3,781 research outputs found
The Complete Jamming Landscape of Confined Hard Discs
An exact description of the complete jamming landscape is developed for a
system of hard discs of diameter , confined between two lines separated
by a distance . By considering all possible local
packing arrangements, the generalized ensemble partition function of jammed
states is obtained using the transfer matrix method, which allows us to
calculate the configurational entropy and the equation of state for the
packings. Exploring the relationship between structural order and packing
density, we find that the geometric frustration between local packing
environments plays an important role in determining the density distribution of
jammed states and that structural "randomness" is a non-monotonic function of
packing density. Molecular dynamics simulations show that the properties of the
equilibrium liquid are closely related to those of the landscape.Comment: 5 Pages, 4 figure
The Inherent Structure Landscape Connection Between Liquids, Granular materials and the Jamming Phase Diagram
We provide a comprehensive picture of the jamming phase diagram by connecting
the athermal, granular ensemble of jammed states and the equilibrium fluid
through the inherent structure paradigm for a system hard discs confined to a
narrow channel. The J-line is shown to be divided into packings that are
thermodynamically accessible from the equilibrium fluid and inaccessible
packings. The J-point is found to occur at the transition between these two
sets of packings and is located at the maximum the inherent structure
distribution. A general thermodynamic argument suggests that the density of the
states at the configurational entropy maximum represents a lower bound on the
J-point density in hard sphere systems. Finally, we find that the granular and
fluid systems only occupy the same set of inherent structures, under the same
thermodynamic conditions, at two points, corresponding to zero and infinite
pressures, where they sample the J-point states and the most dense packing
respectively.Comment: 5 pages, 3 Figure
Correlation of Positive and Negative Reciprocity Fails to Confer an Evolutionary Advantage: Phase Transitions to Elementary Strategies
Economic experiments reveal that humans value cooperation and fairness. Punishing unfair behavior is therefore common, and according to the theory of strong reciprocity, it is also directly related to rewarding cooperative behavior. However, empirical data fail to confirm that positive and negative reciprocity are correlated. Inspired by this disagreement, we determine whether the combined application of reward and punishment is evolutionarily advantageous. We study a spatial public goods game, where in addition to the three elementary strategies of defection, rewarding, and punishment, a fourth strategy that combines the latter two competes for space. We find rich dynamical behavior that gives rise to intricate phase diagrams where continuous and discontinuous phase transitions occur in succession. Indirect territorial competition, spontaneous emergence of cyclic dominance, as well as divergent fluctuations of oscillations that terminate in an absorbing phase are observed. Yet, despite the high complexity of solutions, the combined strategy can survive only in very narrow and unrealistic parameter regions. Elementary strategies, either in pure or mixed phases, are much more common and likely to prevail. Our results highlight the importance of patterns and structure in human cooperation, which should be considered in future experiments
Edwards entropy and compactivity in a model of granular matter
Formulating a statistical mechanics for granular matter remains a significant
challenge, in part, due to the difficulty associated with a complete
characterization of the systems under study. We present a fully characterized
model of a granular material consisting of two-dimensional, frictionless,
hard discs, confined between hard walls, including a complete enumeration of
all possible jammed structures. We show the properties of the jammed packings
are independent of the distribution of defects within the system and that all
the packings are isostatic. This suggests the assumption of equal probability
for states of equal volume, which provides one possible way of constructing the
equivalent of a microcanonical ensemble, is likely to be vaild for our model.
An application of the second law of thermodynamics involving two subsystems in
contact shows that the expected spontaneous equilibration of defects between
the two is accompanied by an increase in entropy and that the equilibirum,
obtained by entropy maximization, is characterized by the equality of
compactivities. Finally, we explore the properties of the equivalent to the
canonical ensemble for this system.Comment: Accepted PR
Impact of generalized benefit functions on the evolution of cooperation in spatial public goods games with continuous strategies
Cooperation and defection may be considered as two extreme responses to a
social dilemma. Yet the reality is much less clear-cut. Between the two
extremes lies an interval of ambivalent choices, which may be captured
theoretically by means of continuous strategies defining the extent of the
contributions of each individual player to the common pool. If strategies are
chosen from the unit interval, where 0 corresponds to pure defection and 1
corresponds to the maximal contribution, the question is what is the
characteristic level of individual investments to the common pool that emerges
if the evolution is guided by different benefit functions. Here we consider the
steepness and the threshold as two parameters defining an array of generalized
benefit functions, and we show that in a structured population there exist
intermediate values of both at which the collective contributions are maximal.
