arXiv subjects

J. A. Santiago

Publications and source records attributed to J. A. Santiago.

At least 19 recordsLinked to original sources

arXiv2026

Mass Generation from Embedding Geometry in Surface Nematics

We show that a nematic field constrained to a curved embedded surface develops an emergent geometric mass in its leading isotropic interaction sector. An auxiliary embedding-space closure mediated by the surface spin connection yields a massive scalar mode $χ_n$ with mass set by the extrinsic curvature invariant $m^2=K_{ab}K^{ab}$. This mass arises directly from embedding geometry, promoting the intrinsic massless nematic interaction into a geometry-controlled massive field. The resulting theory identifies Gaussian curvature as a distributed geometric charge and establishes embedding geometry as the regulator of defect interactions on curved nematic membranes.

cond-mat.soft↗

arXiv2026

Renormalized flow theory of wave turbulence: Kolmogorov-Zakharov spectra as emergent asymptotic states

We develop a continuous Wilsonian renormalized-flow theory of weak wave turbulence directly in spectral frequency space, for finite cascades in experimentally driven Newtonian fluids. The central quantity is a scale-dependent effective coupling that governs nonlinear transfer across logarithmic frequency shells and organizes the cascade as a finite renormalized branch. Within this formulation, the inertial interval is constructed dynamically as a plateau of the running flow, whose non-autonomous character is expressed through its explicit dependence on the logarithmic distance from the injection scale and thereby encodes the cumulative action of forcing and degradation along the cascade. The ultraviolet cutoff follows internally as the terminal scale at which the plateau branch ceases to exist, whereas the integrated spectral response is fixed by infrared matching to the injection scale. In this way, the finite inertial branch is determined by the renormalized dynamics itself, while Kolmogorov--Zakharov (KZ) spectra arise only as its asymptotic constant-flux scaling states. The theory applies to both capillary and gravity wave turbulence and admits a physically transparent realization in monochromatically driven discrete cascades, which fix the topology-dependent exponent structure of the renormalized flow.

physics.flu-dyn↗

arXiv2022

The role of spontaneous curvature in the formation of cell membrane necks

The mechanical effects of membrane compositional inhomogeneities are analyzed in a process analogous of neck formation in cellular membranes. We cast on the Canham-Helfrich model of fluid membranes with both the spontaneous curvature and the surface tension being non-homogeneous functions along the cell membrane. The inhomogeneous distribution is determined by the equilibrium mechanical equations, and, in order to establish the role played by the inhomogeneity, we focus on the catenoid, a surface of zero mean curvature, which can be described in terms of the catenary curve parameterized by arc length. We show that analytic solutions exist for the spontaneous curvature, as well as for both, the surface tension and the radial elastic force. An analytic expression for the constrictive force at the neck, is obtained. From the energetic analysis, it is found that, if we fix the value of the constrictive force at the neck, the set of solutions lies on two branches separated by an energetic barrier. This barrier corresponds to the energy of the maximum catenoid. If instead we fix the axial force, the solution has access to catenoid of any size

cond-mat.soft↗

arXiv2021

Effect of Al content on the hardness and thermal stability study of AlTiN and AlTiBN coatings deposited by HiPIMS

The microstructure, mechanical properties and thermal stability of AlTiN and AlTiBN coatings grown by reactive high-power impulse magnetron sputtering (HiPIMS) have been analyzed as a function of Al/(Al+Ti) ratio, x, between 0.5 and 0.8. The coatings were predominantly formed by a face-centered cubic Ti(Al)N crystalline phase, both with and without B, even for x ratios as high as 0.6, which is higher than the ratio typically encountered for AlTiN coatings deposited by reactive magnetron sputtering. B doping, in combination with the highly energetic deposition conditions offered by HiPIMS, results in the suppression of the columnar grain morphology typically encountered in AlTiN coatings. On the contrary, the AlTiBN coatings grown by HiPIMS present a dense nanocomposite type microstructure, formed by nanocrystalline Ti(Al)N domains and amorphous regions composed of Ti(Al)B2 and BN. As a result, high-Al content (x>0.6) AlTiBN coatings grown by HiPIMS offer higher hardness, elasticity and fracture toughness than AlTiN coatings. Moreover, the thermal stability and the hot hardness are substantially enhanced, delaying the onset of formation of the detrimental hexagonal AlN phase from 850 C in the case of AlTiN, to 1000 C in the case of AlTiBN.

physics.app-ph↗

arXiv2020

Mechanics of nematic membranes: Euler-Lagrange equations, Noether charges, stress, torque and boundary conditions of the surface Frank nematic field

