This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

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The electronic properties of graphene

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

It is possible to say that zeolites are the most widely used catalysts in industry They are crystalline microporous materials which have become extremely successful as catalysts for oil refining, petrochemistry, and organic synthesis in the production of fine and speciality chemicals, particularly when dealing with molecules having kinetic diameters below 10 A The reason for their success in catalysis is related to the following specific features of these materials:1 (1) They have very high surface area and adsorption capacity (2) The adsorption properties of the zeolites can be controlled, and they can be varied from hydrophobic to hydrophilic type materials (3) Active sites, such as acid sites for instance, can be generated in the framework and their strength and concentration can be tailored for a particular application (4) The sizes of their channels and cavities are in the range typical for many molecules of interest (5-12 A), and the strong electric fields2 existing in those micropores together with an electronic confinement of the guest molecules3 are responsible for a preactivation of the reactants (5) Their intricate channel structure allows the zeolites to present different types of shape selectivity, ie, product, reactant, and transition state, which can be used to direct a given catalytic reaction toward the desired product avoiding undesired side reactions (6) All of these properties of zeolites, which are of paramount importance in catalysis and make them attractive choices for the types of processes listed above, are ultimately dependent on the thermal and hydrothermal stability of these materials In the case of zeolites, they can be activated to produce very stable materials not just resistant to heat and steam but also to chemical attacks Avelino Corma Canos was born in Moncofar, Spain, in 1951 He studied chemistry at the Universidad de Valencia (1967−1973) and received his PhD at the Universidad Complutense de Madrid in 1976 He became director of the Instituto de Tecnologia Quimica (UPV-CSIC) at the Universidad Politecnica de Valencia in 1990 His current research field is zeolites as catalysts, covering aspects of synthesis, characterization and reactivity in acid−base and redox catalysis A Corma has written about 250 articles on these subjects in international journals, three books, and a number of reviews and book chapters He is a member of the Editorial Board of Zeolites, Catalysis Review Science and Engineering, Catalysis Letters, Applied Catalysis, Journal of Molecular Catalysis, Research Trends, CaTTech, and Journal of the Chemical Society, Chemical Communications A Corma is coauthor of 20 patents, five of them being for commercial applications He has been awarded with the Dupont Award on new materials (1995), and the Spanish National Award “Leonardo Torres Quevedo” on Technology Research (1996) 2373 Chem Rev 1997, 97, 2373−2419

From Microporous to Mesoporous Molecular-Sieve Materials and Their Use in Catalysis

Graphene — a recently isolated one-atom-thick layered form of graphite — is a hot topic in the materials science and condensed matter physics communities, where it is proving to be a popular model system for investigation. An experiment involving individual graphene sheets suspended over a microscale scaffold has allowed structure determination using transmission electron microscopy and diffraction, perhaps paving the way towards an answer to the question of why graphene can exist at all. The 'two-dimensional' sheets, it seems, are not flat, but wavy. The undulations are less pronounced in a two-layer system, and disappear in multilayer samples. Learning more about this 'waviness' may reveal what makes these extremely thin carbon membranes so stable. Investigations of individual graphene sheets freely suspended on a microfabricated scaffold in vacuum or in air reveal that the membranes are not perfectly flat, but exhibit an intrinsic waviness, such that the surface normal varies by several degrees, and out-of-plane deformations reach 1 nm. The recent discovery of graphene has sparked much interest, thus far focused on the peculiar electronic structure of this material, in which charge carriers mimic massless relativistic particles1,2,3. However, the physical structure of graphene—a single layer of carbon atoms densely packed in a honeycomb crystal lattice—is also puzzling. On the one hand, graphene appears to be a strictly two-dimensional material, exhibiting such a high crystal quality that electrons can travel submicrometre distances without scattering. On the other hand, perfect two-dimensional crystals cannot exist in the free state, according to both theory and experiment4,5,6,7,8,9. This incompatibility can be avoided by arguing that all the graphene structures studied so far were an integral part of larger three-dimensional structures, either supported by a bulk substrate or embedded in a three-dimensional matrix1,2,3,9,10,11,12. Here we report on individual graphene sheets freely suspended on a microfabricated scaffold in vacuum or air. These membranes are only one atom thick, yet they still display long-range crystalline order. However, our studies by transmission electron microscopy also reveal that these suspended graphene sheets are not perfectly flat: they exhibit intrinsic microscopic roughening such that the surface normal varies by several degrees and out-of-plane deformations reach 1 nm. The atomically thin single-crystal membranes offer ample scope for fundamental research and new technologies, whereas the observed corrugations in the third dimension may provide subtle reasons for the stability of two-dimensional crystals13,14,15.

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The structure of suspended graphene sheets

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

Using the renormalization group method we investigate the nonequilibrium relaxation of the (Cardy-Ostlund) 2D random sine-Gordon model, which describes pinned arrays of lines. Its statics exhibit a marginal ($\ensuremath{\theta}=0$) glass phase for $Tl{T}_{g}$ described by a line of fixed points. We obtain the universal scaling functions for two-time dynamical response and correlations near ${T}_{g}$ for various initial conditions, as well as the autocorrelation exponent. The fluctuation dissipation ratio is found to be nontrivial and continuously dependent on $T$.

