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Toan T. Nguyen

Publications and source records attributed to Toan T. Nguyen.

At least 37 records · Page 2Linked to original sources
arXiv2021

Influence of fatty alcohol mixing ratios on the physicochemical properties of Stearyl--Cetyl Alcohol--Polysorbate 60--Water ternary System: Insights from Experiments and Computer Simulations

The structure and stability of ternary systems prepared with polysorbate 60 and various combinations of cetyl (C16) and stearyl (C18) alcohols (fatty alcohol 16g, polysorbate 4g, water 180g) were examined as they aged over 3 months at 25oC. Rheological results showed that the consistency of these systems increased initially during roughly the first week of aging, which was succeeded by little changes in consistency (systems containing from 30% to 70% C18, with the 50% C18 system showing the highest consistencies in viscosity and elasticity) or significant breakdown of structure (remaining systems). The formation and/or disintegration of all ternary systems were also detected by microscopy and differential scanning calorimetry experiments. This study emphasizes the fact that the structure and consistency of ternary systems are dominantly controlled by the swelling capacity of the lamellar $α-$crystalline gel phase. When the conversion of this gel phase into non-swollen $β$- or $γ$-crystals occurs, systems change from semisolids to fluids. Molecular dynamics simulations were performed to provide important details on the molecular mechanism of our ternary systems. Computational results supported the hypothesis experimentally proposed for the stability of the mixed system being due to an increase in the flexibility, hence an increase in the configurational entropy of the chain tip of the alcohol with a longer hydrocarbon chain (with the highest flexibility observed in the 50:50 C18:C16 system). This finding is in excellent agreement with experimental conclusions. Additionally, simulation data show that in the mixed system, the alcohol with shorter hydrocarbon chain becomes more rigid. These molecular details could not be available in experimental measurements

cond-mat.soft↗
arXiv2020

On global stability of optimal rearrangement maps

We study the nonlocal vectorial transport equation $\partial_ty+ (\mathbb{P} y \cdot \nabla) y=0$ on bounded domains of $\mathbb{R}^d$ where $\mathbb{P}$ denotes the Leray projector. This equation was introduced to obtain the unique optimal rearrangement of a given map $y_0$ as the infinite time limit of the solution with initial data $y_0$ (\cite{AHT, Macthesis, Brenier09}). We rigorously justify this expectation by proving that for initial maps $y_0$ sufficiently close to maps with strictly convex potential, the solutions $y$ are global in time and converge exponentially fast to the optimal rearrangement of $y_0$ as time tends to infinity.

math.OC↗
arXiv2020

On the holographic phase transitions at finite topological charge

Exploring the significant impacts of topological charge on the holographic phase transitions and conductivity we start from an Einstein - Maxwell system coupled with a charged scalar field in Anti - de Sitter spacetime. In our set up, the corresponding black hole (BH) is chosen to be the topological AdS one where the pressure is identified with the cosmological constant. Our numerical computation shows that the process of condensation is favored at finite topological charge and, in particular, the pressure variation in the bulk generates a mechanism for changing the order of phase transitions in the boundary: the second order phase transitions occur at pressures higher than the critical pressure of the phase transition from small to large BHs while they become first order at lower pressures. This property is confirmed with the aid of holographic free energy. Finally, the frequency dependent conductivity exhibits a gap when the phase transition is second order and when the phase transition becomes first order this gap is either reduced or totally lost.

hep-th↗
arXiv2020

Plasma echoes near stable Penrose data

In this paper we construct particular solutions to the classical Vlasov-Poisson system near stable Penrose initial data on $\mathbb{T} \times \mathbb{R}$ that are a combination of elementary waves with arbitrarily high frequencies. These waves mutually interact giving birth, eventually, to an infinite cascade of echoes of smaller and smaller amplitude. The echo solutions do not belong to the analytic or Gevrey classes studied by Mouhot and Villani, but do, nonetheless, exhibit damping phenomena for large times.

math.AP↗
arXiv2020

Overcharging of zinc ion in the structure of zinc finger protein is needed for DNA binding stability

