547 research outputs found
Exact Solution of the Discrete (1+1)-dimensional RSOS Model in a Slit with Field and Wall Interactions
We present the solution of a linear Restricted Solid--on--Solid (RSOS) model
confined to a slit. We include a field-like energy, which equivalently weights
the area under the interface, and also include independent interaction terms
with both walls. This model can also be mapped to a lattice polymer model of
Motzkin paths in a slit interacting with both walls and including an osmotic
pressure. This work generalises previous work on the RSOS model in the
half-plane which has a solution that was shown recently to exhibit a novel
mathematical structure involving basic hypergeometric functions .
Because of the mathematical relationship between half-plane and slit this work
hence effectively explores the underlying -orthogonal polynomial structure
to that solution. It also generalises two other recent works: one on Dyck paths
weighted with an osmotic pressure in a slit and another concerning Motzkin
paths without an osmotic pressure term in a slit
Monte Carlo Investigation of Lattice Models of Polymer Collapse in Five Dimensions
Monte Carlo simulations, using the PERM algorithm, of interacting
self-avoiding walks (ISAW) and interacting self-avoiding trails (ISAT) in five
dimensions are presented which locate the collapse phase transition in those
models. It is argued that the appearance of a transition (at least) as strong
as a pseudo-first-order transition occurs in both models. The values of various
theoretically conjectured dimension-dependent exponents are shown to be
consistent with the data obtained. Indeed the first-order nature of the
transition is even stronger in five dimensions than four. The agreement with
the theory is better for ISAW than ISAT and it cannot be ruled out that ISAT
have a true first-order transition in dimension five. This latter difference
would be intriguing if true. On the other hand, since simulations are more
difficult for ISAT than ISAW at this transition in high dimensions, any
discrepancy may well be due to the inability of the simulations to reach the
true asymptotic regime.Comment: LaTeX file, 16 pages incl. 7 figure
Two-dimensional polymer networks at a mixed boundary: Surface and wedge exponents
We provide general formulae for the configurational exponents of an arbitrary
polymer network connected to the surface of an arbitrary wedge of the
two-dimensional plane, where the surface is allowed to assume a general mixture
of boundary conditions on either side of the wedge. We report on a
comprehensive study of a linear chain by exact enumeration, with various
attachments of the walk's ends to the surface, in wedges of angles and
, with general mixed boundary conditions.Comment: 4 pages, Latex2e, 3 figures, Eur. Phys. J. B macro
Exact Solution of Semi-Flexible and Super-Flexible Interacting Partially Directed Walks
We provide the exact generating function for semi-flexible and super-flexible
interacting partially directed walks and also analyse the solution in detail.
We demonstrate that while fully flexible walks have a collapse transition that
is second order and obeys tricritical scaling, once positive stiffness is
introduced the collapse transition becomes first order. This confirms a recent
conjecture based on numerical results. We note that the addition of an
horizontal force in either case does not affect the order of the transition. In
the opposite case where stiffness is discouraged by the energy potential
introduced, which we denote the super-flexible case, the transition also
changes, though more subtly, with the crossover exponent remaining unmoved from
the neutral case but the entropic exponents changing
First-order scaling near a second-order phase transition: Tricritical polymer collapse
The coil-globule transition of an isolated polymer has been well established
to be a second-order phase transition described by a standard tricritical O(0)
field theory. We provide compelling evidence from Monte Carlo simulations in
four dimensions, where mean-field theory should apply, that the approach to
this (tri)critical point is dominated by the build-up of first-order-like
singularities masking the second-order nature of the coil-globule transition:
the distribution of the internal energy having two clear peaks that become more
distinct and sharp as the tricritical point is approached. However, the
distance between the peaks slowly decays to zero. The evidence shows that the
position of this (pseudo) first-order transition is shifted by an amount from
the tricritical point that is asymptotically much larger than the width of the
transition region. We suggest an explanation for the apparently contradictory
scaling predictions in the literature.Comment: 4 pages, 2 figures included in tex
A self-interacting partially directed walk subject to a force
We consider a directed walk model of a homopolymer (in two dimensions) which
is self-interacting and can undergo a collapse transition, subject to an
applied tensile force. We review and interpret all the results already in the
literature concerning the case where this force is in the preferred direction
of the walk. We consider the force extension curves at different temperatures
as well as the critical-force temperature curve. We demonstrate that this model
can be analysed rigorously for all key quantities of interest even when there
may not be explicit expressions for these quantities available. We show which
of the techniques available can be extended to the full model, where the force
has components in the preferred direction and the direction perpendicular to
this. Whilst the solution of the generating function is available, its analysis
is far more complicated and not all the rigorous techniques are available.