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Aging in the glass phase of a two-dimensional random periodic elastic system.

The functional RG (FRG) approach to pinning of $d$-dimensional manifolds is reexamined at any temperature $T$. A simple relation between the coupling function $R(u)$ and a physical observable is shown in any $d$. In $d=0$ its beta function is displayed to a high order, ambiguities resolved; for random field disorder (Sinai model) we obtain exactly the T=0 fixed point $R(u)$ as well as its thermal boundary layer (TBL) form (i.e. for $u \sim T$) at $T>0$. Connection between FRG in $d=0$ and decaying Burgers is discussed. An exact solution to the functional RG hierarchy in the TBL is obtained for any $d$ and related to droplet probabilities.

Finite temperature Functional RG, droplets and decaying Burgers Turbulence

We develop a method, the exact multilocal renormalization group (EMRG) which applies to a broad set of theories. It is based on the systematic multilocal expansion of the Polchinski-Wilson exact renormalization group (ERG) equation together with a scheme to compute correlation functions. Integrating out explicitly the nonlocal interactions, we reduce the ERG equation obeyed by the full interaction functional to a flow equation for a function, its local part. This is done perturbatively around fixed points, but exactly to any given order in the local part. It is thus controlled, at variance with projection methods, e.g., derivative expansions or local potential approximations. Our EMRG method is well-suited to problems such as the pinning of disordered elastic systems, previously described via functional renormalization group (FRG) approach based on a hard cutoff scheme. Since it involves arbitrary cutoff functions, we explicitly verify universality to O(epsilon=4-D), both of the T=0 FRG equation and of correlations. Extension to finite temperature T yields the finite size (L) susceptibility fluctuations characterizing mesoscopic behavior (Deltachi)2 approximately L(straight theta)/T, where straight theta is the energy exponent. Finally, we obtain the universal scaling function to O(epsilon(1/3)) which describes the ground state of a domain wall in a random field confined by a field gradient, compare with exact results and variational method. Explicit two loop exact RG equations are derived and the application to the FRG problem is sketched.

Exact multilocal renormalization group and applications to disordered problems

We study the model of a discrete directed polymer (DP) on the square lattice with homogeneous inverse gamma distribution of site random Boltzmann weights, introduced by Seppalainen. The integer moments of the partition sum, $\overline{Z^n}$, are studied using a transfer matrix formulation, which appears as a generalization of the Lieb-Liniger quantum mechanics of bosons to discrete time and space. In the present case of the inverse gamma distribution the model is integrable in terms of a coordinate Bethe Ansatz, as discovered by Brunet. Using the Brunet-Bethe eigenstates we obtain an exact expression for the integer moments of $\overline{Z^n}$ for polymers of arbitrary lengths and fixed endpoint positions. Although these moments do not exist for all integer n, we are nevertheless able to construct a generating function which reproduces all existing integer moments, and which takes the form of a Fredholm determinant (FD). This suggests an analytic continuation via a Mellin-Barnes transform and we thereby propose a FD ansatz representation for the probability distribution function (PDF) of $Z$ and its Laplace transform. In the limit of very long DP, this ansatz yields that the distribution of the free energy converges to the GUE Tracy-Widom distribution up to a non-trivial average and variance that we calculate. Our asymptotic predictions coincide with a result by Borodin et al. based on a formula obtained by Seppalainen using the gRSK correspondence. In addition we obtain the dependence on the endpoint position and the exact elastic coefficient at large time. We argue the equivalence between our formula and the one of Borodin et al. As we discuss, this open the way to explore the connections between quantum integrability and tropical geometry.

Log-Gamma directed polymer with fixed endpoints via the replica Bethe Ansatz

We solve the large deviations of the Kardar-Parisi-Zhang (KPZ) equation in one dimension at short time by introducing an approach which combines field theoretical, probabilistic, and integrable techniques We expand the program of the weak noise theory, which maps the large deviations onto a nonlinear hydrodynamic problem, and unveil its complete solvability through a connection to the integrability of the Zakharov-Shabat system Exact solutions, depending on the initial condition of the KPZ equation, are obtained using the inverse scattering method and a Fredholm determinant framework recently developed These results, explicit in the case of the droplet geometry, open the path to obtain the complete large deviations for general initial conditions

Pierre Le Doussal

Papers

Aging in the glass phase of a two-dimensional random periodic elastic system.

Finite temperature Functional RG, droplets and decaying Burgers Turbulence

Exact multilocal renormalization group and applications to disordered problems

Log-Gamma directed polymer with fixed endpoints via the replica Bethe Ansatz

Inverse Scattering of the Zakharov-Shabat System Solves the Weak Noise Theory of the Kardar-Parisi-Zhang Equation.