The mechanics of a flexible membrane decorated with a nematic liquid-crystal texture is considered in a variational framework. The variations on the splay, twist and the bend energy of the nematics are obtained from the local deformations leading to changes in the shape membrane. The Euler-Lagrange derivatives and the Noether charges are identified from the variational equations. The nematic stress tensor is obtained as a consequence of translational invariance. Likewise, the rotational invariance implies the torque nematic tensor. The corresponding boundary conditions are obtained for free edges in the open-membrane configuration. These results constitute the basis of a generalized theory of elasticity for anisotropic nematic membranes. Some relevant consequences of the presence of nematic ordering are visualized at revolution surfaces with axial symmetry.

cond-mat.soft↗

arXiv2019

Membrane stress and torque induced by Frank's nematic textures: A geometric perspective using surface-based constraints

An elastic membrane with embedded nematic molecules is considered as a model of anisotropic fluid membrane with internal ordering. By considering the geometric coupling between director field and membrane curvature, the nematic texture is shown to induce anisotropic stresses additional to Canham-Helfrich elasticity. Building upon differential geometry, analytical expressions are found for the membrane stress and torque induced by splaying, twisting and bending of the nematic director as described by the Frank energy of liquid crystals. The forces induced by prototypical nematic textures are visualized on the sphere and on cylindrical surfaces.

cond-mat.soft↗

arXiv2018

Induced stresses in quasi-spherical elastic vesicles: local and global Laplace-Young law

On elastic spherical membranes, there is no stress induced by the bending energy and the corresponding Laplace-Young law does not involve the elastic bending stiffness. However, when considering an axially symmetrical perturbation that pinches the sphere, it induces nontrivial stresses on the entire membrane. In this paper we introduce a theoretical framework to examine the stress induced by perturbations of geometry around the sphere. We find the local balance force equations along the normal direction to the vesicle, and along the unit binormal, tangent to the membrane; likewise, the global balance force equation on closed loops is also examined. We analyze the distribution of stresses on the membrane as the budding transition occurs. For closed membranes we obtain the modified Young-Laplace law that appears as a consequence of this perturbation.

cond-mat.soft↗

arXiv2018

Stresses in curved nematic membranes

Ordering configurations of a director field on a curved membrane induce stress. In this work, we present a theoretical framework to calculate the stress tensor and the torque as a consequence of the nematic ordering; we use the variational principle and invariance of the energy under Euclidean motions. Euler-Lagrange equations of the membrane as well as the corresponding boundary conditions also appear as natural results. The stress tensor found includes attraction-repulsion forces between defects; likewise, defects are attracted to patches with the same sign in gaussian curvature. These forces are mediated by the Green function of Laplace-Beltrami operator of the surface. In addition, we find non-isotropic forces that involve derivatives of the Green function and the gaussian curvature, even in the normal direction to the membrane. We examine the case of axial membranes to analyze the spherical one. For spherical vesicles we find the modified Young-Laplace law as a consequence of the nematic texture. In the case of spherical cap with defect at the north pole, we find that the force is repulsive respect to the north pole, indicating that it is an unstable equilibrium point.

cond-mat.soft↗

arXiv2016

Solution for the nonlinear relativistic harmonic oscillator via Laplace-Adomian decomposition method

Far as we know there are not exact solutions to the equation of motion for a relativistic harmonic oscillator. In this paper, the relativistic harmonic oscillator equation which is a nonlinear ordinary differential equation is studied by means of a combined use of the Adomian Decomposition Method and the Laplace Transform (LADM). The results that we have obtained, a series of powers of functions, have never been reported and show a very good match when compared with other approximate solutions, obtained by different methods. The method here proposed works with high degree of accuracy and because it requires less computational effort, it is very convenient to solve this kind of nonlinear differential equations.

math.CA↗

arXiv2013

Elastic curves and surfaces under long-range forces: A geometric approach

Using classical differential geometry, the problem of elastic curves and surfaces in the presence of long-range interactions $Φ$, is posed. Starting from a variational principle, the balance of elastic forces and the corresponding projections ${\bf n}_i\cdot \nablaΦ$, are found. In the case of elastic surfaces, a force coupling the mean curvature with the external potential, $KΦ$, appears; it is also present in the shape equation along the normal principal in the case of curves. The potential $Φ$ contributes to the effective tension of curves and surfaces and also to the orbital torque. The confinement of a curve on a surface is also addressed, in such a case, the potential contributes to the normal force through the terms $-κΦ-{\bf n}\cdot \nablaΦ$. In general, the equation of motion becomes integro-differential that must be numerically solved.

cond-mat.stat-mech↗

arXiv2011

Effective Hamiltonian of Liquid-Vapor Curved Interfaces in Mean Field

We analyze a one-component simple fluid in a liquid-vapor coexistence state, which forms an arbitrarily curved interface. By using an approach based on density functional theory, we obtain an exact and simple expression for the grand potential at the level of mean field approximation that depends on the density profile and the short-range interaction potential. By introducing the step-function approximation for the density profile, and using general geometric arguments, we expand the grand potential in powers of the principal curvatures of the surface and find consistency with the Helfrich phenomenological model in the second order approximation.

