arXiv subjects

Joseph O. Indekeu

Publications and source records attributed to Joseph O. Indekeu.

At least 19 recordsLinked to original sources

arXiv2025

Nucleation and wetting transitions in three-component Bose-Einstein condensates in Gross-Pitaevskii theory: exact results

Nucleation and wetting transitions are studied in a three-component Bose-Einstein condensate mixture within Gross-Pitaevskii theory. For special cases of intermediate segregation between components 1 and 2, the nucleation phase transition of a surfactant film of component 3 is obtained by exact solution. Additional exact results for the nucleation transition are derived in the limit of strong segregation between components 1 and 2. In this limit the exact first-order wetting phase boundary is obtained using analytical and numerical methods, and is contrasted with the exact nucleation and wetting phase boundary derived previously for a two-component Bose-Einstein condensate mixture at a hard optical wall. Exact results for the three-component mixture are compared with results from the double-parabola approximation used in an earlier work.

cond-mat.quant-gas↗

arXiv2025

Critical exponents of fluid-fluid interfacial tensions near a critical endpoint in a nonwetting gap

Fluid three-phase equilibria, with phases $α, β, γ$, are studied close to a tricritical point, analytically and numerically, in a mean-field density-functional theory with two densities. Employing Griffiths' scaling for the densities, the interfacial tensions of the wet and nonwet interfaces are analysed. The mean-field critical exponent is obtained for the vanishing of the critical interfacial tension $σ_{βγ}$ as a function of the deviation of the noncritical interfacial tension $σ_{αγ}$ from its limiting value at a critical endpoint $σ_{α,βγ}$. In the wet regime, this exponent is $3/2$ as expected. In the nonwetting gap of the model, the exponent is again $3/2$, except for the approach to the critical endpoint on the neutral line where $σ_{αβ} = σ_{αγ}$. When this point is approached along any path with $σ_{αβ} \neq σ_{αγ}$, or along the neutral line, $σ_{βγ} \propto | σ_{αγ} - σ_{α,βγ}|^{3/4}$, featuring an anomalous critical exponent $3/4$, which is an exact result derived by analytic calculation and explained by geometrical arguments.

cond-mat.stat-mech↗

arXiv2025

Statistical physics of active matter, cell division and cell aggregation

In these Lecture Notes we aim at clarifying how soft matter physics, and herein notably statistical mechanics and fluid mechanics, can be engaged to understand and manipulate non-equilibrium systems consisting of numerous (microscopic) constituents that convert (chemical) energy to mechanical energy, or vice versa, and that are known as active matter. Hydrodynamic theory, vitally extended to include (anisotropic) active stress, provides an astonishingly successful scaffold for tackling the problem of spontaneous flow in active nematics, all the way to active turbulence. The laws of physics, nonchalantly tresspassing the border crossing between inanimate particle and living cell, are seen to perform cum laude in describing the bi-directional coupling between division and apoptosis on the one hand and mechanical stress on the other. Fluidization of cellular tissue by cell division is a conceptual leap in this arena. The active behavior of nematic tissues (cell extrusion, multilayer formation, ...) turns out to be controlled by topological defects in the orientational order. Playgrounds by excellence for exhibiting stress-growth coupling are multicellular spheroids serving as model tumors, and cysts used as stem cell factories for cell therapy. Finally, our study of villi and crypts in the intestine furnishes a synthesis of various concepts explored. Cell mechanical pressure and cell layer geometrical curvature turn out to provide the dynamical ingredients which, when coupled to the cell division rate, allow one to develop a physical theory of tissue morphology which hopefully will have practical impact on cancer research.

cond-mat.soft↗

arXiv2025

Three-component Bose-Einstein condensates and wetting without walls

In previous work within Gross-Pitaevskii (GP) theory for ultracold gases wetting phase transitions were predicted for a phase-segregated two-component Bose-Einstein condensate (BEC) adsorbed at an optical wall. The wetting phase diagram was found to depend on intrinsic atomic parameters, being the masses and the scattering lengths, and on the extrinsic wall boundary condition. Here we study wetting transitions in GP theory without an optical wall in a setting with three phase-segregated BEC components instead of two. The boundary condition is removed by replacing the wall with the third component and treating the three phases on an equal footing. This leads to an unequivocal wetting phase diagram that depends only on intrinsic atomic parameters. It features first-order and critical wetting transitions, and prewetting phenomena. The phase boundaries are computed by numerical solution of the GP equations. In addition, useful analytic results are obtained by extending the established double-parabola approximation to three components.

