carlos mendoza - Academia.edu (original) (raw)
Papers by carlos mendoza
Studia Mathematica, 2012
A bounded linear operator T on a Banach space X is called an (m, p)-isometry for a positive integ... more A bounded linear operator T on a Banach space X is called an (m, p)-isometry for a positive integer m and a real number p ≥ 1 if, for any
Studia Mathematica, 2012
A bounded linear operator T on a Banach space X is called an (m, p)-isometry for a positive integ... more A bounded linear operator T on a Banach space X is called an (m, p)-isometry for a positive integer m and a real number p ≥ 1 if, for any
We propose a simple and general model accounting for the dependence of the viscosity of a hard sp... more We propose a simple and general model accounting for the dependence of the viscosity of a hard sphere suspension at arbitrary volume fractions. The model constitutes a continuum-medium description based on a recursive-differential method where correlations between the spheres are introduced through an effective volume fraction. In contrast to other differential methods, the introduction of the effective volume fraction as the integration variable implicitly considers interactions between the spheres of the same recursive stage. The final expression for the viscosity scales with this effective volume fraction which allows to construct a master curve that contains all the experimental situations considered. The agreement of our expression for the viscosity with experiments at low- and high-shear rates and in the high-frequency limit is remarkable for all volume fractions.
We propose an improved viscosity model accounting for experiments of emulsions of two immiscible ... more We propose an improved viscosity model accounting for experiments of emulsions of two immiscible liquids at arbitrary volume fractions and low shear rates. The model is based on a recursive-differential method formulated in terms of the appropriate scaling variable which emerges from an analysis of excluded volume effects in the system. This variable, called the effective filling fraction, incorporates the geometrical information of the system which determines the maximum packing and reduces to the bare filling fraction for infinitely diluted emulsions. The agreement of our model for the viscosity with experiments is remarkable for all the range of volume fractions and viscosity ratio.
Macromolecular Chemistry and Physics
We propose a model to describe the concentration dependence of the viscosity of soft particles. W... more We propose a model to describe the concentration dependence of the viscosity of soft particles. We incorporate in a very simple way the softness of the particles into expressions originally developed for rigid spheres. This is done by introducing a concentration-dependent critical packing, which is the packing at which the suspension looses fluidity. The resultant expression reproduces with high accuracy the experimental results for suspensions of star polymers in good solvents. The model allows to explain a weak increase of the viscosity observed in the case of diblock copolymer stars suggesting that the reason for this peculiar behavior is mainly a consequence of the softness of the particles. In the semi-dilute regime, suspensions of star polymers are modeled using the Daoud-Cotton picture to complete the description in the whole concentration regime.
We consider a solid cylindrical dielectric waveguide with an extremely thin coaxial cylindrical s... more We consider a solid cylindrical dielectric waveguide with an extremely thin coaxial cylindrical shell of higher refraction index inserted on it. We calculate the propagation parameters and the band structure of this fiber as function of the contrast index, and show that there exist propagating modes whose transverse distribution of amplitudes are both oscillating and evanescent. The oscillating modes exhibit the usual dispersion relation of a standard wave guide, whereas the evanescent modes gives rise to regions for which the group velocity almost vanishes and with propagation direction opposed to the Poynting vector, as seen in metamaterials.
We report Monte Carlo simulations on the pattern formation in a binary mixture of colloidal parti... more We report Monte Carlo simulations on the pattern formation in a binary mixture of colloidal particles interacting via short ranged potentials. Such potentials consist of a hard-core square-shoulder interaction if the particles are of the same type and of a hard-core square-well if they are of different type. For 50/50 mixtures, we find a rich variety of patterns that can be grouped mainly in alternate strips each one consisting of particles of the same type or aggregates that self-assembly in a regular square lattice. For mixtures in which the are more particles of one of the species then a phase separation is observed, one of the separated phases consists only of particles of the dominant type while the other is a mixture of both types of particles.
