arXiv subjects

T. Garel

Publications and source records attributed to T. Garel.

33 records · Page 2Linked to original sources

arXiv2003

Wave propagation in a chiral fluid: an undergraduate study

We study the propagation of electromagnetic waves in a chiral fluid, where the molecules are described by a simplified version of the Kuhn coupled oscillator model. The eigenmodes of Maxwell's equations are circularly polarized waves. The application of a static magnetic field further leads to a magnetochiral term in the index of refraction of the fluid, which is independent of the wave polarization. A similar result holds when absorption is taken into account. Interference experiments and photochemical reactions have recently demonstrated the existence of the magnetochiral term. The comparison with Faraday rotation in an achiral fluid emphasizes the different symmetry properties of the two effects.

physics.ed-ph↗

arXiv2001

A simple model for DNA denaturation

Following Poland and Scheraga, we consider a simplified model for the denaturation transition of DNA. The two strands are modeled as interacting polymer chains. The attractive interactions, which mimic the pairing between the four bases, are reduced to a single short range binding term. Furthermore, base-pair misalignments are forbidden, implying that this binding term exists only for corresponding (same curvilinear abscissae) monomers of the two chains. We take into account the excluded volume repulsion between monomers of the two chains, but neglect intra-chain repulsion. We find that the excluded volume term generates an effective repulsive interaction between the chains, which decays as $1/r^{d-2}$. Due to this long-range repulsion between the chains, the denaturation transition is first order in any dimension, in agreement with previous studies.

cond-mat.soft↗

arXiv2000

Copolymer at a selective interface and two dimensional wetting: a grand canonical approach

We consider two different problems involving the localization of a single polymer chain: (i) a periodic $AB$ copolymer at a selective fluid-fluid interface, with the upper (resp. lower) fluid attracting $A$ (resp. $B$) monomers (ii) a homopolymer chain attracted to a hard wall (wetting). Self avoidance is neglected in both models, which enables us to study their localization transition in a grand canonical approach. We recover the results obtained in previous studies via transfer matrix methods. Moreover, we calculate in this way the loop length distribution functions in the localized phase. Some finite size effects are also determined and tested numerically.

cond-mat.soft↗

arXiv1999

Phase diagram of magnetic polymers

We consider polymers made of magnetic monomers (Ising or Heisenberg-like) in a good solvent. These polymers are modeled as self-avoiding walks on a cubic lattice, and the ferromagnetic interaction between the spins carried by the monomers is short-ranged in space. At low temperature, these polymers undergo a magnetic induced first order collapse transition, that we study at the mean field level. Contrasting with an ordinary $Θ$ point, there is a strong jump in the polymer density, as well as in its magnetization. In the presence of a magnetic field, the collapse temperature increases, while the discontinuities decrease. Beyond a multicritical point, the transition becomes second order and $Θ$-like. Monte Carlo simulations for the Ising case are in qualitative agreement with these results.

cond-mat.stat-mech↗

arXiv1998

Overlap properties and adsorption transition of two Hamiltonian paths

We consider a model of two (fully) compact polymer chains, coupled through an attractive interaction. These compact chains are represented by Hamiltonian paths (HP), and the coupling favors the existence of common bonds between the chains. Using a ($n=0$ component) spin representation for these paths, we show the existence of a phase transition for strong coupling (i.e. at low temperature) towards a ``frozen'' phase where one chain is completely adsorbed onto the other. By performing a Legendre transform, we obtain the probability distribution of overlaps. The fraction of common bonds between two HP, i.e. their overlap $q$, has both lower ($q_m$) and upper ($q_M$) bounds. This means in particuliar that two HP with overlap greater than $q_M$ coincide. These results may be of interest in (bio)polymers and in optimization problems.