cond-mat.quant-gas↗

arXiv2022

Wetting and nonwetting near a tricritical point

The dihedral contact angles between interfaces in three-fluid-phase equilibria must be continuous functions of the bulk thermodynamic fields. This general argument, which we propose, predicts a nonwetting gap in the phase diagram, challenging the common belief in "critical-point wetting", even for short-range forces. A demonstration is provided by exact solution of a mean-field two-density functional theory for three-phase equilibria near a tricritical point (TCP). Complete wetting is found in a tiny vicinity of the TCP. Away from it, nonwetting prevails and no wetting transition takes place, not even when a critical endpoint is approached. Far from the TCP, reentrant wetting may occur, with a different wetting phase. These findings shed light on hitherto unexplained experiments on ternary water-oil-nonionic amphiphile mixtures in which nonwetting continues to exist as one approaches either one of the two critical endpoints.

cond-mat.stat-mech↗

arXiv2022

The BLUES function method for second-order partial differential equations: application to a nonlinear telegrapher equation

An analytic iteration sequence based on the extension of the BLUES (Beyond Linear Use of Equation Superposition) function method to partial differential equations (PDEs) with second-order time derivatives is studied. The original formulation of the BLUES method is modified by introducing a matrix formalism that takes into account the initial conditions for higher-order time derivatives. The initial conditions of both the solution and its derivatives now play the role of a source vector. The method is tested on a nonlinear telegrapher equation, which can be reduced to a nonlinear wave equation by a suitable choice of parameters. In addition, a comparison is made with three other methods: the Adomian decomposition method, the variational iteration method (with Green function) and the homotopy perturbation method. The matrix BLUES function method is shown to be a worthwhile alternative for the other methods.

physics.comp-ph↗

arXiv2022

Interface potential and line tension for Bose-Einstein condensate mixtures near a hard wall

Within Gross-Pitaevskii (GP) theory we derive the interface potential V (l) which describes the interaction between the interface separating two demixed Bose-condensed gases and an optical hard wall at a distance l. Previous work revealed that this interaction gives rise to extraordinary wetting and prewetting phenomena. Calculations that explore non-equilibrium properties by using l as a constraint provide a thorough explanation for this behavior. We find that at bulk two-phase coexistence, V (l) for both complete wetting and partial wetting is monotonic with exponential decay. Remarkably, at the first-order wetting phase transition, V(l) is independent of l. This anomaly explains the infinite continuous degeneracy of the grand potential reported earlier. As a physical application, using V(l) we study the three-phase contact line where the interface meets the wall under a contact angle theta. Employing an interface displacement model we calculate the structure of this inhomogeneity and its line tension tau. Contrary to what happens at a usual first-order wetting transition in systems with short-range forces, tau does not approach a nonzero positive constant for theta going to zero, but instead approaches zero (from below) as would be expected for a critical wetting transition. This hybrid character of tau is a consequence of the absence of a barrier in V(l) at wetting. For a typical V(l) we provide a conjecture for the exact line tension within GP theory.

cond-mat.quant-gas↗

arXiv2021

The BLUES function method applied to partial differential equations and analytic approximants for interface growth under shear

An iteration sequence based on the BLUES (beyond linear use of equation superposition) function method is presented for calculating analytic approximants to solutions of nonlinear partial differential equations. This extends previous work using this method for nonlinear ordinary differential equations with an external source term. Now, the initial condition plays the role of the source. The method is tested on three examples: a reaction-diffusion-convection equation, the porous medium equation with growth or decay, and the nonlinear Black-Scholes equation. A comparison is made with three other methods: the Adomian decomposition method (ADM), the variational iteration method (VIM), and the variational iteration method with Green function (GVIM). As a physical application, a deterministic differential equation is proposed for interface growth under shear, combining Burgers and Kardar- Parisi-Zhang nonlinearities. Thermal noise is neglected. This model is studied with Gaussian and space-periodic initial conditions. A detailed Fourier analysis is performed and the analytic coefficients are compared with those of ADM, VIM, GVIM, and standard perturbation theory. The BLUES method turns out to be a worthwhile alternative to the other methods. The advantages that it offers ensue from the freedom of choosing judiciously the linear part, with associated Green function, and the residual containing the nonlinear part of the differential operator at hand.

