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Articles 1 - 30 of 46
Full-Text Articles in Physical Sciences and Mathematics
Post-Speleogenetic Biogenic Modification Of Gomantong Caves, Sabah, Borneo, Joyce Lundberg, Donald A. Mcfarlane
Post-Speleogenetic Biogenic Modification Of Gomantong Caves, Sabah, Borneo, Joyce Lundberg, Donald A. Mcfarlane
WM Keck Science Faculty Papers
The Gomantong cave system of eastern Sabah, Malaysia, is well-known as an important site for harvesting edible bird-nests and, more recently, as a tourist attraction. Although the biology of the Gomantong system has been repeatedly studied, very little attention has been given to the geomorphology. Here, we report on the impact of geobiological modification in the development of the modern aspect of the cave, an important but little recognized feature of tropical caves. Basic modeling of the metabolic outputs from bats and birds (CO2, H2O, heat) reveals that post-speleogenetic biogenic corrosion can erode bedrock by between …
Subaerial Freshwater Stromatolites In Deer Cave, Sarawak – A Unique Geobiological Cave Formation, Joyce Lundberg, Donald A. Mcfarlane
Subaerial Freshwater Stromatolites In Deer Cave, Sarawak – A Unique Geobiological Cave Formation, Joyce Lundberg, Donald A. Mcfarlane
WM Keck Science Faculty Papers
A suite of distinctive freshwater subaerial phosphatic stromatolites is developed close to the northeastern entrance of Deer Cave, Gunung Mulu National Park, Sarawak, Borneo, in conditions of very low light but ample supply of nutrients from guano. These stromatolites are not particulate; they are composed of alternating layers of more porous and more dense amorphous hydroxylapatite. This biomineralization occurs as moulds of coccoid (the majority) and filamentous (less abundant) cyanobacteria. Mineralization occurs at a pH of ~ 7.0 in the extracellular sheaths and in micro-domains of varying carbonate content in the surrounding mucus of the biofilm. The most recent surfaces …
An Extraordinary Example Of Photokarren In A Sandstone Cave, Cueva Charles Brewer, Chimantá Plateau, Venezuela: Biogeomorphology On A Small Scale, Joyce Lundberg, Donald A. Mcfarlane, Charles Brewer-Carias
An Extraordinary Example Of Photokarren In A Sandstone Cave, Cueva Charles Brewer, Chimantá Plateau, Venezuela: Biogeomorphology On A Small Scale, Joyce Lundberg, Donald A. Mcfarlane, Charles Brewer-Carias
WM Keck Science Faculty Papers
A distinctive suite of small-scale erosional forms that are oriented towards the light occur close to the entrance of Cueva Charles Brewer, a large cave in a sandstone tepui, in SE Venezuela. These are the third example of photokarren ever studied in the world, the other two being from Borneo and Ireland. They are the only photokarren ever described from sandstone, and the only example from a non-carbonate environment. The host rock is a poorly-lithified unit of the Precambrian quartz arenite of the Roraima Supergroup. The forms are all oriented towards the light at 30° regardless of rock surface orientation. …
A Unique Population Of Cave Bears (Carnivora: Ursidae) From The Middle Pleistocene Of Kents Cavern, England, Based On Dental Morphometrics, Donald A. Mcfarlane, Martin Sabol, Joyce Lundberg
A Unique Population Of Cave Bears (Carnivora: Ursidae) From The Middle Pleistocene Of Kents Cavern, England, Based On Dental Morphometrics, Donald A. Mcfarlane, Martin Sabol, Joyce Lundberg
WM Keck Science Faculty Papers
The ‘breccia’ stratum from Kents (we follow local tradition in using the form ‘Kents’, without an apostrophe) Cavern, England, has been well known for its rich yield of cave-bear material since excavations began in the mid-19th century. Recent work has established that the bears are of latest MIS 12 or earliest MIS 11 age. A life table based on a collection of 67 molariform teeth is consistent with the use of the cave as a hibernaculum. Univariate and morphological assessment of the teeth shows an unusual range of primitive and more derived characters. Multivariate morphometric analysis of cave-bear teeth from …
A Geographic Information Systems Approach To The 19th Century Excavation Of Brixham Cavern, Devon, England, Donald A. Mcfarlane, Joyce Lundberg, Warren Roberts
A Geographic Information Systems Approach To The 19th Century Excavation Of Brixham Cavern, Devon, England, Donald A. Mcfarlane, Joyce Lundberg, Warren Roberts
WM Keck Science Faculty Papers
The oldest known spatially-explicit archaeological excavation, conducted in Brixham cave, Devon, in 1858, is reconstructed using geographic information systems technology. Two dimensional plots of individual fossil taxa and flint artefacts demonstrate the utility of the technique for elucidating taphonomy and palaeobiology. The cave served as a den for hibernating brown bears, as a den for hyena and cave lion, and as a reliquary for their prey.
