Center for Theoretical and Computational Physics

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Ordering of oblate hard particles between hybrid penetrable walls

Publication . Anquetil-Deck, Candy; Cleaver, Douglas J.; Teixeira, Paulo

We report a Monte Carlo (MC) simulation study of a model discotic liquid crystal (DLC) confined between hybrid walls with controllable penetrability. The model consists of oblate hard Gaussian overlap (HGO) particles. Particle-substrate interactions are modeled as follows: each substrate sees a particle as a disc of zero thickness and diameter D less than or equal to that of the actual particle, sigma(0), embedded inside the particle and located halfway along, and perpendicular to, its minor axis. This allows us to control the anchoring properties of the substrates, from planar (edge-on) for D approximate to 0 to homeotropic (face-on) for D approximate to sigma(0), which can be done independently at either substrate. Depending on the values of D-s = D/sigma(0) at the top (D-s(t)) and bottom (D-s(b)) substrates, we find domains in (D-s(b), D-s(t)) space in which particle alignment is uniform planar (UP), is uniform homeotropic (UH), or varies linearly from planar at one substrate to homeotropic at the other (Lin). These domains are separated by regions of bistability (P-Lin and H-Lin), which appear to be wider than for prolate HGOs, and there may be also a small tristable (P-H-Lin) region. Results are compared with the predictions of density functional theory, implemented at the level of Onsager's second-virial approximation with Parsons-Lee rescaling. As in the case of symmetric confinement studied previously, the agreement between theory and simulation is substantially less good than for prolate HGOs: in particular, for the investigated substrate separation L = 6 sigma(0), the Lin configuration is never predicted. These discrepancies are likely a consequence of the fact that Onsager's theory is less accurate for discs than for rods.

2020-09-03Journal article

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Phase behavior of a binary mixture of patchy colloids: Effect of particle size and gravity

Publication . Braz Teixeira, Rodrigo; de las Heras, Daniel; Tavares, Jose; Gama, Margarida

We study theoretically the effect of size difference and that of gravity in the phase behavior of a binary mixture of patchy particles. The species, 2A and 3B, have two A and three B patches, respectively, and only bonds between patches A and B (AB bonds) are allowed. This model describes colloidal systems where the aggregation of particles (3B) is mediated and controlled by a second species, the linkers (2A) to which they bind strongly. Thermodynamic calculations are performed using Wertheim’s perturbation theory with a hard sphere reference term that accounts for the difference in the size of the two species. Percolation lines are determined employing a generalized Flory–Stockmayer theory, and the effects of gravity are included through a local density approximation. The bulk phase diagrams are calculated, and all the stacking sequences generated in the presence of gravity are determined and classified in a stacking diagram. The relative size of the particles can be used to control the phase behavior of the mixture. An increase in the size of particles 3B, relative to the size of the linkers 2A, is found to promote mixing while keeping the percolating structures and, in certain cases, leads to changes in the stacking sequence under gravity.

2021-07-26Journal article

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Vacuum structure of the Z(2) symmetric Georgi-Machacek model

Publication . Azevedo, Duarte; Ferreira, Pedro Miguel; Logan, Heather E.; Santos, Rui

We discuss the vacuum structure of a version of the Georgi-Machecek model with an exact Z(2) symmetry acting on the triplet fields. Besides the usual custodial-symmetric model, with rho = 1 at tree-level, a model with a dark matter candidate is also viable. The other phases of the model lead to electric charge breaking, a wrong pattern of electroweak symmetry breaking or to rho not equal 1 at tree-level. We derive conditions to have an absolute minimum in each of the two viable phases, the custodial and the dark matter phases.

2021-03-23Journal article

Open access

Inheritances, social classes, and wealth distribution

Publication . Patricio, Pedro; Araujo, Nuno

We consider a simple theoretical model to investigate the impact of inheritances on the wealth distribution. Wealth is described as a finite resource, which remains constant over different generations and is divided equally among offspring. All other sources of wealth are neglected. We consider different societies characterized by a different offspring probability distribution. We find that, if the population remains constant, the society reaches a stationary wealth distribution. We show that inequality emerges every time the number of children per family is not always the same. For realistic offspring distributions from developed countries, the model predicts a Gini coefficient of G approximate to 0.3. If we divide the society into wealth classes and set the probability of getting married to depend on the distance between classes, the stationary wealth distribution crosses over from an exponential to a power-law regime as the number of wealth classes and the level of class distinction increase.

2021-10-27Journal article

Open access

Dynamics of two-dimensional liquid bridges

Publication . Coelho, Rodrigo; Cordeiro, Luis A. R. G.; Gazola, Rodrigo B.; Teixeira, Paulo

We have simulated the motion of a single vertical, two-dimensional liquid bridge spanning the gap between two flat, horizontal solid substrates of given wettabilities, using a multicomponent pseudopotential lattice Boltzmann method. For this simple geometry, the Young-Laplace equation can be solved (quasi-)analytically to yield the equilibrium bridge shape under gravity, which provides a check on the validity of the numerical method. In steady-state conditions, we calculate the drag force exerted by the moving bridge on the confining substrates as a function of its velocity, for different contact angles and Bond numbers. We also study how the bridge deforms as it moves, as parametrized by the changes in the advancing and receding contact angles at the substrates relative to their equilibrium values. Finally, starting from a bridge within the range of contact angles and Bond numbers in which it can exist at equilibrium, we investigate how fast it must move in order to break up.

2022-05-18Journal article

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