A mathematical theorem as the basis for the second law: Thomson's formulation applied to equilibrium

There are several formulations of the second law, and they may, in principle, have different domains of validity. Here a simple mathematical theorem is proven which serves as the most general basis for the second law, namely the Thomson formulation (`cyclic changes cost energy'), applied to equilibrium. This formulation of the second law is a property akin to particle conservation (normalization of the wavefunction). It has been stricktly proven for a canonical ensemble, and made plausible for a micro-canonical ensemble. As the derivation does not assume time-inversion-invariance, it is applicable to situations where persistent current occur. This clear-cut derivation allows to revive the ``no perpetuum mobile in equilibrium'' formulation of the second law and to criticize some assumptions which are widespread in literature. The result puts recent results devoted to foundations and limitations of the second law in proper perspective, and structurizes this relatively new field of research.Comment: Revised version. Redundant assumption omitted. Microcanonical ensemble included. Reference added. 7 pages revte

Constraint methods for determining pathways and free energy of activated processes

Activated processes from chemical reactions up to conformational transitions of large biomolecules are hampered by barriers which are overcome only by the input of some free energy of activation. Hence, the characteristic and rate-determining barrier regions are not sufficiently sampled by usual simulation techniques. Constraints on a reaction coordinate r have turned out to be a suitable means to explore difficult pathways without changing potential function, energy or temperature. For a dense sequence of values of r, the corresponding sequence of simulations provides a pathway for the process. As only one coordinate among thousands is fixed during each simulation, the pathway essentially reflects the system's internal dynamics. From mean forces the free energy profile can be calculated to obtain reaction rates and insight in the reaction mechanism. In the last decade, theoretical tools and computing capacity have been developed to a degree where simulations give impressive qualitative insight in the processes at quantitative agreement with experiments. Here, we give an introduction to reaction pathways and coordinates, and develop the theory of free energy as the potential of mean force. We clarify the connection between mean force and constraint force which is the central quantity evaluated, and discuss the mass metric tensor correction. Well-behaved coordinates without tensor correction are considered. We discuss the theoretical background and practical implementation on the example of the reaction coordinate of targeted molecular dynamics simulation. Finally, we compare applications of constraint methods and other techniques developed for the same purpose, and discuss the limits of the approach

Simulations of cubic-tetragonal ferroelastics

We study domain patterns in cubic-tetragonal ferroelastics by solving numerically equations of motion derived from a Landau model of the phase transition, including dissipative stresses. Our system sizes, of up to 256^3 points, are large enough to reveal many structures observed experimentally. Most patterns found at late stages in the relaxation are multiply banded; all three tetragonal variants appear, but inequivalently. Two of the variants form broad primary bands; the third intrudes into the others to form narrow secondary bands with the hosts. On colliding with walls between the primary variants, the third either terminates or forms a chevron. The multipy banded patterns, with the two domain sizes, the chevrons and the terminations, are seen in the microscopy of zirconia and other cubic-tetragonal ferroelastics. We examine also transient structures obtained much earlier in the relaxation; these show the above features and others also observed in experiment.Comment: 7 pages, 6 colour figures not embedded in text. Major revisions in conten

Mixed symmetry superconductivity in two-dimensional Fermi liquids

We consider a 2D isotropic Fermi liquid with attraction in both $s$ and $d$ channels and examine the possibility of a superconducting state with mixed $s$ and $d$ symmetry of the gap function. We show that both in the weak coupling limit and at strong coupling, a mixed $s+id$ symmetry state is realized in a certain range of interaction. Phase transitions between the mixed and the pure symmetry states are second order. We also show that there is no stable mixed $s+d$ symmetry state at any coupling.Comment: 3 figures attached in uuencoded gzipped file

Partially Annealed Disorder and Collapse of Like-Charged Macroions

Charged systems with partially annealed charge disorder are investigated using field-theoretic and replica methods. Charge disorder is assumed to be confined to macroion surfaces surrounded by a cloud of mobile neutralizing counterions in an aqueous solvent. A general formalism is developed by assuming that the disorder is partially annealed (with purely annealed and purely quenched disorder included as special cases), i.e., we assume in general that the disorder undergoes a slow dynamics relative to fast-relaxing counterions making it possible thus to study the stationary-state properties of the system using methods similar to those available in equilibrium statistical mechanics. By focusing on the specific case of two planar surfaces of equal mean surface charge and disorder variance, it is shown that partial annealing of the quenched disorder leads to renormalization of the mean surface charge density and thus a reduction of the inter-plate repulsion on the mean-field or weak-coupling level. In the strong-coupling limit, charge disorder induces a long-range attraction resulting in a continuous disorder-driven collapse transition for the two surfaces as the disorder variance exceeds a threshold value. Disorder annealing further enhances the attraction and, in the limit of low screening, leads to a global attractive instability in the system.Comment: 21 pages, 2 figure

Enhancing Osteogenic Differentiation of Mouse Embryonic Stem Cells by Nanofibers

Controlled differentiation of embryonic stem cells (ESC) is necessary to their use as a cell source for tissue engineering or regeneration. To date, most studies have concentrated on chemical cues to direct ESC differentiation. However, during normal embryonic development, multiple factors beyond chemical cues play a role, including the extracellular matrix (ECM) in bone development. In this study, we use nanofibrous (NF) matrices to mimic the morphology of the ECM to examine the contribution of the ECM morphology to the differentiation of mouse ESC. After 12h of differentiation culture, mouse ESC form protrusions interacting with NF matrices, while they appear not to interact with flat films. Immunofluorescence staining after 26 days of differentiation culture indicates a greater degree of differentiation for mouse ESC on NF matrices compared to flat films. Polymerase chain reaction results, also, show greater degree of osteogenic differentiation on NF matrices compared to flat films when osteogenic supplements are added to the culture. Overall, these results demonstrate that NF morphology contributes to the controlled differentiation of mouse ESC.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/78135/1/ten.tea.2008.0227.pd

Possible Z-width probe of a "brane-world" scenario for neutrino masses

The possibility that the accurately known value of the Z width might furnish information about the coupling of two neutrinos to the Majoron (Nambu-Goldstone boson of spontaneous lepton number violation) is proposed and investigated in detail. Both the "ordinary" case and the case in which one adopts a "brane" world picture with the Majoron free to travel in extra dimensions are studied. Bounds on the dimensionless coupling constants are obtained, allowing for any number of extra dimensions and any intrinsic mass scale. These bounds may be applied to a variety of different Majoron models. If a technically natural see-saw model is adopted, the predicted coupling constants are far below these upper bounds. In addition, for this natural model, the effect of extra dimensions is to decrease the predicted partial Z width, the increase due to many Kaluza-Klein excitations being compensated by the decrease of their common coupling constant.Comment: RevTeX, 12 pages, 3 figure

Integrating fluctuations into distribution of resources in transportation networks

We propose a resource distribution strategy to reduce the average travel time in a transportation network given a fixed generation rate. Suppose that there are essential resources to avoid congestion in the network as well as some extra resources. The strategy distributes the essential resources by the average loads on the vertices and integrates the fluctuations of the instantaneous loads into the distribution of the extra resources. The fluctuations are calculated with the assumption of unlimited resources, where the calculation is incorporated into the calculation of the average loads without adding to the time complexity. Simulation results show that the fluctuation-integrated strategy provides shorter average travel time than a previous distribution strategy while keeping similar robustness. The strategy is especially beneficial when the extra resources are scarce and the network is heterogeneous and lowly loaded.Comment: 14 pages, 4 figure