An Undescribed Gecko (Gekkonidae: Cyrtodactylus) From Deer Cave, Gunung Mulu National Park, Sarawak, With Comments On The Distribution Of Bornean Cave Geckos, Donald A. Mcfarlane, Joyce Lundberg, Keith Christenson
An Undescribed Gecko (Gekkonidae: Cyrtodactylus) From Deer Cave, Gunung Mulu National Park, Sarawak, With Comments On The Distribution Of Bornean Cave Geckos, Donald A. Mcfarlane, Joyce Lundberg, Keith Christenson
WM Keck Science Faculty Papers
Geckos of the genus Cyrtodactylus are a speciose group in Southeast Asia, with at least nine species known from the island of Borneo (Das & Ismail, 2001; Das, 2006). Of these species, Cyrtodactylus cavernicolus has the smallest known range and is therefore the most vulnerable, a status that is reflected in the species having been designated a Totally Protected Species in Sarawak. Confirmed records of C. cavernicolus are known only from Niah Cave, located in an isolated limestone block known as the Gunung Subis massif, approximately 13 km² in extent. The Niah Cave Gecko is presumed to be dependent on …
Bats And Bell Holes: The Microclimatic Impact Of Bat Roosting, Using A Case Study From Runaway Bay Caves, Jamaica, Joyce Lundberg, Donald A. Mcfarlane
Bats And Bell Holes: The Microclimatic Impact Of Bat Roosting, Using A Case Study From Runaway Bay Caves, Jamaica, Joyce Lundberg, Donald A. Mcfarlane
WM Keck Science Faculty Papers
The microclimatic effect of bats roosting in bell holes (blind vertical cylindrical cavities in cave roofs) in Runaway Bay Caves, Jamaica, was measured and the potential impact of their metabolism on dissolution modelled. Rock temperature measurements showed that bell holes with bats get significantly hotter than those without bats during bat roosting periods (by an average of 1.1 °C). The relationship is clearest for bell holes with more than about 300 g aggregate bat body mass and for bell holes that are moderately wide and deep, of W:D ratio between 0.8 and 1.6. Measurement of temperature decay after abandonment showed …
Nonlinear Dynamics In Combinatorial Games: Renormalizing Chomp, Eric J. Friedman, Adam S. Landsberg
Nonlinear Dynamics In Combinatorial Games: Renormalizing Chomp, Eric J. Friedman, Adam S. Landsberg
WM Keck Science Faculty Papers
We develop a new approach to combinatorial games that reveals connections between such games and some of the central ideas of nonlinear dynamics: scaling behaviors, complex dynamics and chaos, universality, and aggregation processes. We take as our model system the combinatorial game Chomp, which is one of the simplest in a class of "unsolved" combinatorial games that includes Chess, Checkers, and Go. We discover that the game possesses an underlying geometric structure that "grows" (reminiscent of crystal growth), and show how this growth can be analyzed using a renormalization procedure adapted from physics. In effect, this methodology allows one to …
Spatial And Temporal Expression Of Vegetation And Atmospheric Variability From Stable Carbon And Nitrogen Isotope Analysis Of Bat Guano In The Southern United States, Christopher M. Wurster, Donald A. Mcfarlane, Michael I. Bird
Spatial And Temporal Expression Of Vegetation And Atmospheric Variability From Stable Carbon And Nitrogen Isotope Analysis Of Bat Guano In The Southern United States, Christopher M. Wurster, Donald A. Mcfarlane, Michael I. Bird
WM Keck Science Faculty Papers
Stable isotopes of faeces contain information related to the animals feeding ecology. The use of stable isotope values from subfossil faeces as a palaeoenvironmental indicator depends on how faithfully the animal records their local environment. Here we present insectivorous bat guano δ13C and δ15N values from a precipitation gradient across the southern United States and northern Mexico to compare with local vegetation and climate. We find δ13C values to be an excellent predictor of expected C4/CAM vegetation, indicating that the bats are non-selective in their diet. Moreover, we find bat guano δ …