However, many results can be extracted including the location of the critical
point which gives the general critical-force temperature curve. Lastly, we
generalise the model to a three-dimensional analogue and show that several key
properties can be analysed if the force is restricted to the plane of preferred
directions.Comment: 35 pages, 14 figure
Four-dimensional polymer collapse II: Pseudo-First-Order Transition in Interacting Self-avoiding Walks
In earlier work we provided the first evidence that the collapse, or
coil-globule, transition of an isolated polymer in solution can be seen in a
four-dimensional model. Here we investigate, via Monte Carlo simulations, the
canonical lattice model of polymer collapse, namely interacting self-avoiding
walks, to show that it not only has a distinct collapse transition at finite
temperature but that for any finite polymer length this collapse has many
characteristics of a rounded first-order phase transition. However, we also
show that there exists a `-point' where the polymer behaves in a simple
Gaussian manner (which is a critical state), to which these finite-size
transition temperatures approach as the polymer length is increased. The
resolution of these seemingly incompatible conclusions involves the argument
that the first-order-like rounded transition is scaled away in the
thermodynamic limit to leave a mean-field second-order transition. Essentially
this happens because the finite-size \emph{shift} of the transition is
asymptotically much larger than the \emph{width} of the pseudo-transition and
the latent heat decays to zero (algebraically) with polymer length. This
scenario can be inferred from the application of the theory of Lifshitz,
Grosberg and Khokhlov (based upon the framework of Lifshitz) to four
dimensions: the conclusions of which were written down some time ago by
Khokhlov. In fact it is precisely above the upper critical dimension, which is
3 for this problem, that the theory of Lifshitz may be quantitatively
applicable to polymer collapse.Comment: 30 pages, 14 figures included in tex
Is Kinetic Growth Walk equivalent to canonical Self Avoiding Walk?
We present a Monte Carlo study of Kinetic Growth Walk on square as well as
triangular lattice to show that it is not equivalent to canonical Self Avoiding
Walk.Comment: Eight pages LaTex file, three eps figures; Eq.(3) is corrected now.
Physica A (accepted
Physicochemical Characterization and Dissolution Studies of Solid Dispersions of Clotrimazole with Pluronic F127
Purpose: To evaluate the physicochemical properties of clotrimazole (CLT) solid dispersion with Pluronic F127 (PLU).Methods: Solid dispersions of the antifungal drug, clotrimazole, were prepared with Pluronic F127 using grinding (PM) and fusion (FUS) methods. Physicochemical characterization of the dispersions were performed using differential scanning calorimetry (DSC), x-ray powder diffraction (XRPD) and Fourier transform infrared spectroscopy (FTIR). In vitro drug release was carried out using the rotating disc method.Results: These studies showed that there was no chemical interaction between CLT and PLU. Release studies on the SDs showed a significant (> 90-fold) improvement in dissolution rate compared to pure CLT. The greatest increase in dissolution (< 80 %) was observed for the solid dispersion (CLT/PLU) prepared by FUS in the ratio 60:40 % w/w.Conclusion: The results demonstrate that the developed solid dispersion system is a suitable approach for enhancing the dissolution rate of CLT.Keywords: Clotrimazole, Pluronic F127, Solid dispersion, Dissolution, Differential scanning calorimetry, Phase diagra
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