The Canadian Journal of Chemical Engineering, 2015
ABSTRACT In a recent article [1] a “new” model for the viscosity of asphaltene solutions is propo... more ABSTRACT In a recent article [1] a “new” model for the viscosity of asphaltene solutions is proposed. The main result of that work can be summarized by the two equations. This article is protected by copyright. All rights reserved
We extend the model of a cubic quantum box proposed by Ribeiro and Latge to carry out a variation... more We extend the model of a cubic quantum box proposed by Ribeiro and Latge to carry out a variational calculation of the bindingenergy of impurities in such a structure as function of anelectric field.The binding energy of the impurities increases with the electric field. In addition, the electric field splits the energy of impurities on the faces of the box
Physical Review B, 1996
We investigate the electromagnetic instabilities of an infinite periodic superlattice consisting ... more We investigate the electromagnetic instabilities of an infinite periodic superlattice consisting of alternating spatially dispersive (nonlocal) and nonspatially dispersive (local) layers. We extend the results of Martin and Wallis [Phys. Rev. B 46, 12 448 (1992)] to include the effects of the electron thermal pressure gradient besides a dc drift current. In the case of zero pressure gradient, the dispersion
Nature Communications, 2015
Many physical systems including lattices near structural phase transitions, glasses, jammed solid... more Many physical systems including lattices near structural phase transitions, glasses, jammed solids, and bio-polymer gels have coordination numbers that place them at the edge of mechanical instability. Their properties are determined by an interplay between soft mechanical modes and thermal fluctuations. In this paper we investigate a simple square-lattice model with a φ 4 potential between next-nearest-neighbor sites whose quadratic coefficient κ can be tuned from positive negative. We show that its zero-temperature ground state for κ < 0 is highly degenerate, and we use analytical techniques and simulation to explore its finite temperature properties. We show that a unique rhombic ground state is entropically favored at nonzero temperature at κ < 0 and that the existence of a subextensive number of "floppy" modes whose frequencies vanish at κ = 0 leads to singular contributions to the free energy that render the square-to-rhombic transition first order and lead to power-law behavior of the shear modulus as a function of temperature. We expect our study to provide a general framework for the study of finite-temperature mechanical and phase behavior of other systems with a large number of floppy modes.
MRS Proceedings, 2006
ABSTRACT We present an off-lattice numerical algorithm based upon pure diffusion to construct two... more ABSTRACT We present an off-lattice numerical algorithm based upon pure diffusion to construct twodimensional star-branched polymers with one, three, six and twelve branches. We built up structures with a total of up to 30,000 monomer units. For each one of them ...
Soft Matter, 2015
A major goal in nanoscience and nanotechnology is the self-assembly of any desired complex struct... more A major goal in nanoscience and nanotechnology is the self-assembly of any desired complex structure with a system of particles interacting through simple potentials. To achieve this objective, intense experimental and theoretical efforts are currently concentrated in the development of the so-called &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;quot;patchy&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;quot; particles. Here we follow a completely different approach and introduce a very accessible model to produce a large variety of pre-programmed two-dimensional (2D) complex structures. Our model consists of a binary mixture of particles that interact through isotropic interactions that enable them to self-assemble into targeted lattices by the appropriate choice of a small number of geometrical parameters and interaction strengths. We study the system using Monte Carlo computer simulations and, despite its simplicity, we are able to self-assemble potentially useful structures such as chains, stripes, and Kagomé, twisted Kagomé, honeycomb, square, Archimedean and quasicrystalline tilings. Our model is designed in such a way that it may be implemented using discotic particles or, alternatively, using exclusively spherical particles interacting isotropically. Thus, it represents a promising strategy for bottom-up nano-fabrication.
We present a numerical algorithm to construct polydisperse star branched polymers in two and thre... more We present a numerical algorithm to construct polydisperse star branched polymers in two and three dimensions whose morphology is fully determined by diffusion. We analyze the monomer-monomer correlation function to calculate the fractal dimension of the structures. In addition, we carry out a finite-size analysis to determine the scaling properties of the radius of gyration.
