Ultrafast creation and annihilation of space-charge domains in a semiconductor superlattice observed by use of Terahertz fields

We report an experimental study indicating ultrafast creation and annihilation of space-charge domains in a semiconductor superlattice under the action of a THz field. Our experiment was performed for an InGaAs/InAlAs superlattice with the conduction electrons undergoing miniband transport. We applied to a superlattice a dc bias that was slightly smaller than a critical bias necessary for the formation of space-charge domains caused by a static negative differential conductivity. Additionally subjecting the superlattice to a strong THz field, resulted in a dc transport governed by the formation of domains if the frequency of the field was smaller than an upper frequency limit (~3 THz). From this frequency limit for the creation and annihilation of domains we determined the characteristic time of the domain buildup. Our analysis shows that the buildup time of domains in a wide miniband and heavily doped superlattice is limited by the relaxation time due to scattering of the miniband electrons at polar optic phonons. Our results are of importance for both an understanding of ultrafast dynamics of pattern formation in nanostructures and the development of THz electronic devices.Received: 25 March 2004, Published online: 23 July 2004PACS: 72.20.Ht High-field and nonlinear effects - 72.30. + q High-frequency effects; plasma effects - 73.21.Cd SuperlatticesK.N. Alekseev: Permanent address: Department of Physical Sciences, P.O. Box 3000, University of Oulu FIN-90014, Finland.     

泛代数的二次扩张

在本文中引入了泛代数的二次扩张的概念，解决了ＴＵ－ＥＣ（Ａ）和ＵＴ－ＥＣ（Ａ）的存在、真类和基数问题，范畴ＴＵ－ＥＣ（Ａ）（及ＵＴ－ＥＣ（Ａ）），并得到了有关二次扩张的几个同构定理，还对一点二次扩张作了讨论。     

Constructing one-parameter families of elliptic curves with moderate rank

We give several new constructions for moderate rank elliptic curves over Q(T). In particular we construct infinitely many rational elliptic surfaces (not in Weierstrass form) of rank 6 over Q using polynomials of degree two in T. While our method generates linearly independent points, we are able to show the rank is exactly 6 without having to verify the points are independent. The method generalizes; however, the higher rank surfaces are not rational, and we need to check that the constructed points are linearly independent.     

Avoider-Enforcer games

Let p and q be positive integers and let H be any hypergraph. In a (p,q,H) Avoider-Enforcer game two players, called Avoider and Enforcer, take turns selecting previously unclaimed vertices of H. Avoider selects p vertices per move and Enforcer selects q vertices per move. Avoider loses if he claims all the vertices of some hyperedge of H; otherwise Enforcer loses. We prove a sufficient condition for Avoider to win the (p,q,H) game. We then use this condition to show that Enforcer can win the (1,q) perfect matching game on K2n for every q?cn/logn for an appropriate constant c, and the (1,q) Hamilton cycle game on Kn for every q?cnloglogloglogn/lognlogloglogn for an appropriate constant c. We also determine exactly those values of q for which Enforcer can win the (1,q) connectivity game on Kn. This result is quite surprising as it substantially differs from its Maker-Breaker analog. Our method extends easily to improve a result of Lu [X. Lu, A note on biased and non-biased games, Discrete Appl. Math. 60 (1995) 285-291], regarding forcing an opponent to pack many pairwise edge disjoint spanning trees in his graph.     

The effect of nanoparticle shape on polymer‐nanocomposite rheology and tensile strength

Nanoparticles can influence the properties of polymer materials by a variety of mechanisms. With fullerene, carbon nanotube, and clay or graphene sheet nanocomposites in mind, we investigate how particle shape influences the melt shear viscosity η and the tensile strength τ, which we determine via molecular dynamics simulations. Our simulations of compact (icosahedral), tube or rod‐like, and sheet‐like model nanoparticles, all at a volume fraction ? ≈ 0.05, indicate an order of magnitude increase in the viscosity η relative to the pure melt. This finding evidently can not be explained by continuum hydrodynamics and we provide evidence that the η increase in our model nanocomposites has its origin in chain bridging between the nanoparticles. We find that this increase is the largest for the rod‐like nanoparticles and least for the sheet‐like nanoparticles. Curiously, the enhancements of η and τ exhibit opposite trends with increasing chain length N and with particle shape anisotropy. Evidently, the concept of bridging chains alone cannot account for the increase in τ and we suggest that the deformability or flexibility of the sheet nanoparticles contributes to nanocomposite strength and toughness by reducing the relative value of the Poisson ratio of the composite. The molecular dynamics simulations in the present work focus on the reference case where the modification of the melt structure associated with glass‐formation and entanglement interactions should not be an issue. Since many applications require good particle dispersion, we also focus on the case where the polymer‐particle interactions favor nanoparticle dispersion. Our simulations point to a substantial contribution of nanoparticle shape to both mechanical and processing properties of polymer nanocomposites. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1882–1897, 2007     

Calculation of number and free energy of the conformers of linear alkanes with medium and long chains. Implications for catalysis

A method for calculating the number of rotamers of a linear alkane and of the number of rotamers with a given number of gauche conformations along the chain as a function of the total number of atoms in the chain, using general equations, is presented. A graphical method for generating individual rotamers was applied to the homologs up to decane, which has 1134 rotamers. The steric energies calculated by molecular mechanics (MM2 force field) were used as measures of the heat of formation for the coiled conformations relative to the anti conformer for each molecule, whereas the statistical entropy differences were calculated for classes of coiled rotamers grouped by the number of gauche bonds and steric energy. The free energy values calculated from these components show that already at 400 K hexane exists preferentially in conformations containing gauche bonds. For larger chains the free energy advantage for the coiled chains increases very steeply. The implications for the question of reactions of linear alkanes occurring on the surface or inside the channels of small- and medium-pore zeolites are briefly examined.     

Effect of Incident Intensity on Films Growth in Pulsed Laser Deposition

Incident intensity, defined by the amount of particles deposited per pulse, is an important parameter in the film growth process of pulsed laser deposition （PLD）. Different from previous models, we investigate the irreversible and reversible growth processes by using a kinetic Monte Carlo method and find that island density and film morphology strongly depend on pulse intensity. At higher pulse intensities, lots of adatoms instantaneously diffuse on the substrate surface, and then nucleation easily occurs between the moving adatoms resulting in more smaller-size islands. In contrast, at the lower pulse intensities, nucleation event occurs preferentially between the single adatom and existing islands rather than forming new islands, and therefore the average island size becomes larger in this case. Additionally, our results show that substrate temperature plays an important role in film growth. In particular, it can determine the films shape and weaken the effect of pulse intensity on film growth at the lower temperatures by controlling the mobility rate of atoms. Our results can match the related theoretical and experimental results.