The 19th Century Excavation Of Kent's Cavern, England, Donald A. Mcfarlane, Joyce Lundberg
The 19th Century Excavation Of Kent's Cavern, England, Donald A. Mcfarlane, Joyce Lundberg
WM Keck Science Faculty Papers
Between 1858 and 1880, William Pengelly developed revolutionary new techniques for the archeological and paleontological excavation of cave deposits. His work at Brixham Cave and Kent’s Cavern, England, yielded tens of thousands of specimens from the mid-Pleistocene to the Holocene, settled the intellectual debate over the co-existence of humans and extinct mammals, and accumulated an unparalleled resource for continued study. Although the Brixham Cave work was thoroughly summarized in print, Pengelly never published the plans of his much more thorough and extensive excavations at Kent’s Cavern. Here we present a reconstructed plan of the Pengelly excavations that we hope will …
Behavior Of Coupled Automata, Reuben Gann, Jessica Venable, Eric J. Friedman, Adam S. Landsberg
Behavior Of Coupled Automata, Reuben Gann, Jessica Venable, Eric J. Friedman, Adam S. Landsberg
WM Keck Science Faculty Papers
We study the nature of statistical correlations that develop between systems of interacting self-organized critical automata (sandpiles). Numerical and analytical findings are presented describing the emergence of "synchronization" between sandpiles and the dependency of this synchronization on factors such as variations in coupling strength, toppling rule probabilities, symmetric versus asymmetric coupling rules, and numbers of sandpiles.
An Unusual Lava Cave From Ol Doinyo Lengai, Tanzania, Donald A. Mcfarlane, Joyce Lundberg, Frederick Belton
An Unusual Lava Cave From Ol Doinyo Lengai, Tanzania, Donald A. Mcfarlane, Joyce Lundberg, Frederick Belton
WM Keck Science Faculty Papers
A new type of lava cave is described from the summit crater of Ol Doinyo Lengai, a unique active carbonatite volcano in Tanzania. This and other similar caves on Ol Doinyo Lengai are formed by thermal erosion and aqueous dissolution of otherwise solid spatter cones. Meteoritic water and endogenous condensates act to form speleothems of complex mineralogy up to 3 m in length. We propose the new classification of “polygenetic spatter cone cave”.
Guano, Donald A. Mcfarlane
Guano, Donald A. Mcfarlane
WM Keck Science Faculty Papers
This is an encyclopedia article.
A New Megalonychid Sloth From The Late Wisconsinan Of The Dominican Republic, Elizabeth Rega, Donald A. Mcfarlane, Joyce Lundberg, Keith Christenson
A New Megalonychid Sloth From The Late Wisconsinan Of The Dominican Republic, Elizabeth Rega, Donald A. Mcfarlane, Joyce Lundberg, Keith Christenson
WM Keck Science Faculty Papers
An unusually well preserved skull, mandible, and indisputably associated post-cranial elements of new sloth, Acratocnus (Miocnus), were recovered from a cave in Jaragua National Park, Dominican Republic. The animal died lying in a rimstone pool and was rapidly coated with a thin calcite patina. We have documented a late Wisconsinan age for this specimen by inorganic 14C radiometric dating of the patina, with supporting data on the carbon systematics of the speleothems in this cave. This sloth is described as a new species on the basis of the distinctive morphology and relative size of cranial and mandibular features. We consider …
A Middle Pleistocene Age And Biogeography For The Extinct Rodent Megalomys Curazensis From Curaçao, Netherlands Antilles, Donald A. Mcfarlane, Joyce Lundberg
A Middle Pleistocene Age And Biogeography For The Extinct Rodent Megalomys Curazensis From Curaçao, Netherlands Antilles, Donald A. Mcfarlane, Joyce Lundberg
WM Keck Science Faculty Papers
The extinct oryzomyine rodent Megalomys curazensis has been known from abundant but fragmentary remains on the island of Curaçao since 1959. Here we demonstrate an age of 130 000 to 400 000 years before present based on geomorphological context, and propose a biogeographical model for the genus.
