scholarly journals Collaboration between HPMC and NaCMC in order to Reach the Polymer Critical Point in Theophylline Hydrophilic Matrices

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
L. Contreras ◽  
L. M. Melgoza ◽  
A. Aguilar-de-Leyva ◽  
I. Caraballo
Keyword(s):  
Percolation Threshold ◽  
Critical Point ◽  
Critical Points ◽  
Percolation Theory ◽  
Minimum Concentration ◽  
Hydrophilic Matrices ◽  
Gel Layer ◽  
The Matrix ◽  
Effective Collaboration ◽  
First Time

Percolation theory has been applied in order to study the existence of critical points as well as the possibility to find a “combined percolation threshold” for ternary hydrophilic matrices prepared with HPMC, NaCMC, and theophylline. For this purpose, different batches of ternary as well as binary hydrophilic matrices have been prepared. Critical points have been found for binary hydrophilic matrices between 21.5 and 31.3% (v/v) of HPMC and between 39 and 54% (v/v) of NaCMC, respectively. In a previous work carried out with the same polymers but a much more soluble drug (KCl), it was demonstrated the existence of a partial collaboration between the polymers in order to establish the gel layer. In this work, it has been observed for the first time the need of a minimum concentration of one of the matrix-forming polymer (between 10 and 20% v/v, approximately) for establishing an effective collaboration.

scholarly journals Constraints on quasinormal modes and bounds for critical points from pole-skipping

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Navid Abbasi ◽  
Matthias Kaminski
Keyword(s):  
Critical Points ◽  
Thermal State ◽  
Quasinormal Modes ◽  
Scalar Perturbation ◽  
Black Brane ◽  
Massive Scalar ◽  
Dual Operator ◽  
Conformal Dimension ◽  
Scalar Operator ◽  
First Time

Abstract We consider a holographic thermal state and perturb it by a scalar operator whose associated real-time Green’s function has only gapped poles. These gapped poles correspond to the non-hydrodynamic quasinormal modes of a massive scalar perturbation around a Schwarzschild black brane. Relations between pole-skipping points, critical points and quasinormal modes in general emerge when the mass of the scalar and hence the dual operator dimension is varied. First, this novel analysis reveals a relation between the location of a mode in the infinite tower of quasinormal modes and the number of pole-skipping points constraining its dispersion relation at imaginary momenta. Second, for the first time, we consider the radii of convergence of the derivative expansions about the gapped quasinormal modes. These convergence radii turn out to be bounded from above by the set of all pole-skipping points. Furthermore, a transition between two distinct classes of critical points occurs at a particular value for the conformal dimension, implying close relations between critical points and pole-skipping points in one of those two classes. We show numerically that all of our results are also true for gapped modes of vector and tensor operators.

Optimization of thermal conductivity in composites loaded with the solid-solid phase-change materials

2018 ◽  
Vol 25 (6) ◽  
pp. 1157-1165
Author(s):  
Taoufik Mnasri ◽  
Adel Abbessi ◽  
Rached Ben Younes ◽  
Atef Mazioud
Keyword(s):  
Thermal Conductivity ◽  
Phase Change ◽  
Phase Change Materials ◽  
Solid Phase ◽  
Spherical Inclusions ◽  
First Case ◽  
The Matrix ◽  
Composite Conductivity ◽  
First Time

AbstractThis work focuses on identifying the thermal conductivity of composites loaded with phase-change materials (PCMs). Three configurations are studied: (1) the PCMs are divided into identical spherical inclusions arranged in one plane, (2) the PCMs are inserted into the matrix as a plate on the level of the same plane of arrangement, and (3) the PCMs are divided into identical spherical inclusions arranged periodically in the whole matrix. The percentage PCM/matrix is fixed for all cases. A comparison among the various situations is made for the first time, thus providing a new idea on how to insert PCMs into composite matrices. The results show that the composite conductivity is the most important consideration in the first case, precisely when the arrangement plane is parallel with the flux and diagonal to the entry face. In the present work, we are interested in exploring the solid-solid PCMs. The PCM polyurethane and a wood matrix are particularly studied.

scholarly journals Characterization of percolation behavior in conductor–dielectric 0-3 composites

2014 ◽  
Vol 04 (04) ◽  
pp. 1450035 ◽  
Author(s):  
Lin Zhang ◽  
Patrick Bass ◽  
Zhi-Min Dang ◽  
Z.-Y. Cheng
Keyword(s):  
Dielectric Constant ◽  
Percolation Threshold ◽  
Frequency Dependence ◽  
Experimental Results ◽  
Effective Dielectric Constant ◽  
Filler Concentration ◽  
Percolation Behavior ◽  
The Matrix ◽  
The Relationship