cond-mat.stat-mech↗

arXiv2010

Electrodynamics a la Horava

We study an electrodynamics consistent with anisotropic transformations of space-time with an arbitrary dynamic exponent $z$. The equations of motion and conserved quantities are explicitly obtained. We show that the propagator of this theory can be regarded as a quantum correction to the usual propagator. Moreover we obtain that both the momentum and angular momentum are not modified, but their conservation laws do change. We also show that in this theory the speed of light and the electric charge are modified with $z$. The magnetic monopole in this electrodynamics and its duality transformations are also investigated. For that we found that there exists a dual electrodynamics, with higher derivatives in the electric field, invariant under the same anisotropic transformations.

hep-th↗

arXiv2010

Two-Loop Crossover Scaling Functions of the O(N) Model

Using Environmentally Friendly Renormalization, we present an analytic calculation of the series for the renormalization constants that describe the equation of state for the $O(N)$ model in the whole critical region. The solution of the beta-function equation, for the running coupling to order two loops, exhibits crossover between the strong coupling fixed point, associated with the Goldstone modes, and the Wilson-Fisher fixed point. The Wilson functions $γ_λ$, $γ_ϕ$ and $γ_{ϕ^2}$, and thus the effective critical exponents associated with renormalization of the transverse vertex functions, also exhibit non-trivial crossover between these fixed points.

cond-mat.stat-mech↗

arXiv2008

An ab initio Calculation of the Universal Equation of State for the O(N) Model

Using an Environmentally Friendly Renormalization Group we derive an ab initio universal scaling form for the equation of state for the O(N) model, y=f(x), that exhibits all required analyticity properties in the limits $x\to 0$, $x\to\infty$ and $x\to -1$. Unlike current methodologies based on a phenomenological scaling ansatz the scaling function is derived solely from the underlying Landau-Ginzburg-Wilson Hamiltonian and depends only on the three Wilson functions $γ_λ$, $γ_ϕ$ and $γ_{ϕ^2}$ which exhibit a non-trivial crossover between the Wilson-Fisher fixed point and the strong coupling fixed point associated with the Goldstone modes on the coexistence curve. We give explicit results for N=2, 3 and 4 to one-loop order and compare with known results.

cond-mat.stat-mech↗

arXiv2007

Noncommutative spaces, the quantum of time and the Lorentz symmetry

We introduce three space-times that are discrete in time and compatible with the Lorentz symmetry. We show that these spaces are no commutative, with commutation relations similar to the relations of the Snyder and Yang spaces. Furthermore, using a reparametrized relativistic particle we obtain a realization of the Snyder type spaces and we construct an action for them.

hep-th↗

arXiv2006

An Analytic Equation of State for Ising-like Models

Using an Environmentally Friendly Renormalization we derive, from an underlying field theory representation, a formal expression for the equation of state, $y=f(x)$, that exhibits all desired asymptotic and analyticity properties in the three limits $x\to 0$, $x\to \infty$ and $x\to -1$. The only necessary inputs are the Wilson functions $γ_λ$, $γ_ϕ$ and $γ_{ϕ^2}$, associated with a renormalization of the transverse vertex functions. These Wilson functions exhibit a crossover between the Wilson-Fisher fixed point and the fixed point that controls the coexistence curve. Restricting to the case N=1, we derive a one-loop equation of state for $2< d<4$ naturally parameterized by a ratio of non-linear scaling fields. For $d=3$ we show that a non-parameterized analytic form can be deduced. Various asymptotic amplitudes are calculated directly from the equation of state in all three asymptotic limits of interest and comparison made with known results. By positing a scaling form for the equation of state inspired by the one-loop result, but adjusted to fit the known values of the critical exponents, we obtain better agreement with known asymptotic amplitudes.

cond-mat.stat-mech↗

arXiv2005

The one-loop elastic coefficients for the Helfrich membrane in higher dimensions

Using a covariant geometric approach we obtain the effective bending couplings for a 2-dimensional rigid membrane embedded into a $(2+D)$-dimensional Euclidean space. The Hamiltonian for the membrane has three terms: The first one is quadratic in its mean extrinsic curvature. The second one is proportional to its Gaussian curvature, and the last one is proportional to its area. The results we obtain are in agreement with those finding that thermal fluctuations soften the 2-dimensional membrane embedded into a 3-dimensional Euclidean space.

cond-mat.soft↗

arXiv2004

Cosmological Constant and Noncommutativity: A Newtonian point of view

We study a Newtonian cosmological model in the context of a noncommutative space. It is shown that the trajectories of a test particle undergo modifications such that it no longer satisfies the cosmological principle. For the case of a positive cosmological constant, spiral trajectories are obtained and corrections to the Hubble constant appear. It is also shown that, in the limit of a strong noncommutative parameter, the model is closely related to a particle in a Gödel-type metric.

hep-th↗