130 research outputs found
Entropy Crisis, Ideal Glass Transition and Polymer Melting: Exact Solution on a Husimi Cactus
We introduce an extension of the lattice model of melting of semiflexible
polymers originally proposed by Flory. Along with a bending penalty, present in
the original model and involving three sites of the lattice, we introduce an
interaction energy that corresponds to the presence of a pair of parallel bonds
and a second interaction energy associated with the presence of a hairpin turn.
Both these new terms represent four-site interactions. The model is solved
exactly on a Husimi cactus, which approximates a square lattice. We study the
phase diagram of the system as a function of the energies. For a proper choice
of the interaction energies, the model exhibits a first-order melting
transition between a liquid and a crystalline phase. The continuation of the
liquid phase below this temperature gives rise to a supercooled liquid, which
turns continuously into a new low-temperature phase, called metastable liquid.
This liquid-liquid transition seems to have some features that are
characteristic of the critical transition predicted by the mode-coupling
theory.Comment: To be published in Physical Review E, 68 (2) (2003
Configurational Entropy and its Crisis in Metastable States: Ideal Glass Transition in a Dimer Model as a Paragidm of a Molecular Glass
We discuss the need for discretization to evaluate the configurational
entropy in a general model. We also discuss the prescription using restricted
partition function formalism to study the stationary limit of metastable
states. We introduce a lattice model of dimers as a paradigm of molecular fluid
and study metastability in it to investigate the root cause of glassy behavior.
We demonstrate the existence of the entropy crisis in metastable states, from
which it follows that the entropy crisis is the root cause underlying the ideal
glass transition in systems with particles of all sizes. The orientational
interactions in the model control the nature of the liquid-liquid transition
observed in recent years in molecular glasses.Comment: 36 pages, 9 figure
Thermodynamic Comparison and the Ideal Glass Transition of A Monatomic Systems Modeled as an Antiferromagnetic Ising Model on Husimi and Cubic Recursive Lattices of the Same Coordination Number
Two kinds of recursive lattices with the same coordination number but
different unit cells (2-D square and 3-D cube) are constructed and the
antiferromagnetic Ising model is solved exactly on them to study the stable and
metastable states. The Ising model with multi-particle interactions is designed
to represent a monatomic system or an alloy. Two solutions of the model exhibit
the crystallization of liquid, and the ideal glass transition of supercooled
liquid respectively. Based on the solutions, the thermodynamics on both
lattices was examined. In particular, the free energy, energy, and entropy of
the ideal glass, supercooled liquid, crystal, and liquid state of the model on
each lattice were calculated and compared with each other. Interactions between
particles farther away than the nearest neighbor distance are taken into
consideration. The two lattices show comparable properties on the transition
temperatures and the thermodynamic behaviors, which proves that both of them
are practical to describe the regular 3-D case, while the different effects of
the unit types are still obvious.Comment: 27 pages, 13 figure
Non-equilibrium Thermodynamics: Structural Relaxation, Fictive temperature and Tool-Narayanaswamy phenomenology in Glasses
Starting from the second law of thermodynamics applied to an isolated system
consisting of the system surrounded by an extremely large medium, we formulate
a general non-equilibrium thermodynamic description of the system when it is
out of equilibrium. We then apply it to study the structural relaxation in
glasses and establish the phenomenology behind the concept of the fictive
temperature and of the empirical Tool-Narayanaswamy equation on firmer
theoretical foundation.Comment: 20 pages, 1 figur
contact.engineering -- Create, analyze and publish digital surface twins from topography measurements across many scales
The optimization of surface finish to improve performance occurs largely
through trial and error, despite significant advancements in the relevant
science. There are three central challenges that account for this disconnect:
(1) the challenge of integration of many different types of measurement for the
same surface to capture the multi-scale nature of roughness; (2) the technical
complexity of implementing spectral analysis methods, and of applying
mechanical or numerical models to describe surface performance; (3) a lack of
consistency between researchers and industries in how surfaces are measured,
quantified, and communicated. Here we present a freely-available internet-based
application which attempts to overcome all three challenges. First, the
application enables the user to upload many different topography measurements
taken from a single surface, including using different techniques, and then
integrates all of them together to create a digital surface twin. Second, the
application calculates many of the commonly used topography metrics, such as
root-mean-square parameters, power spectral density (PSD), and autocorrelation
function (ACF), as well as implementing analytical and numerical calculations,
such as boundary element modeling (BEM) for elastic and plastic deformation.
Third, the application serves as a repository for users to securely store
surfaces, and if they choose, to share these with collaborators or even publish
them (with a digital object identifier) for all to access. The primary goal of
this application is to enable researchers and manufacturers to quickly and
easily apply cutting-edge tools for the characterization and
properties-modeling of real-world surfaces. An additional goal is to advance
the use of open-science principles in surface engineering by providing a FAIR
database where researchers can choose to publish surface measurements for all
to use.Comment: 19 pages, 6 figure
Exact correlation functions of Bethe lattice spin models in external fields
We develop a transfer matrix method to compute exactly the spin-spin
correlation functions of Bethe lattice spin models in the external magnetic
field h and for any temperature T. We first compute the correlation function
for the most general spin - S Ising model, which contains all possible
single-ion and nearest-neighbor pair interactions. This general spin - S Ising
model includes the spin-1/2 simple Ising model and the Blume-Emery-Griffiths
(BEG) model as special cases. From the spin-spin correlation functions, we
obtain functions of correlation length for the simple Ising model and BEG
model, which show interesting scaling and divergent behavior as T approaches
the critical temperature. Our method to compute exact spin-spin correlation
functions may be applied to other Ising-type models on Bethe and Bethe-like
lattices.Comment: 19 page
Spanning forests and the q-state Potts model in the limit q \to 0
We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta
J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially,
this limit gives rise to the generating polynomial of spanning forests;
physically, it provides information about the Potts-model phase diagram in the
neighborhood of (q,v) = (0,0). We have studied this model on the square and
triangular lattices, using a transfer-matrix approach at both real and complex
values of w. For both lattices, we have computed the symbolic transfer matrices
for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves
of partition-function zeros in the complex w-plane. For real w, we find two
distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp.
