A continuum model of melt pond evolution on Arctic sea ice

[1] During the Northern Hemisphere summer, absorbed solar radiation melts snow and the upper surface of Arctic sea ice to generate meltwater that accumulates in ponds. The melt ponds reduce the albedo of the sea ice cover during the melting season, with a significant impact on the heat and mass budget of the sea ice and the upper ocean. We have developed a model, designed to be suitable for inclusion into a global circulation model (GCM), which simulates the formation and evolution of the melt pond cover. In order to be compatible with existing GCM sea ice models, our melt pond model builds upon the existing theory of the evolution of the sea ice thickness distribution. Since this theory does not describe the topography of the ice cover, which is crucial to determining the location, extent, and depth of individual ponds, we have needed to introduce some assumptions. We describe our model, present calculations and a sensitivity analysis, and discuss our results.

Psychotic-like experiences in a community sample of adolescents: implications for the continuum model of psychosis and prediction of schizophrenia

Studies conducted in community samples suggest that psychotic-like experiences are common in the general population, leading to suggestions that they are either variations of normal personality or are different expressions of underlying vulnerability to psychotic disorder. Different types of psychotic symptoms may exist, some being normal variants and some having implications for mental health and functioning. The aim of the present study was to determine if different subtypes of psychotic-like experiences could be identified in a community sample of adolescents and to investigate if particular subtypes were more likely to be associated with psychosocial difficulties, that is, distress, depression and poor functioning, than other subtypes. Eight hundred and seventy-five Year 10 students from 34 schools participated in a cross-sectional survey that measured psychotic-like experiences using the Community Assessment of Psychic Experiences; depression using the Centre for Epidemiologic Studies Depression Scale; and psychosocial functioning using the Revised Multidimensional Assessment of Functioning Scale. Factor analysis was conducted to identify any subtypes of psychotic experiences. Four subtypes of psychotic-like experiences were identified: Bizarre Experiences, Perceptual Abnormalities, Persecutory Ideas, and Magical Thinking. Intermittent, infrequent psychotic experiences were common, but frequent experiences were not. Bizarre Experiences, Perceptual Abnormalities and Persecutory Ideas were strongly associated with distress, depression and poor functioning. Magical Thinking was only weakly associated with these variables. Overall these findings may suggest that infrequent psychotic-like experiences are unlikely to be a specific risk factor for onset of a psychotic disorder in community samples. Given that the different subtypes had varying associations with current difficulties it is suggested that not all subtypes confer the same risk for onset of psychotic disorder and poor outcome. Bizarre Experiences, Perceptual Abnormalities and Persecutory Ideas may represent expressions of underlying vulnerability to psychotic disorder, but Magical Thinking may be a normal personality variant.

Fluid dynamics of air in a packed bed: velocity profiles and the continuum model assumption

Air flow through packed beds was analyzed experimentally under conditions ranging from those that reinforce the effect of the wall on the void fraction to those that minimize it. The packing was spherical particles, with a tube-to-particle diameter ratio (D/dp) between 3 and 60. Air flow rates were maintained between 1.3 and 4.44 m3/min, and gas velocity was measured with a Pitot tube positioned above the bed exit. Measurements were made at various radial and angular coordinate values, allowing the distribution of air flow across the bed to be described in detail. Comparison of the experimentally observed radial profiles with those derived from published equations revealed that at high D/dp ratios the measured and calculated velocity profiles behaved similarly. At low ratios, oscillations in the velocity profiles agreed with those in the voidage profiles, signifying that treating the porous medium as a continuum medium is questionable in these cases.

A new continuum model for traffic flow. Final report.

Transportation Department, Office of University Research, Washington, D.C.

A new continuum model for traffic flow /

"Final report under contract DOT-RD-82018."

Aggregation and caking processes of granular materials:continuum model and simulation with application to sugar

Aggregation and caking of particles are common severe problems in many operations and processing of granular materials, where granulated sugar is an important example. Prevention of aggregation and caking of granular materials requires a good understanding of moisture migration and caking mechanisms. In this paper, the modeling of solid bridge formation between particles is introduced, based on moisture migration of atmospheric moisture into containers packed with granular materials through vapor evaporation and condensation. A model for the caking process is then developed, based on the growth of liquid bridges (during condensation), and their hardening and subsequent creation of solid bridges (during evaporation). The predicted caking strengths agree well with some available experimental data on granulated sugar under storage conditions.

Continuum Double Exchange Model

We present a continuum model for doped manganites which consist of two species of quantum spin-1 / 2 fermions interacting with classical spin fields. The phase structure at zero temperature turns out to be considerably rich: antiferromagnetic insulator, antiferromagnetic two band conducting, canted two band conducting, canted one band conducting, and ferromagnetic one band conducting phases are identified, all of them being stable against phase separation. There are also regions in the phase diagram where phase separation occurs

A model for mesoscale patterns in motile populations

Experimental observations of cell migration often describe the presence of mesoscale patterns within motile cell populations. These patterns can take the form of cells moving as aggregates or in chain-like formation. Here we present a discrete model capable of producing mesoscale patterns. These patterns are formed by biasing movements to favor a particular configuration of agent–agent attachments using a binding function f(K), where K is the scaled local coordination number. This discrete model is related to a nonlinear diffusion equation, where we relate the nonlinear diffusivity D(C) to the binding function f. The nonlinear diffusion equation supports a range of solutions which can be either smooth or discontinuous. Aggregation patterns can be produced with the discrete model, and we show that there is a transition between the presence and absence of aggregation depending on the sign of D(C). A combination of simulation and analysis shows that both the existence of mesoscale patterns and the validity of the continuum model depend on the form of f. Our results suggest that there may be no formal continuum description of a motile system with strong mesoscale patterns.