The equation ε eff ∝ (ϕc - ϕ)-s which shows the relationship between effective dielectric constant (εeff) and the filler concentration (φ), is widely used to determine the percolation behavior and obtain parameters, such as percolation threshold φc and the power constant s in conductor–dielectric composites (CDCs). Six different systems of CDCs were used to check the expression by fitting experimental results. It is found that the equation can fit the experimental results at any frequency. However, it is found that the fitting constants do not reflect the real percolation behavior of the composites. It is found that the dielectric constant is strongly dependent on the frequency, which is mainly due to the fact that the frequency dependence of the dielectric constant for the composites close to φc is almost independent of the matrix.

scholarly journals LMI-Based Stability Criterion of Impulsive T-S Fuzzy Dynamic Equations via Fixed Point Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Ruofeng Rao ◽  
Zhilin Pu
Keyword(s):  
Fixed Point ◽  
Stability Criterion ◽  
High Efficiency ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Linear Matrix ◽  
The Matrix ◽  
Matrix Exponential Function ◽  
Takagi Sugeno ◽  
First Time

By formulating a contraction mapping and the matrix exponential function, the authors apply linear matrix inequality (LMI) technique to investigate and obtain the LMI-based stability criterion of a class of time-delay Takagi-Sugeno (T-S) fuzzy differential equations. To the best of our knowledge, it is the first time to obtain the LMI-based stability criterion derived by a fixed point theory. It is worth mentioning that LMI methods have high efficiency and other advantages in largescale engineering calculations. And the feasibility of LMI-based stability criterion can efficiently be computed and confirmed by computer Matlab LMI toolbox. At the end of this paper, a numerical example is presented to illustrate the effectiveness of the proposed methods.

Phase space correspondence between Jordan and Einstein frames

2021 ◽  
pp. 2150087
Author(s):  
Amin Salehi
Keyword(s):  
Phase Space ◽  
Critical Point ◽  
Critical Points ◽  
Dynamical Behavior ◽  
Cosmological Parameters ◽  
Jordan Frame ◽  
Field Equations ◽  
Theories Of Gravity ◽  
The Stability ◽  
Jordan And Einstein Frames

Scalar–tensor theories of gravity can be formulated in the Einstein frame or in the Jordan frame (JF) which are related with each other by conformal transformations. Although the two frames describe the same physics and are equivalent, the stability of the field equations in the two frames is not the same. Here, we implement dynamical system and phase space approach as a robustness tool to investigate this issue. We concentrate on the Brans–Dicke theory in a Friedmann–Lemaitre–Robertson–Walker universe, but the results can easily be generalized. Our analysis shows that while there is a one-to-one correspondence between critical points in two frames and each critical point in one frame is mapped to its corresponds in another frame, however, stability of a critical point in one frame does not guarantee the stability in another frame. Hence, an unstable point in one frame may be mapped to a stable point in another frame. All trajectories between two critical points in phase space in one frame are different from their corresponding in other ones. This indicates that the dynamical behavior of variables and cosmological parameters is different in two frames. Hence, for those features of the study, which focus on observational measurements, we must use the JF where experimental data have their usual interpretation.

Percolation Theory Applied to Study the Effect of Shape and Size of the Filler Particles in Thermal Interface Materials

2000 ◽  
Author(s):  
Amit Devpura ◽  
Patrick E. Phelan ◽  
Ravi S. Prasher
Keyword(s):  
Percolation Theory ◽  
Flip Chip ◽  
Filler Concentration ◽  
Thermal Interface Materials ◽  
Thermal Interface ◽  
Chip Technology ◽  
The Matrix ◽  
Different Shapes ◽  
Filler Particles ◽  
Interface Materials

Abstract An important aspect in electronic packaging is the heat dissipation. Flip-chip technology is widely being used to increase the rate of heat transfer from the chip. A method to further enhance the thermal conductivity is by the use of a thermal interface material between the device and the heat sink attached to it in the flip-chip technology. Percolation theory holds a key to understanding the behavior of thermal interface materials. Percolation, used widely in electrical engineering, is a physical phenomenon in which the highly conducting particles distributed randomly in the matrix form at least one continuous chain connecting the opposite faces of the matrix. This phenomenon was simulated using the matrix method, to study the effect of different shapes and size of the filler particles. The different shapes considered were spherical, vertical or horizontal rods, and flakes in horizontal or vertical orientation. The effect of the size of these particles was also examined. The results indicate that the composites with particles having the largest side in the direction of heat flow will always have a better conductivity than the particles oriented normal to it. Also, from the results, we can choose the best filler size in the composite if we know the filler concentration we are aiming at.