We introduce an algorithm to generate two-dimensional diffusion-limited star-branched polymers (D... more We introduce an algorithm to generate two-dimensional diffusion-limited star-branched polymers (DLSP) attaching monomers successively to a central colloidal particle with any desired number of reactive sites. The proposed algorithm produces star-shaped aggregates whose final structure at relatively large distances from the central colloid has five-fold symmetry independently of the initial number of reactive sites. Therefore, the final morphology can be
Physica A-statistical Mechanics and Its Applications, 2007
We built up star-branched polymers, whose morphology is fully determined by diffusion, with p=1,3... more We built up star-branched polymers, whose morphology is fully determined by diffusion, with p=1,3,6 and 12 branches with a total of 30,000 monomer units. We investigated their structural properties by calculating the monomer–monomer correlation functions. A detailed finite size scaling analysis of the radius of gyration was also performed to determine the exponent and the corrections to scaling. From these
Studia Mathematica, 2012
A bounded linear operator T on a Banach space X is called an (m, p)-isometry for a positive integ... more A bounded linear operator T on a Banach space X is called an (m, p)-isometry for a positive integer m and a real number p ≥ 1 if, for any
Studia Mathematica, 2012
A bounded linear operator T on a Banach space X is called an (m, p)-isometry for a positive integ... more A bounded linear operator T on a Banach space X is called an (m, p)-isometry for a positive integer m and a real number p ≥ 1 if, for any
We propose a simple and general model accounting for the dependence of the viscosity of a hard sp... more We propose a simple and general model accounting for the dependence of the viscosity of a hard sphere suspension at arbitrary volume fractions. The model constitutes a continuum-medium description based on a recursive-differential method where correlations between the spheres are introduced through an effective volume fraction. In contrast to other differential methods, the introduction of the effective volume fraction as the integration variable implicitly considers interactions between the spheres of the same recursive stage. The final expression for the viscosity scales with this effective volume fraction which allows to construct a master curve that contains all the experimental situations considered. The agreement of our expression for the viscosity with experiments at low- and high-shear rates and in the high-frequency limit is remarkable for all volume fractions.
We propose an improved viscosity model accounting for experiments of emulsions of two immiscible ... more We propose an improved viscosity model accounting for experiments of emulsions of two immiscible liquids at arbitrary volume fractions and low shear rates. The model is based on a recursive-differential method formulated in terms of the appropriate scaling variable which emerges from an analysis of excluded volume effects in the system. This variable, called the effective filling fraction, incorporates the geometrical information of the system which determines the maximum packing and reduces to the bare filling fraction for infinitely diluted emulsions. The agreement of our model for the viscosity with experiments is remarkable for all the range of volume fractions and viscosity ratio.
Macromolecular Chemistry and Physics
We propose a model to describe the concentration dependence of the viscosity of soft particles. W... more We propose a model to describe the concentration dependence of the viscosity of soft particles. We incorporate in a very simple way the softness of the particles into expressions originally developed for rigid spheres. This is done by introducing a concentration-dependent critical packing, which is the packing at which the suspension looses fluidity. The resultant expression reproduces with high accuracy the experimental results for suspensions of star polymers in good solvents. The model allows to explain a weak increase of the viscosity observed in the case of diblock copolymer stars suggesting that the reason for this peculiar behavior is mainly a consequence of the softness of the particles. In the semi-dilute regime, suspensions of star polymers are modeled using the Daoud-Cotton picture to complete the description in the whole concentration regime.
We consider a solid cylindrical dielectric waveguide with an extremely thin coaxial cylindrical s... more We consider a solid cylindrical dielectric waveguide with an extremely thin coaxial cylindrical shell of higher refraction index inserted on it. We calculate the propagation parameters and the band structure of this fiber as function of the contrast index, and show that there exist propagating modes whose transverse distribution of amplitudes are both oscillating and evanescent. The oscillating modes exhibit the usual dispersion relation of a standard wave guide, whereas the evanescent modes gives rise to regions for which the group velocity almost vanishes and with propagation direction opposed to the Poynting vector, as seen in metamaterials.
We report Monte Carlo simulations on the pattern formation in a binary mixture of colloidal parti... more We report Monte Carlo simulations on the pattern formation in a binary mixture of colloidal particles interacting via short ranged potentials. Such potentials consist of a hard-core square-shoulder interaction if the particles are of the same type and of a hard-core square-well if they are of different type. For 50/50 mixtures, we find a rich variety of patterns that can be grouped mainly in alternate strips each one consisting of particles of the same type or aggregates that self-assembly in a regular square lattice. For mixtures in which the are more particles of one of the species then a phase separation is observed, one of the separated phases consists only of particles of the dominant type while the other is a mixture of both types of particles.