w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w >
w_0 we find a non-critical disordered phase, while for w < w_0 our results are
compatible with a massless Berker-Kadanoff phase with conformal charge c = -2
and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w =
w_0 we find a "first-order critical point": the first derivative of the free
energy is discontinuous at w_0, while the correlation length diverges as w
\downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0
seems to be the same for both lattices and it differs from that of the
Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1,
the leading thermal scaling dimension is x_{T,1} = 0, and the critical
exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65
Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and
forests_tri_2-9P.m. Final journal versio
Thermodynamics and structure of self-assembled networks
We study a generic model of self-assembling chains which can branch and form
networks with branching points (junctions) of arbitrary functionality. The
physical realizations include physical gels, wormlike micells, dipolar fluids
and microemulsions. The model maps the partition function of a solution of
branched, self-assembling, mutually avoiding clusters onto that of a Heisenberg
magnet in the mathematical limit of zero spin components. The model is solved
in the mean field approximation. It is found that despite the absence of any
specific interaction between the chains, the entropy of the junctions induces
an effective attraction between the monomers, which in the case of three-fold
junctions leads to a first order reentrant phase separation between a dilute
phase consisting mainly of single chains, and a dense network, or two network
phases. Independent of the phase separation, we predict the percolation
(connectivity) transition at which an infinite network is formed that partially
overlaps with the first-order transition. The percolation transition is a
continuous, non thermodynamic transition that describes a change in the
topology of the system. Our treatment which predicts both the thermodynamic
phase equilibria as well as the spatial correlations in the system allows us to
treat both the phase separation and the percolation threshold within the same
framework. The density-density correlation correlation has a usual
Ornstein-Zernicke form at low monomer densities. At higher densities, a peak
emerges in the structure factor, signifying an onset of medium-range order in
the system. Implications of the results for different physical systems are
discussed.Comment: Submitted to Phys. Rev.
Transient Vestibulopathy in Wallenberg's Syndrome: Pathologic Analysis
Objective: To report an unusual lateral medullary stroke (LMS) associated with transient unidirectional horizontal, nystagmus, and decreased horizontal vestibulo-ocular reflex (h-VOR) gain that mimicked a peripheral vestibulopathy. MRI suggested involvement of caudal medial vestibular nucleus (MVN);however, the rapid resolution of the nystagmus and improved h-VOR gain favored transient ischemia without infarction. Decreased h-VOR gain is expected with peripheral vestibular lesions within the labyrinth or superior vestibular nerve;less frequently lateral pontine strokes involving the vestibular root entry, the vestibular fascicle, or neurons within the MVN may be responsible. The h-VOR is typically normal in LMS. Methods: Clinicopathologic examination of a 61-year-old man with an acute vestibular syndrome (AVS) and left LMS who died 3 weeks after the stroke. Postmortem brainstem analysis was performed. Results: The stroke involved the lateral medulla and pontomedullary junction, near the MVN, sparing the cerebellum and pons. To explain transient vestibular findings there are two possible hypotheses;the first would be that the MVN survived the ischemic process and would be histologically intact, and the second that vestibular afferents in the horizontal semicircular canal were ischemic and recovered after the ischemic process. Neuropathological examination showed a left LMS whose extent matched that seen by imaging. Non-ocular motor signs correlated well with structures affected by the infarction. Neurons and glia within nearby MVN were spared, as predicted by the rapid normalization of the ocular motor signs. Although unlikely, the possibility of transient intralabyrinthine arteriolar ischemia cannot be excluded. Additionally, truncal lateropulsion was due to combined lateral vestibulospinal tract and lateral reticular nucleus infarction. Conclusion: LMS may rarely be associated with an AVS that either represents or mimics a peripheral vestibulopathy. To our knowledge, this is the first neuropathologic examination of the brainstem of an LMS associated with transient vestibular findings occurring in the context of an anterior/posterior (AICA/PICA) cerebellar arterial variant stroke
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Supramolecular approach to new inkjet printing inks
Electronically complementary, low molecular weight polymers that self-assemble through tunable π−π stacking interactions to form extended supramolecular polymer networks have been developed for inkjet printing applications and successfully deposited using three different printing techniques. Sequential overprinting of the complementary components results in supramolecular network formation through complexation of π-electron rich pyrenyl or perylenyl chain-ends in one component with π-electron deficient naphthalene diimide residues in a chain-folding polyimide. The complementary π−π stacked polymer blends generate strongly colored materials as a result of charge-transfer absorption bands in the visible spectrum, potentially negating the need for pigments or dyes in the ink formulation. Indeed, the final color of the deposited material can be tailored by varying the end-groups of the π-electron rich polymer component. Piezoelectric printing techniques were employed in a proof of concept study to allow characterization of the materials deposited, and a thermal inkjet printer adapted with imaging software enabled in situ analysis of the ink drops as they formed and of their physical properties. Finally, continuous inkjet printing allowed greater volumes of material to be deposited, on a variety of different substrate surfaces, and demonstrated the utility and versatility of this novel type of ink for industrial applications
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