physics.comp-ph↗

arXiv2021

Coastlines and percolation in a model for hierarchical random deposition

We revisit a known model in which (conducting) blocks are hierarchically and randomly deposited on a $d$-dimensional substrate according to a hyperbolic size law with the block size decreasing by a factor $λ\, > 1$ in each subsequent generation. In the first part of the paper the number of coastal points (in $D=1)$ or coastlines (in $D=2)$ is calculated, which are points or lines that separate a region at "sea level" and an elevated region. We find that this number possesses a non-universal character, implying a Euclidean geometry below a threshold value $P_c$ of the deposition probability $P$, and a fractal geometry above this value. Exactly at the threshold, the geometry is logarithmic fractal. The number of coastlines in $D=2$ turns out to be exactly twice the number of coastal points in $D=1$. We comment briefly on the surface morphology and derive a roughness exponent $α$. In the second part, we study the percolation probability for a current in this model and two extensions of it, in which both the scale factor and the deposition probability can take on different values between generations. We find that the percolation threshold $P_c$ is located at exactly the same value for the deposition probability as the threshold probability of the number of coastal points. This coincidence suggests that exactly at the onset of percolation for a conducting path, the number of coastal points exhibits logarithmic fractal behaviour.

cond-mat.stat-mech↗

arXiv2020

BLUES iteration applied to nonlinear ordinary differential equations for wave propagation and heat transfer

The iteration sequence based on the BLUES (Beyond Linear Use of Equation Superposition) function method for calculating analytic approximants to solutions of nonlinear ordinary differential equations with sources is elaborated upon. Diverse problems in physics are studied and approximate analytic solutions are found. We first treat a damped driven nonlinear oscillator and show that the method can correctly reproduce oscillatory behaviour. Next, a fractional differential equation describing heat transfer in a semi-infinite rod with Stefan-Boltzmann cooling is handled. In this case, a detailed comparison is made with the Adomian decomposition method, the outcome of which is favourable for the BLUES method. As a final problem, the Fisher equation from population biology is dealt with. For all cases, it is shown that the solutions converge exponentially fast to the numerically exact solution, either globally or, for the Fisher problem, locally.

nlin.PS↗

arXiv2019

Analytic iteration procedure for solitons and traveling wavefronts with sources

A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed BLUES (Beyond Linear Use of Equation Superposition) function method is shown to converge for nonlinear ordinary differential equations. Case studies are presented for solitary wave solutions of the Camassa-Holm equation and for traveling wavefront solutions of the Burgers equation, with source terms. The convergence of the analytical approximations towards the numerically exact solution is exponentially rapid. In practice, the zeroth-order approximation (a simple convolution) is already useful and the first-order approximation is already accurate while still easy to calculate. The type of nonlinearity can be chosen rather freely, which makes the method generally applicable.

nlin.PS↗

arXiv2019

Three-phase equilibria in density-functional theory: interfacial tensions

A mean-field density-functional model for three-phase equilibria in fluids (or other soft condensed matter) with two spatially varying densities is analyzed analytically and numerically. The interfacial tension between any two out of three thermodynamically coexisting phases is found to be captured by a surprisingly simple analytic expression that has a geometric interpretation in the space of the two densities. The analytic expression is based on arguments involving symmetries and invariances. It is supported by numerical computations of high precision and it agrees with earlier conjectures obtained for special cases in the same model. An application is presented to three-phase equilibria in the vicinity of a tricritical point. Using the interfacial tension expression and employing the field variables compatible with tricritical point scaling, the expected mean-field critical exponent is derived for the vanishing of the critical interfacial tension as a function of the deviation of the noncritical interfacial tension from its limiting value, upon approach to a critical endpoint in the phase diagram. The analytic results are again confirmed by numerical computations of high precision.

cond-mat.stat-mech↗

arXiv2018

BLUES function method in computational physics

We introduce a computational method in physics that goes "beyond linear use of equation superposition" (BLUES). A BLUES function is defined as a solution of a nonlinear differential equation (DE) with a delta source that is at the same time a Green's function for a related linear DE. For an arbitrary source, the BLUES function can be used to construct an exact solution to the nonlinear DE with a different, but related source. Alternatively, the BLUES function can be used to construct an approximate piecewise analytical solution to the nonlinear DE with an arbitrary source. For this alternative use the related linear DE need not be known. The method is illustrated in a few examples using analytical calculations and numerical computations. Areas for further applications are suggested.

physics.comp-ph↗

arXiv2017

Paramagnetic Meissner effect in ZrB12 single crystal with non-monotonic vortex-vortex interactions