A Late Quaternary Paleoecological Record From Caves Of Southern Jamaica, West Indies, Donald A. Mcfarlane, Joyce Lundberg, A.G. Fincham
A Late Quaternary Paleoecological Record From Caves Of Southern Jamaica, West Indies, Donald A. Mcfarlane, Joyce Lundberg, A.G. Fincham
WM Keck Science Faculty Papers
Studies of an unusual and diverse system of caves in coastal southern Jamaica have yielded a paleoclimatic record associated with a fossil vertebrate record that provides useful insights into the poorly documented paleoecology of latest Wisconsinan and Holocene Jamaica. Episodes of significantly increased precipitation during the Holocene have left characteristic deposits of speleothems, and have supported both faunal and archaeological communities that were dependent on these mesic conditions. Deposits of fossil bat guano preserved in the caves provide a δ¹³C record of alternating mesic and xeric climatic episodes that supports the interpretation of the faunal and archaeological record.
Puerto Rican Karst - A Vital Resource, Ariel E. Lugo, Leopoldo Miranda Castro, Abel Vale, Tania Del Mar López, Enrique Hernández Prieto, Andrés García Martinó, Alberto R. Puente Rolón, Adrianne G. Tossas, Donald A. Mcfarlane, Tom Miller, Armando Rodríguez, Joyce Lundberg, John Thomlinson, José Colón, Johannes H. Schellekens, Olga Ramos, Eileen Helmer
Puerto Rican Karst - A Vital Resource, Ariel E. Lugo, Leopoldo Miranda Castro, Abel Vale, Tania Del Mar López, Enrique Hernández Prieto, Andrés García Martinó, Alberto R. Puente Rolón, Adrianne G. Tossas, Donald A. Mcfarlane, Tom Miller, Armando Rodríguez, Joyce Lundberg, John Thomlinson, José Colón, Johannes H. Schellekens, Olga Ramos, Eileen Helmer
WM Keck Science Faculty Papers
The limestone region of Puerto Rico covers about 27.5 percent of the island's surface and is subdivided into the northern, southern, and dispersed limestone areas. All limestone areas have karst features. The karst belt is that part of the northern limestone with the most spectacular surficial karst landforms. It covers 142,544 ha or 65 percent of the northern limestone. The karst belt is the focus of this publication, although reference is made to all limestone regions. The northern limestone contains Puerto Rico's most extensive freshwater aquifer, largest continuous expanse of mature forest, and largest coastal wetland, estuary, and underground cave …
Large-Scale Synchrony In Weakly Interacting Automata, Eric J. Friedman, Adam S. Landsberg
Large-Scale Synchrony In Weakly Interacting Automata, Eric J. Friedman, Adam S. Landsberg
WM Keck Science Faculty Papers
We study the behavior of two spatially distributed (sandpile) models which are weakly linked with one another. Using a Monte Carlo implementation of the renormalization-group and algebraic methods, we describe how large-scale correlations emerge between the two systems, leading to synchronized behavior.
Spectral Equivalence Of Bosons And Fermions In One-Dimensional Harmonic Potentials, Michael Crescimanno, Adam S. Landsberg
Spectral Equivalence Of Bosons And Fermions In One-Dimensional Harmonic Potentials, Michael Crescimanno, Adam S. Landsberg
WM Keck Science Faculty Papers
Recently, Schmidt and Schnack [Physica A 260, 479 (1998)], following earlier references, reiterate that the specific heat of N noninteracting bosons in a one-dimensional harmonic well equals that of N noninteracting fermions in the same potential. We show that this peculiar relationship between heat capacities results from a more dramatic equivalence between Bose and Fermi systems. Namely, we prove that the excitations of such Bose and Fermi systems are spectrally equivalent. Two complementary proofs of this equivalence are provided; one based on a combinatoric argument, the other from analysis of the underlying dynamical symmetry group.
A New Species Of Extinct Oryzomyine Rodent From The Quaternary Of Curaçao, Netherlands Antilles, Donald A. Mcfarlane, Adolphe O. Debrot
A New Species Of Extinct Oryzomyine Rodent From The Quaternary Of Curaçao, Netherlands Antilles, Donald A. Mcfarlane, Adolphe O. Debrot
WM Keck Science Faculty Papers
An extinct new species of Oryzomyine rodent, known since 1936 from the cave of Grot van Hato on the island of Curaçao, is described from abundant new specimens collected from owl-pellet deposits at three localities on the island.