cond-mat.stat-mech↗

arXiv1998

Collapse transitions of a periodic hydrophilic hydrophobic chain

We study a single self avoiding hydrophilic hydrophobic polymer chain, through Monte Carlo lattice simulations. The affinity of monomer $i$ for water is characterized by a (scalar) charge $λ_{i}$, and the monomer-water interaction is short-ranged. Assuming incompressibility yields an effective short ranged interaction between monomer pairs $(i,j)$, proportional to $(λ_i+λ_j)$. In this article, we take $λ_i=+1$ (resp. ($λ_i=- 1$)) for hydrophilic (resp. hydrophobic) monomers and consider a chain with (i) an equal number of hydro-philic and -phobic monomers (ii) a periodic distribution of the $λ_{i}$ along the chain, with periodicity $2p$. The simulations are done for various chain lengths $N$, in $d=2$ (square lattice) and $d=3$ (cubic lattice). There is a critical value $p_c(d,N)$ of the periodicity, which distinguishes between different low temperature structures. For $p >p_c$, the ground state corresponds to a macroscopic phase separation between a dense hydrophobic core and hydrophilic loops. For $p <p_c$ (but not too small), one gets a microscopic (finite scale) phase separation, and the ground state corresponds to a chain or network of hydrophobic droplets, coated by hydrophilic monomers. We restrict our study to two extreme cases, $p \sim O(N)$ and $p\sim O(1)$ to illustrate the physics of the various phase transitions. A tentative variational approach is also presented.

cond-mat↗

arXiv1997

Protein folding and heteropolymers

We present a statistical mechanics approach to the protein folding problem. We first review some of the basic properties of proteins, and introduce some physical models to describe their thermodynamics. These models rely on a random heteropolymeric description of these non random biomolecules. Various kinds of randomness are investigated, and the connection with disordered systems is discussed. We conclude by a brief study of the dynamics of proteins.

cond-mat.dis-nn↗

arXiv1997

Protein folding, anisotropic collapse and blue phases

We study a homopolymer model of a protein chain, where each monomer carries a dipole moment. To mimic the geometry of the peptidic bond, these dipoles are constrained to be locally perpendicular to the chain. The tensorial character of the dipolar interaction leads naturally to a (tensorial) liquid crystal-like order parameter. For non chiral chains, a mean field study of this model shows that a classical $θ$ collapse transition occurs first; at lower temperature, nematic order sets in. For chiral chains, an anisotropic (tensorial) collapse transition may occur before the $θ$ temperature is reached: the ordered phase can be described as a ``compact phase of secondary structures'', and possesses great similarities with the liquid crystal blue phases.

cond-mat.soft↗

arXiv1996

Directed polymers in a random medium: a variational approach

A disorder-dependent Gaussian variational approach is applied to the problem of a $d$ dimensional polymer chain in a random medium (or potential). Two classes of variational solutions are obtained. For $d<2$, these two classes may be interpreted as domain and domain wall. The critical exponent $ν$ describing the polymer width is $ν={1\over (4-d)}$ (domain solution) or $ν={3\over (d+4)}$ (domain wall solution). The domain wall solution is equivalent to the (full) replica symmetry breaking variational result. For $d>2$, we find $ν={1\over 2}$. No evidence of a phase transition is found for $2< d< 4$: one of the variational solutions suggests that the polymer chain breaks into Imry-Ma segments, whose probability distribution is calculated. For $d>4$, the other variational solution undergoes a phase transition, which has some similarity with B. Derrida's random energy models.

cond-mat↗

arXiv1995

Phase diagram of a semiflexible polymer chain in a $θ$ solvent: application to protein folding

We consider a lattice model of a semiflexible homopolymer chain in a bad solvent. Beside the temperature $T$, this model is described by (i) a curvature energy $\varepsilon_h$, representing the stiffness of the chain (ii) a nearest-neighbour attractive energy $\varepsilon_v$, representing the solvent (iii) the monomer density $ρ={N \over Ω}$, where $N$ and $Ω$ denote respectively the number of monomers and the number of lattice sites. This model is a simplified view of the protein folding problem, which encompasses the geometrical competition between secondary structures (the curvature term modelling helix formation) and the global compactness (modeled here by the attractive energy), but contains no side chain information...