The magnetic response related to paramagnetic Meissner effect (PME) is studied in a high quality single crystal ZrB12 with non-monotonic vortex-vortex interactions. We observe the expulsion and penetration of magnetic flux in the form of vortex clusters with increasing temperature. A vortex phase diagram is constructed which shows that the PME can be explained by considering the interplay among the flux compression, the different temperature dependencies of the vortex-vortex and the vortex-pin interactions, and thermal fluctuations. Such a scenario is in good agreement with the results of the magnetic relaxation measurements.

cond-mat.supr-con↗

arXiv2016

Capillary wave dynamics and interface structure modulation in binary Bose-Einstein condensate mixtures

The localized low-energy interfacial excitations, or Nambu-Goldstone modes, of phase-segregated binary mixtures of Bose-Einstein condensates are investigated analytically by means of a double-parabola approximation (DPA) to the Lagrangian density in Gross-Pitaevskii theory for a system in a uniform potential. Within this model analytic expressions are obtained for the excitations underlying capillary waves or "ripplons" for arbitrary strength $K\,(>1)$ of the phase segregation. The dispersion relation $ω\propto k^{3/2}$ is derived directly from the Bogoliubov-de Gennes equations in limit that the wavelength $2π/k$ is much larger than the healing length $ξ$. The proportionality constant in the dispersion relation provides the static interfacial tension. A correction term in $ω(k)$ of order $k^{5/2}$ is calculated analytically, entailing a finite-wavelength correction factor $(1+\frac{\sqrt{K-1} \,kξ}{4\sqrt{2}\,(\sqrt{2}+\sqrt{K-1})})$. This prediction may be tested experimentally using (quasi-)uniform optical-box traps. Explicit expressions are obtained for the structural deformation of the interface due to the passing of the capillary wave. It is found that the amplitude of the wave is enhanced by an amount that is quadratic in the ratio of the phase velocity $ω/k$ to the sound velocity $c$. For generic asymmetric mixtures consisting of condensates with unequal healing lengths an additional modulation is predicted of the common value of the condensate densities at the interface.

cond-mat.quant-gas↗

arXiv2016

Engines with ideal efficiency and nonzero power for sublinear transport laws

It is known that an engine with ideal efficiency ($η=1$ for a chemical engine and $e = e_{\rm Carnot}$ for a thermal one) has zero power because a reversible cycle takes an infinite time. However, at least from a theoretical point of view, it is possible to conceive (irreversible) engines with nonzero power that can reach ideal efficiency. Here this is achieved by replacing the usual linear transport law by a sublinear one and taking the step-function limit for the particle current (chemical engine) or heat current (thermal engine) versus the applied force. It is shown that in taking this limit exact thermodynamic inequalities relating the currents to the entropy production are not violated.

physics.chem-ph↗

arXiv2015

Interfacial tension and wall energy of a Bose-Einstein condensate binary mixture: triple-parabola approximation

Accurate and useful analytic approximations are developed for order parameter profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates. The pure condensates 1 and 2, each of which contains a particular species of atoms, feature healing lengths $ξ_1$ and $ξ_2$. The inter-atomic interactions are repulsive. In particular, the effective inter-species repulsive interaction strength is $K$. A triple-parabola approximation (TPA) is proposed, to represent closely the energy density featured in Gross-Pitaevskii (GP) theory. This TPA allows us to define a model, which is a handy alternative to the full GP theory, while still possessing a simple analytic solution. The TPA offers a significant improvement over the recently introduced double-parabola approximation (DPA). In particular, a more accurate amplitude for the wall energy (of a single condensate) is derived and, importantly, a more correct expression for the interfacial tension (of two condensates) is obtained, which describes better its dependence on $K$ in the strong segregation regime, while also the interface profiles undergo a qualitative improvement.

cond-mat.stat-mech↗

arXiv2015

Static interfacial properties of Bose-Einstein condensate mixtures

Interfacial profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates are studied theoretically. The two condensates are characterized by their respective healing lengths $ξ_1$ and $ξ_2$ and by the inter-species repulsive interaction $K$. An exact solution to the Gross-Pitaevskii (GP) equations is obtained for the special case $ξ_2/ξ_1 = 1/2$ and $K = 3/2$. Furthermore, applying a double-parabola approximation (DPA) to the energy density featured in GP theory allows us to define a DPA model, which is much simpler to handle than GP theory but nevertheless still captures the main physics. In particular, a compact analytic expression for the interfacial tension is derived that is useful for all $ξ_1, ξ_2$ and $K$. An application to wetting phenomena is presented for condensates adsorbed at an optical wall. The wetting phase boundary obtained within the DPA model nearly coincides with the exact one in GP theory.

cond-mat.stat-mech↗