The Age Of The Woolly Rhino From Dream Cave, Derbyshire, Uk, Donald A. Mcfarlane, Joyce Lundberg, Derek C. Ford
The Age Of The Woolly Rhino From Dream Cave, Derbyshire, Uk, Donald A. Mcfarlane, Joyce Lundberg, Derek C. Ford
WM Keck Science Faculty Papers
The Dream Cave woolly rhinoceros, Coelodonta antiquitatis, is a "classic" specimen of a "cold-stage" fossil fauna from central England. The find was illustrated and described by Dean William Buckland in his seminal tome Reliquiae Diluvianae (1823) during the first half of the 19th century, and made a significant contribution to the development of Buckland's views on the origin of extinct and extirpated fossil vertebrates. The report presents the first, albeit indirect, radiometric dates on the specimen, and argues that the animal fell into the cave just before 37,000 years BP, during the middle of Marine Isotope Stage 3 Interstadial (41 …
Disorder-Induced Desynchronization In A 2x2 Circular Josephson Junction Array, Adam S. Landsberg
Disorder-Induced Desynchronization In A 2x2 Circular Josephson Junction Array, Adam S. Landsberg
WM Keck Science Faculty Papers
Analytical results are presented which characterize the behavior of a dc-biased, two-dimensional circular array of overdamped Josephson junctions subject to increasing levels of disorder. It is shown that high levels of disorder can abruptly destroy the synchronous functioning of the array. We identify the transition boundary between synchronized and desynchronized behavior, along with the mechanism responsible for the loss of frequency locking. Comparisons with recent results for arrays with rectangular lattice geometries are described.
New Specimens Of Late Quaternary Extinct Mammals From Caves In Sanchez Ramirez Province, Dominican Republic, Donald A. Mcfarlane, Abel Vale, Keith Christenson, Joyce Lundberg, Gabriel Atilles, Stein Erik Lauritzen
New Specimens Of Late Quaternary Extinct Mammals From Caves In Sanchez Ramirez Province, Dominican Republic, Donald A. Mcfarlane, Abel Vale, Keith Christenson, Joyce Lundberg, Gabriel Atilles, Stein Erik Lauritzen
WM Keck Science Faculty Papers
During the late Quaternary, the island of Hispaniola supported one of the most diverse mammalian faunas in the West Indies. Much of this diversity was lost to extinction in the past 100,000 years, but the timing of these events is poorly known. Here we report the paleontological findings of a multidisciplinary investigation of caves in the central Dominican Republic. These findings include new 'last occurrence' dates for the rodents Isolobodon portoricensis and Brotomys cf. voratus that take these genera to the dawn of the historic era; a first record of a last-interglacial sloth, and the first report of the upper …
Late Quaternary Fossil Mammals And Last Occurrence Dates From Caves At Barahona, Puerto Rico, Donald A. Mcfarlane
Late Quaternary Fossil Mammals And Last Occurrence Dates From Caves At Barahona, Puerto Rico, Donald A. Mcfarlane
WM Keck Science Faculty Papers
Puerto Rico supported at least five genera of endemic terrestrial mammals in the late Quaternary, all of which are extinct. Whether these animals died out in the late Pleistocene, the mid-Holocene, or in post-Columbian time has not been established. This paper is the first attempt at radiometrically dating the 'last occurrences' of these taxa, together with the first unambiguous descriptions of localities reported by previous workers. Last occurrence dates for Nesophontes, Elasmodontomys and Heteropsomys are shown to be mid-Holocene and overlap with Amerindian occupation of the island. Acratocnus is known only from the late Pleistocene. No Puerto Rican taxon has …
New Caribbean Locality For The Extinct Great White Shark Carcharodon, Clare Flemming, Donald A. Mcfarlane
New Caribbean Locality For The Extinct Great White Shark Carcharodon, Clare Flemming, Donald A. Mcfarlane
WM Keck Science Faculty Papers
Carcharodon is represented by a single upper tooth (Fig. 1) which we extracted from the eroding Pliocene limestone wall, some six meters above the floor at the northern end of Darby Sink. Much of the tooth is missing, but the remaining portion includes features diagnostic of this genus. The tooth conforms in size and morphology to Carcharodon megalodon (Agassiz, 1843), an extinct great white shark.