However, as the cost-to-benefit ratio of cooperation increases the
characteristic threshold decreases, while the corresponding steepness
increases. Our observations remain valid if more complex sigmoid functions are
used, thus reenforcing the importance of carefully adjusted benefits for high
levels of public cooperation.Comment: 8 two-column pages, 8 figures; accepted for publication in Physical
Review
Conditional strategies and the evolution of cooperation in spatial public goods games
The fact that individuals will most likely behave differently in different
situations begets the introduction of conditional strategies. Inspired by this,
we study the evolution of cooperation in the spatial public goods game, where
besides unconditional cooperators and defectors, also different types of
conditional cooperators compete for space. Conditional cooperators will
contribute to the public good only if other players within the group are likely
to cooperate as well, but will withhold their contribution otherwise. Depending
on the number of other cooperators that are required to elicit cooperation of a
conditional cooperator, the latter can be classified in as many types as there
are players within each group. We find that the most cautious cooperators, such
that require all other players within a group to be conditional cooperators,
are the undisputed victors of the evolutionary process, even at very low
synergy factors. We show that the remarkable promotion of cooperation is due
primarily to the spontaneous emergence of quarantining of defectors, which
become surrounded by conditional cooperators and are forced into isolated
convex "bubbles" from where they are unable to exploit the public good. This
phenomenon can be observed only in structured populations, thus adding to the
relevance of pattern formation for the successful evolution of cooperation.Comment: 7 two-column pages, 7 figures; accepted for publication in Physical
Review
Salt Loading from Efflorescence and Suspended Sediments in the Price River Basin
Salinity control is a major component of water management in arid climates and irrigated areas and one of particular concern in the Colorado River Basin. The alts enter the water as it flows over land or moves through the soil or geologic formations. The principal salt collection processes are 1) dissolution from the soil surface during runoff events, 2) transpiration of soil water leaving salt residuals, 3) efflorescence left by evaporating seepage and then dissolved by subsequent runoff, 4) dissolution with weathering of fixed bed channels, 5) salts released by sediments entering the channel from sheet, gulley, and bank erosion, and 6) deep percolation through saline aquifer reaching the stream as base flow. This study examined processes 3 and 5. Salt efflorescence was examined by field observation and instrumentation, laboratory experiments, and mathematical modeling. The field data showed near saturation conditions of sodium sulfate waters below crusts of densities between 0.14 and 0.36 g/cm^2 and which formed over abouta 10-day period following channel cleaning by storm runoff. Laboratory data on salt crusting in soil columns were also used in developing a model which when applied to the Price River Basin estimated that no more than 7.5 percent of the total salt loading comes from salt efflorescence being carried away in the stream flow. The conditions favorable to the accumulation of salt efflorescence are highly saline water just below the soil surface and a source of heat for vaporizing the water. Salt release from suspended sediments was studied by laboratory experimentation with sediment material obtained from various locations in the Price River Basin. The Buckinham Pi Theorem was employed to derive relationships expressing the EC of a sediment water system as a function o fthe controlling factors. The results were presented in two salt release equations, one excluding the effect of initial EC and the other providing for initially saline solutions. The salt release equations were incorporated into an adapted version of the Watershed Erosion and Sediment Transport (WEST) model and applied to a small tributary of Coal Creek. Extrapolation to the entire Price River Basin led to an estimate that about 0.50 percent of the total annual salt load is released from suspened sediments. This study concludes that surface salt sources produce a relatvely small fraction of the total loading. Future studies need to go underground. They need to quantify and examine the flow lines of water movement from mountain source and valley floow recharge areas to points of emergence as base flow in the larger stream channels. They need to investigate the aquifers and their soluble salt content
Evolutionary Roots of Property Rights; The Natural and Cultural Nature of Human Cooperation
Debates about the role of natural and cultural selection in the development of prosocial, antisocial and socially neutral mechanisms and behavior raise questions that touch property rights, cooperation, and conflict. For example, some researchers suggest that cooperation and prosociality evolved by natural selection (Hamilton 1964, Trivers 1971, Axelrod and Hamilton 1981, De Waal 2013, 2014), while others claim that natural selection is insufficient for the evolution of cooperation, which required in addition cultural selection (Sterelny 2013, Bowles and Gintis 2003, Seabright 2013, Norenzayan 2013). Some scholars focus on the complexity and hierarchical nature of the evolution of cooperation as involving different tools associated with lower and the higher levels of competition (Nowak 2006, Okasha 2006); others suggest that humans genetically inherited heuristics that favor prosocial behavior such as generosity, forgiveness or altruistic punishment (Ridley 1996, Bowles and Gintis 2004, Rolls 2005). We argue these mechanisms are not genetically inherited; rather, they are features inherited through cultural selection. To support this view we invoke inclusive fitness theory, which states that individuals tend to maximize their inclusive fitness, rather than maximizing group fitness. We further reject the older notion of natural group selection - as well as more recent versions (West, Mouden, Gardner 2011) – which hold that natural selection favors cooperators within a group (Wynne-Edwards 1962). For Wynne-Edwards, group selection leads to group adaptations; the survival of individuals therefore depends on the survival of the group and a sharing of resources. Individuals who do not cooperate, who are selfish, face extinction due to rapid and over-exploitation of resources
Estimated glomerular filtration rate and risk of poor outcomes after stroke
We thank the data team of the Norfolk and Norwich University Hospital Stroke Services.Peer reviewedPostprin
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