The Canadian Journal of Chemical Engineering, 2015
ABSTRACT In a recent article [1] a “new” model for the viscosity of asphaltene solutions is propo... more ABSTRACT In a recent article [1] a “new” model for the viscosity of asphaltene solutions is proposed. The main result of that work can be summarized by the two equations. This article is protected by copyright. All rights reserved
We extend the model of a cubic quantum box proposed by Ribeiro and Latge to carry out a variation... more We extend the model of a cubic quantum box proposed by Ribeiro and Latge to carry out a variational calculation of the bindingenergy of impurities in such a structure as function of anelectric field.The binding energy of the impurities increases with the electric field. In addition, the electric field splits the energy of impurities on the faces of the box
Physical Review B, 1996
We investigate the electromagnetic instabilities of an infinite periodic superlattice consisting ... more We investigate the electromagnetic instabilities of an infinite periodic superlattice consisting of alternating spatially dispersive (nonlocal) and nonspatially dispersive (local) layers. We extend the results of Martin and Wallis [Phys. Rev. B 46, 12 448 (1992)] to include the effects of the electron thermal pressure gradient besides a dc drift current. In the case of zero pressure gradient, the dispersion
Nature Communications, 2015
Many physical systems including lattices near structural phase transitions, glasses, jammed solid... more Many physical systems including lattices near structural phase transitions, glasses, jammed solids, and bio-polymer gels have coordination numbers that place them at the edge of mechanical instability. Their properties are determined by an interplay between soft mechanical modes and thermal fluctuations. In this paper we investigate a simple square-lattice model with a φ 4 potential between next-nearest-neighbor sites whose quadratic coefficient κ can be tuned from positive negative. We show that its zero-temperature ground state for κ < 0 is highly degenerate, and we use analytical techniques and simulation to explore its finite temperature properties. We show that a unique rhombic ground state is entropically favored at nonzero temperature at κ < 0 and that the existence of a subextensive number of "floppy" modes whose frequencies vanish at κ = 0 leads to singular contributions to the free energy that render the square-to-rhombic transition first order and lead to power-law behavior of the shear modulus as a function of temperature. We expect our study to provide a general framework for the study of finite-temperature mechanical and phase behavior of other systems with a large number of floppy modes.
MRS Proceedings, 2006
ABSTRACT We present an off-lattice numerical algorithm based upon pure diffusion to construct two... more ABSTRACT We present an off-lattice numerical algorithm based upon pure diffusion to construct twodimensional star-branched polymers with one, three, six and twelve branches. We built up structures with a total of up to 30,000 monomer units. For each one of them ...
Soft Matter, 2015
A major goal in nanoscience and nanotechnology is the self-assembly of any desired complex struct... more A major goal in nanoscience and nanotechnology is the self-assembly of any desired complex structure with a system of particles interacting through simple potentials. To achieve this objective, intense experimental and theoretical efforts are currently concentrated in the development of the so-called &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;quot;patchy&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;quot; particles. Here we follow a completely different approach and introduce a very accessible model to produce a large variety of pre-programmed two-dimensional (2D) complex structures. Our model consists of a binary mixture of particles that interact through isotropic interactions that enable them to self-assemble into targeted lattices by the appropriate choice of a small number of geometrical parameters and interaction strengths. We study the system using Monte Carlo computer simulations and, despite its simplicity, we are able to self-assemble potentially useful structures such as chains, stripes, and Kagomé, twisted Kagomé, honeycomb, square, Archimedean and quasicrystalline tilings. Our model is designed in such a way that it may be implemented using discotic particles or, alternatively, using exclusively spherical particles interacting isotropically. Thus, it represents a promising strategy for bottom-up nano-fabrication.
We present a numerical algorithm to construct polydisperse star branched polymers in two and thre... more We present a numerical algorithm to construct polydisperse star branched polymers in two and three dimensions whose morphology is fully determined by diffusion. We analyze the monomer-monomer correlation function to calculate the fractal dimension of the structures. In addition, we carry out a finite-size analysis to determine the scaling properties of the radius of gyration.
We introduce an algorithm to generate two-dimensional diffusion-limited star-branched polymers (D... more We introduce an algorithm to generate two-dimensional diffusion-limited star-branched polymers (DLSP) attaching monomers successively to a central colloidal particle with any desired number of reactive sites. The proposed algorithm produces star-shaped aggregates whose final structure at relatively large distances from the central colloid has five-fold symmetry independently of the initial number of reactive sites. Therefore, the final morphology can be
Physica A-statistical Mechanics and Its Applications, 2007
We built up star-branched polymers, whose morphology is fully determined by diffusion, with p=1,3... more We built up star-branched polymers, whose morphology is fully determined by diffusion, with p=1,3,6 and 12 branches with a total of 30,000 monomer units. We investigated their structural properties by calculating the monomer–monomer correlation functions. A detailed finite size scaling analysis of the radius of gyration was also performed to determine the exponent and the corrections to scaling. From these