A Second Pre-Wisconsinan Locality For The Extinct Jamaican Rodent, Clidomys (Rodentia: Heptaxodontidae), Donald A. Mcfarlane, Joyce Lundberg, Clare Flemming, Ross D. E. Macphee, Stein-Erik Lauritzen
A Second Pre-Wisconsinan Locality For The Extinct Jamaican Rodent, Clidomys (Rodentia: Heptaxodontidae), Donald A. Mcfarlane, Joyce Lundberg, Clare Flemming, Ross D. E. Macphee, Stein-Erik Lauritzen
WM Keck Science Faculty Papers
Clidomys is the most distinctive but least well known member of the late Quaternary terrestrial mammal fauna of Jamaica. Here we report the second dated locality for this genus. The Illinoisan age we report further strengthens arguments we have made elsewhere, that Clidomys represents an early - probably pre-Wisconsinan - extinction that contrasts with the growing record of Holocene extinctions in the Antilles.
The Age Of The Kirkdale Cave Palaeofauna, Donald A. Mcfarlane, Derek C. Ford
The Age Of The Kirkdale Cave Palaeofauna, Donald A. Mcfarlane, Derek C. Ford
WM Keck Science Faculty Papers
The Kirkdale Cave palaeofauna represents the original and classic 'warm', interglacial mammalian cave deposit in Britain. Although long considered to be 'Ipswichian' in age, no previous attempts to obtain radiometric dates have been recorded. Here we report a uranium-series disequilibrium date of 121,000 ± 4000 yr BP on a flowstone capping that overlay the original bone bed. The precision of the date exceeds that obtained at any other British Interglacial cave site, and permits tentative correlation with the high precision ice core records now available.
Magnetostratigraphy Of Cueva Del Aleman, Isla De Mona, Puerto Rico And The Species Duration Of Audobon's Shearwater, Bruce C. Panuska, John M. Mylroie, Darrell Armentrout, Donald A. Mcfarlane
Magnetostratigraphy Of Cueva Del Aleman, Isla De Mona, Puerto Rico And The Species Duration Of Audobon's Shearwater, Bruce C. Panuska, John M. Mylroie, Darrell Armentrout, Donald A. Mcfarlane
WM Keck Science Faculty Papers
Magnetostratigraphic analysis of deposits exposed in Cueva del Aleman shows two reversed and two normal chronozones. The lower normal polarity event is observed in a clastic dike and probably predates initial cave formation. Sediments deposited inside the cave proper show a R-N-R sequence and probably date to at least 1.8 Ma. A fossiliferous clastic dike contains normal polarity with an overlying reversed magnetozone. Audubon’s Shearwater (bird) bones occur in the dike, which is tentatively correlated with the lower N polarity zone predating cave formation. If this correlation is correct, the Audubon’s Shearwater (Puffinus lherminieri) range can be extended back to …
Jamaican Cave Vertebrates, Donald A. Mcfarlane
Jamaican Cave Vertebrates, Donald A. Mcfarlane
WM Keck Science Faculty Papers
Limestone caves in the tropics are typically associated with a more diverse assemblage of vertebrates than are caves in temperate regions. Chapman [87] for example, has reported 37 species from the caves of Gunung Mulu National Park, Sarawak, whereas Bailey [43] lists only 13 for the equally cavernicolous Guadeloupe Mountains National Park, New Mexico, USA. Twenty-eight vertebrate species have been recorded from Jamaican caves. The relative importance of the five Classes differ in these three areas as shown in Table 1 (overleaf).
Dynamical Effects Of Partial Orderings In Physical Systems, Adam S. Landsberg, Eric J. Friedman
Dynamical Effects Of Partial Orderings In Physical Systems, Adam S. Landsberg, Eric J. Friedman
WM Keck Science Faculty Papers
We demonstrate that many physical systems possess an often overlooked property known as a partial-ordering structure. The detection and analysis of this special geometric property can be crucial for understanding a system's dynamical behavior. We review here the fundamental dynamical features common to all such systems, and describe how the partial ordering imposes interesting restrictions on their possible behavior. We show, for instance, that though such systems are capable of displaying highly complex and even chaotic behaviors, most of their experimentally observable behaviors will be simple. Partial orderings are illustrated with examples drawn from many branches of physics, including solid …