A hybrid model for studying spatial aspects of infectious diseases

We consider a hybrid model, created by coupling a continuum and an agent-based model of infectious disease. The framework of the hybrid model provides a mechanism to study the spread of infection at both the individual and population levels. This approach captures the stochastic spatial heterogeneity at the individual level, which is directly related to deterministic population level properties. This facilitates the study of spatial aspects of the epidemic process. A spatial analysis, involving counting the number of infectious agents in equally sized bins, reveals when the spatial domain is nonhomogeneous.

Continuum mechanics modelling of microfilament networks with different architectures based on molecular investigation of single F-actin

The actin microfilament plays a critical role in many cellular processes including embryonic development, wound healing, immune response, and tissue development. It is commonly organized in the form of networks whose mechanical properties change with changes in their architecture due to cell evolution processes. This paper presents a new nonlinear continuum mechanics model of single filamentous actin (F-actin) that is based on nanoscale molecular simulations. Following this continuum model of the single F-actin, mechanical properties of differently architected lamellipodia are studied. The results provide insight that can contribute to the understanding of the cell edge motions of living cells.

Molecular expression for dielectric friction on a rotating dipole: Reduction to the continuum theory

Recently we presented a microscopic expression for dielectric friction on a rotating dipole. This expression has a rather curious structure, involving the contributions of the transverse polarization modes of the solvent and also of the molecular length scale processes. It is shown here that under proper limiting conditions, this expression reduces exactly to the classical continuum model expression of Nee and Zwanzig [J. Chem. Phys. 52, 6353 (1970)]. The derivation requires the use of the asymptotic form of the orientation‐dependent total pair correlation function, the neglect of the contributions of translational modes of the solvent, and also the use of the limit that the size of the solvent molecules goes to zero. Thus, the derivation can be important in understanding the validity of the continuum model and can also help in explaining the results of a recent computer simulation study of dielectric relaxation in a Brownian dipolar lattice.

A model for heat transfer in a honey bee swarm

A swarm is a temporary structure formed when several thousand honey bees leave their hive and settle on some object such as the branch of a tree. They remain in this position until a suitable site for a new home is located by the scout bees. A continuum model based on heat conduction and heat generation is used to predict temperature profiles in swarms. Since internal convection is neglected, the model is applicable only at low values of the ambient temperature T-a. Guided by the experimental observations of Heinrich (1981a-c, J. Exp. Biol. 91, 25-55; Science 212, 565-566; Sci. Am. 244, 147-160), the analysis is carried out mainly for non-spherical swarms. The effective thermal conductivity is estimated using the data of Heinrich (1981a, J. Exp. Biol. 91, 25-55) for dead bees. For T-a = 5 and 9 degrees C, results based on a modified version of the heat generation function due to Southwick (1991, The Behaviour and Physiology of Bees, PP 28-47. C.A.B. International, London) are in reasonable agreement with measurements. Results obtained with the heat generation function of Myerscough (1993, J. Theor. Biol. 162, 381-393) are qualitatively similar to those obtained with Southwick's function, but the error is more in the former case. The results suggest that the bees near the periphery generate more heat than those near the core, in accord with the conjecture of Heinrich (1981c, Sci. Am. 244, 147-160). On the other hand, for T-a = 5 degrees C, the heat generation function of Omholt and Lonvik (1986, J. Theor. Biol. 120, 447-456) leads to a trivial steady state where the entire swarm is at the ambient temperature. Therefore an acceptable heat generation function must result in a steady state which is both non-trivial and stable with respect to small perturbations. Omholt and Lonvik's function satisfies the first requirement, but not the second. For T-a = 15 degrees C, there is a considerable difference between predicted and measured values, probably due to the neglect of internal convection in the model.

Elasto-plastic analysis of jointed rocks using discrete continuum and equivalent continuum approaches

Results from elasto-plastic numerical simulations of jointed rocks using both the equivalent continuum and discrete continuum approaches are presented, and are compared with experimental measurements. Initially triaxial compression tests on different types of rocks with wide variation in the uniaxial compressive strength are simulated using both the approaches and the results are compared. The applicability and relative merits and limitations of both the approaches for the simulation of jointed rocks are discussed. It is observed that both the approaches are reasonably good in predicting the real response. However, the equivalent continuum approach has predicted somewhat higher stiffness values at low strains. Considering the modelling effort involved in case of discrete continuum approach, for problems with complex geometry, it is suggested that a proper equivalent continuum model can be used, without compromising much on the accuracy of the results. Then the numerical analysis of a tunnel in Japan is taken up using the continuum approach. The deformations predicted are compared well against the field measurements and the predictions from discontinuum analysis. (C) 2012 Elsevier Ltd. All rights reserved.