The zinc finger structure where a Zn2+ ion binds to 4 cysteine or histidine amino acids in a tetrahedral structure is very common motif of nucleic acid binding proteins. The corresponding interaction model is present in 3% of the genes of human genome. As a result, zinc finger has been shown to be extremely useful in various therapeutic and research capacities, as well as in biotechnology. In stable configuration, the cysteine amino acids are deprotonated and become negatively charged. This means the Zn2+ ion is overscreened by 4 cysteine charges (overcharged). It is question of whether this overcharged configuration is also stable when such negatively charged zinc finger binds to negatively charged DNA molecule. Using all atom molecular dynamics simulation up to microsecond range of an androgen receptor protein dimer, we investigate how the deprotonated state of cysteine influences its structure, dynamics, and function in binding o DNA molecules. Our results show that the deprotonated state of cysteine residues are essential for mechanical stabilization of the functional, folded conformation. Not only this state stabilizes the protein structure, it also stabilizes the protein-DNA binding complex. The differences in structural and energetic properties of the two (sequence-identical) monomers are also investigated showing the strong influence of DNA on the structure of zinc fingers upon complexation. Our result has potential impact on better molecular understanding of one of the most common classes of zinc fingers

q-bio.BM↗
arXiv2019

Sharp bounds for the resolvent of linearized Navier Stokes equations in the half space around a shear profile

In this paper, we derive sharp bounds on the semigroup of the linearized incompressible Navier-Stokes equations near a stationary shear layer in the half plane and in the half space ($\mathbb{R}_+^2$ or $\mathbb{R}_+^3$), with Dirichlet boundary conditions, assuming that this shear layer in spectrally unstable for Euler equations. In the inviscid limit, due to the prescribed no-slip boundary conditions, vorticity becomes unbounded near the boundary. The novelty of this paper is to introduce boundary layer norms that capture the unbounded vorticity and to derive sharp estimates on this vorticity that are uniform in the inviscid limit.

math.AP↗
arXiv2019

Enhanced thermoelectricity at the ultra-thin film limit

At the ultra-thin film limit, quantum confinement strongly improves thermoelectric figure of merit in materials such as Sb$_2$Te$_3$ and Bi$_2$Te$_3$. These high quality films have only been realized using well controlled techniques such as molecular beam epitaxy. We report a two fold increase in the Seebeck coefficient for both p-type Sb$_2$Te$_3$ and n-type Bi$_2$Te$_3$ using thermal co-evaporation, an affordable approach. At the thick film limit greater than 100 nm, their Seebeck coefficients are around 100 $μV/K$, similar to results obtained in other work. When the films are thinner than 50 nm, the Seebeck coefficient increases to about 500 $μV/K$. With a total Seebeck coefficient $\sim$ 1 mV/K and an estimate ZT $\sim$ 2, this pair of materials is the first step to a practical micro-cooler at room temperature.

cond-mat.mtrl-sci↗
arXiv2019

Generator functions and their applications

In [Grenier-Nguyen], we introduced so called {\em generators} functions to precisely follow the regularity of analytic solutions of Navier Stokes equations. In this short note, we give a presentation of these generator functions and use them to give existence results of analytic solutions to some classical equations, namely to hyperbolic equations, to incompressible Euler equations, and to hydrostatic Euler and Vlasov models. The use of these generator functions appear to be an alternative way to the use of the classical abstract Cauchy-Kovalevskaya theorem [Asano,Caflisch,Nirenberg,Safonov].

math.AP↗
arXiv2019

$L^\infty$ instability of Prandtl layers

In $1904$, Prandtl introduced his famous boundary layer in order to describe the behavior of solutions of incompressible Navier Stokes equations near a boundary as the viscosity goes to $0$. His Ansatz was that the solution of Navier Stokes equations can be described as a solution of Euler equations, plus a boundary layer corrector, plus a vanishing error term in $L^\infty$ in the inviscid limit. In this paper we prove that, for a class of smooth solutions of Navier Stokes equations, namely for shear layer profiles which are unstable for Rayleigh equations, this Ansatz is false if we consider solutions with Sobolev regularity, in strong contrast with the analytic case, pioneered by R.E. Caflisch and M. Sammartino \cite{SammartinoCaflisch1,SammartinoCaflisch2}. Meanwhile we address the classical problem of the nonlinear stability of shear layers near a boundary and prove that if a shear flow is spectrally unstable for Euler equations, then it is non linearly unstable for the Navier Stokes equations provided the viscosity is small enough.

math.AP↗
arXiv2019

Asymptotic stability of equilibria for screened Vlasov-Poisson systems via pointwise dispersive estimates

We revisit the proof of Landau damping near stable homogenous equilibria of Vlasov-Poisson systems with screened interactions in the whole space $\mathbb{R}^d$ (for $d\geq3$) that was first established by Bedrossian, Masmoudi and Mouhot. Our proof follows a Lagrangian approach and relies on precise pointwise in time dispersive estimates in the physical space for the linearized problem that should be of independent interest. This allows to cut down the smoothness of the initial data required in Bedrossian at al. (roughly, we only need Lipschitz regularity). Moreover, the time decay estimates we prove are essentially sharp, being the same as those for free transport, up to a logarithmic correction.

