1,083 research outputs found
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 and
channels and examine the possibility of a superconducting state with mixed
and symmetry of the gap function. We show that both in the weak coupling
limit and at strong coupling, a mixed 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
symmetry state at any coupling.Comment: 3 figures attached in uuencoded gzipped file
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
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
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
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