Graphite/UPE Nanocomposite: Transport, Thermal, Mechanical and Viscoelastic Properties

2019 ◽  
Vol 23 ◽  
pp. 201-212
Author(s):  
Shivkumari Panda ◽  
Dibakar Behera ◽  
Tapan Kumar Bastia
Keyword(s):  
Transport Properties ◽  
Unsaturated Polyester ◽  
Homogeneous Distribution ◽  
Thermo Gravimetric ◽  
New Class ◽  
The Matrix ◽  
Novel Method ◽  
Water Transport Properties ◽  
First Time

This chapter presents the preparation and characterization of some unique properties of nanocomposites by dispersing graphite flakes in commercial unsaturated polyester (UPE) matrix. The composite was prepared by a novel method with the use of solvent swelling technique. Three different specimens of UPE/graphite nanocomposites were fabricated with addition of 1, 2 and 3 wt% of graphite flakes. Except mechanical, viscoelastic and thermo gravimetric properties, transport properties like electrical conductivity, thermal conductivity and water transport properties were studied for the first time. Graphite flakes propose enhanced properties to the composites suggesting homogeneous distribution of the nanofiller in the matrix and strong interaction with the matrix. 2wt% nanofiller loading showed superior essential characteristics and after that the properties reduced may be due to the nucleating tendency of the nanofiller particles. The XRD pattern showed the compatibility of the graphite flakes by introducing a peak around 26.550 in the nanocomposites. SEM Properties are also in agreement with the compatibility. Nanocomposite with 2wt% graphite also showed remarkable enhancement in transport, mechanical, viscoelastic and thermo gravimetric properties. So by introduction of a small quantity of graphite endow the new class of multiphase nanocomposites with inimitable structure and tremendous application.

scholarly journals Global Phase Portrait and Bifurcation Diagram for a Multi-Parametric Linear System

2020 ◽  
Vol 55 (4) ◽  
Author(s):  
Jorge Rodríguez Contreras ◽  
Alberto Reyes Linero ◽  
Juliana Vargas Sánchez
Keyword(s):  
Linear System ◽  
Critical Point ◽  
Phase Portrait ◽  
Bifurcation Diagram ◽  
Critical Points ◽  
Global Dynamics ◽  
Parametric Surfaces ◽  
Critical Points At Infinity ◽  
Global Phase Portrait ◽  
The Stability

The goal of this article is to conduct a global dynamics study of a linear multiparameter system (real parameters (a,b,c) in R^3); for this, we take the different changes that these parameters present. First, we find the different parametric surfaces in which the space is divided, where the stability of the critical point is defined; we then create a bifurcation diagram to classify the different bifurcations that appear in the system. Finally, we determine and classify the critical points at infinity, considering the canonical shape of the Poincaré sphere, and thus, obtain a global phase portrait of the multiparametric linear system.

scholarly journals Explore the Effects of Fertilization on Polyphenols Content in Autumn of Forages from Hill Permanent Grassland by Principal Component & Classifications Analysis

2011 ◽  
Vol 68 (1) ◽  
Author(s):  
Monica HARMANESCU
Keyword(s):  
Colorimetric Method ◽  
Principal Component ◽  
Floristic Composition ◽  
Classification Analysis ◽  
Permanent Grassland ◽  
Different Types ◽  
The Matrix ◽  
Chemometric Techniques ◽  
First Time

Principal Components and Classification Analysis (PC&CA) represents one of the most utilised multivariate chemometric techniques, having the advantage to use many measurements for a single sample in the same time, being recommended for understanding better the complexity of one phenomenon. The aim of this paper was to use PC&CA to study the effects of different types of fertilizers on polyphenols content of forages harvested in autumn from permanent grassland. Gravimetrically was established the matrix of floristic composition. The experimental field was fertilized first time in 2003, organic and/or NPK mineral. The determination of polyphenols contents was made using UV-VIS SPECORD 205 spectrophotometer, in conformity to chemical Folin and Ciocalteu colorimetric method. The highest polyphenols content was identified in forages from unfertilized variant (108 µM gallic acid/g). PC&CA can be a useful tool in describing the modification of polyphenols contents of forages under the effects of organic and/or mineral fertilisation of permanent grassland.

Matrix Valued Orthogonal Polynomials on the Unit Circle: Some Extensions of the Classical Theory

2009 ◽  
Vol 52 (1) ◽  
pp. 95-104 ◽  
Author(s):  
L. Miranian
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Classical Theory ◽  
Recurrence Relations ◽  
Matrix Representation ◽  
The Matrix ◽  
Classical Subject ◽  
First Time

AbstractIn the work presented below the classical subject of orthogonal polynomials on the unit circle is discussed in the matrix setting. An explicit matrix representation of the matrix valued orthogonal polynomials in terms of the moments of the measure is presented. Classical recurrence relations are revisited using the matrix representation of the polynomials. The matrix expressions for the kernel polynomials and the Christoffel–Darboux formulas are presented for the first time.

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