirrus canopy to a DC in the strength of eyewall convection, later studies considered it a direct response to the DC of radiation in the cirrus canopy. In this study, an idealized linear model is used to examine the extent to which linear dynamics can capture the DC in TCs, in particular the transition between balanced and radiating responses to diurnal heating. The model heat forcing is physically motivated by the diabatic heating output from a realistic simulation, which illustrates the presence of a DC in moist convective heating and radiative heating in the eyewall, and a DC in radiative heating in the cirrus canopy. This study finds that the DCs of heating in the eyewall yield a response that is restricted to inside the RMW by the high inertial stability in the inner core. The DC of radiative heating in the cirrus canopy yields a response throughout the entire cyclone. Lowerfrequency responses, of diurnal and semidiurnal frequency, are balanced throughout much of the cyclone. Highfrequency waves with periods under 8 h, created at sunrise and sunset, can radiate outward and downward. These results indicate that diurnal responses are balanced in the majority of a TC and originate in the cirrus canopy, instead of the eyewall. The DC in cirrus canopy vertical motion also appears to originate in the cirrus canopy.