math.AP↗
arXiv2019

Investigating molecular mechanism for the stability of ternary systems containing cetrimide, fatty alcohol and water by using computer simulation

Computer simulations using atomistic model are carried out to investigate the stability of ternary systems of pure or mixed fatty alcohols, cetrimide, and water. These semi$-$solid oil-in-water systems are used as the main component of pharmaceutical creams. Experiments show that the mixed alcohol systems are more stable than pure ones. The current experimental hypothesis is that this is the result of the length mismatch of the alkyl chains. This leads to higher configurational entropy of the chain tip of the longer alcohol molecules. Our simulation results support this hypothesis. The results also show that the shorter alcohol molecules become stiffer with higher values of the deuterium order parameters and smaller area per molecule. The magnitude in fluctuations in the area per molecule also increases in mixed systems, indicating a higher configurational entropy. Analysis of the molecular structure of simulated systems also shows good agreements with experimental data.

cond-mat.soft↗
arXiv2019

Green function of Orr Sommerfeld equations away from critical layers

The classical Orr-Sommerfeld equations are the resolvent equations of the linearized Navier Stokes equations around a stationary shear layer profile in the half plane. In this paper, we derive pointwise bounds on the Green function of the Orr Sommerfeld problem away from its critical layers.

math.AP↗
arXiv2019

Onsager type conjecture and renormalized solutions for the relativistic Vlasov Maxwell system

In this paper we give a proof of an Onsager type conjecture on conservation of energy and entropies of weak solutions to the relativistic Vlasov--Maxwell equations. As concerns the regularity of weak solutions, say in Sobolev spaces $W^{α,p}$, we determine Onsager type exponents $α$ that guarantee the conservation of all entropies. In particular, the Onsager exponent $α$ is smaller than $α= 1/3$ established for fluid models. Entropies conservation is equivalent to the renormalization property, which have been introduced by DiPerna--Lions for studying well-posedness of passive transport equations and collisionless kinetic equations. For smooth solutions renormalization property or entropies conservation are simply the consequence of the chain rule. For weak solutions the use of the chain rule is not always justified. Then arises the question about the minimal regularity needed for weak solutions to guarantee such properties. In the DiPerna--Lions and Bouchut--Ambrosio theories, renormalization property holds under sufficient conditions in terms of the regularity of the advection field, which are roughly speaking an entire derivative in some Lebesgue spaces (DiPerna--Lions) or an entire derivative in the space of measures with finite total variation (Bouchut--Ambrosio). In return there is no smoothness requirement for the advected density, except some natural a priori bounds. Here we show that the renormalization property holds for an electromagnetic field with only a fractional space derivative in some Lebesgue spaces. To compensate this loss of derivative for the electromagnetic field, the distribution function requires an additional smoothness, typically fractional Sobolev differentiability in phase-space. As concerns the conservation of total energy, if the macroscopic kinetic energy is in $L^2$, then total energy is preserved.

math.AP↗
arXiv2019

The inviscid limit of Navier-Stokes equations for vortex-wave data on $\mathbb{R}^2$

We establish the inviscid limit of the incompressible Navier-Stokes equations on the whole plane $\mathbb{R}^2$ for initial data having vorticity as a superposition of point vortices and a regular component. In particular, this rigorously justifies the vortex-wave system from the physical Navier-Stokes flows in the vanishing viscosity limit, a model that was introduced by Marchioro and Pulvirenti in the early 90s to describe the dynamics of point vortices in a regular ambient vorticity background. The proof rests on the previous analysis of Gallay in his derivation of the vortex-point system.

math.AP↗
arXiv2018

The inviscid limit of Navier-Stokes for analytic data on the half-space

In their classical work Caflisch and Sammartino proved the inviscid limit of the incompressible Navier-Stokes equations for well-prepared data with analytic regularity in the half-space. Their proof is based on the detailed construction of Prandtl's boundary layer asymptotic expansions. In this paper, we give a direct proof of the inviscid limit for general analytic data without having to construct Prandtl's boundary layer correctors. Our analysis makes use of the boundary vorticity formulation and the abstract Cauchy-Kovalevskaya theorem on analytic boundary layer function spaces that capture unbounded vorticity.

math.AP↗
arXiv2018

Uniform in time lower bound for solutions to a quantum Boltzmann equation of bosons

We consider the quantum Boltzmann equation, which describes the growth of the condensate, or in other words, models the interaction between excited atoms and a condensate. In this work, the full form of Bogoliubov dispersion law is considered, which leads to a detailed study of surface integrals inside the collision operator on energy manifolds. We prove that positive radial solutions of the quantum Boltzmann equation are bounded from below by a Gaussian, uniformly in time.

math.AP↗