cond-mat↗

arXiv1995

A variational study of the random-field XY model

A disorder-dependent Gaussian variational approach is applied to the $d$-dimensional ferromagnetic XY model in a random field. The randomness yields a non extensive contribution to the variational free energy, implying a random mass term in correlation functions. The Imry-Ma low temperature result, concerning the existence ($d>4$) or absence ($d < 4$) of long-range order is obtained in a transparent way. The physical picture which emerges below $d=4$ is that of a marginally stable mixture of domains. We also calculate within this variational scheme, disorder dependent correlation functions, as well as the probability distribution of the Imry-Ma domain size.

cond-mat↗

arXiv1995

Physical Meaning of the Affleck-Kennedy-Lieb-Tasaki S=1 Quantum spin chain

Most of the present understanding of the S=1 quantum spin chains displaying the Haldane gap is coming from the so-called valence-bond-solid Hamiltonian which has an exactly known ground state. We show that this point is characterized by the onset of short-range incommensurate spin correlations in the one-parameter family of Hamiltonians with biquadratic coupling: H = sum_i S_i S_{i+1} +alpha sum_i ( S_i S_{i+1} )^2. This gives a physical meaning to this special point. We establish precise values for the gaps, correlations, the string order parameter, and identify the VBS point as a *disorder* point in the sense of classical statistical mechanics. It is a quantum remnant of the classical transition between a ground state with long-range Néel order and a ground state with incommensurate long-range order.

cond-mat↗

arXiv1994

Adsorption of polymers on a fluctuating surface

We study the adsorption of polymer chains on a fluctuating surface. Physical examples are provided by polymer adsorption at the rough interface between two non-miscible liquids, or on a membrane. In a mean-field approach, we find that the self--avoiding chains undergo an adsorption transition, accompanied by a stiffening of the fluctuating surface. In particular, adsorption of polymers on a membrane induces a surface tension and leads to a strong suppression of roughness.

cond-mat↗

arXiv1994

Random Hydrophilic-Hydrophobic Copolymers

We study a single statistical amphiphilic copolymer chain AB in a selective solvent (e.g.water). Two situations are considered. In the annealed case, hydrophilic (A) and hydrophobic (B) monomers are at local chemical equilibrium and both the fraction of A monomers and their location along the chain can vary, whereas in the quenched case (which is relevant to proteins), the chemical sequence along the chain is fixed by synthesis. In both cases, the physical behaviour depends on the average hydrophobicity of the polymer chain. For a strongly hydrophobic chain (large fraction of B), we find an ordinary continuous $θ$ collapse, with a large conformational entropy in the collapsed phase. For a weakly hydrophobic, or a hydrophilic chain, there is an unusual first-order collapse transition. In particular, for the case of Gaussian disorder, this discontinuous transition is driven by a change of sign of the third virial coefficient. The entropy of this collapsed phase is strongly reduced with respect to the $θ$ collapsed phase. Email contact: orland@amoco.saclay.cea.fr

cond-mat↗

arXiv1993

Structural and ultrametric properties of twenty(L-alanine)

We study local energy minima of twenty(L-alanine). The minima are generated using high-temperature Molecular Dynamics and Chain-Growth Monte Carlo simulations, with subsequent minimization. We find that the lower-energy configurations are $ α$-helices for a wide range of dielectric constant values $ (ε= 1,10,80), $ and that there is no noticeable difference between the distribution of energy minima in $ ϕψ$ space for different values of $ ε. $ Ultrametricity tests show that lower-energy $ (α$ -helical) $ ε=1 $ configurations form a set which is ultrametric to a certain degree, providing evidence for the presence of fine structure among those minima. We put forward a heuristic argument for this fine structure. We also find evidence for ultrametricity of a different kind among $ ε=10 $ and $ ε=80 $ energy minima. We analyze the distribution of lengths of $ α$-helical portions among the minimized configurations and find a persistence phenomenon for the $ ε=1 $ ones, in qualitative agreement with previous studies of critical lengths. Email contact: bascle@amoco.saclay.cea.fr

cond-mat↗