Quasiperiodic Envelope Solitons

We analyse nonlinear wave propagation and cascaded self-focusing due to second-harmonic generation in Fibbonacci optical superlattices and introduce a novel concept of nonlinear physics, the quasiperiodic soliton, which describes spatially localized self-trapping of a quasiperiodic wave. We point out a link between the quasiperiodic soliton and partially incoherent spatial solitary waves recently generated experimentally.Comment: Submitted to PRL. 4 pages with 5 figure

Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional 5-fold and 8-fold symmetric quasiperiodic photonic crystals

We measured and calculated transmission spectra of two-dimensional quasiperiodic photonic crystals (PCs) based on a 5-fold (Penrose) or 8-fold (octagonal) symmetric quasiperiodic pattern. The photonic crystal consisted of dielectric cylindrical rods in air placed normal to the basal plane on vertices of tiles composing the quasiperiodic pattern. An isotropic photonic band gap (PBG) appeared in the TM mode, where electric fields were parallel to the rods, even when the real part of a dielectric constant of the rod was as small as 2.4. An isotropic PBG-like dip was seen in tiny Penrose and octagonal PCs with only 6 and 9 rods, respectively. These results indicate that local multiple light scattering within the tiny PC plays an important role in the PBG formation. Besides the isotropic PBG, we found dips depending on the incident angle of the light. This is the first report of anisotropic structures clearly observed in transmission spectra of quasiperiodic PCs. Based on rod-number and rod-arrangement dependence, it is thought that the shapes and positions of the anisotropic dips are determined by global multiple light scattering covering the whole system. In contrast to the isotropic PBG due to local light scattering, we could not find any PBGs due to global light scattering even though we studied transmission spectra of a huge Penrose PC with 466 rods.Comment: One tex file for manuscript and 12 PNG files for figures consisting of Fig.1a-d, 2,3, ...

Physical nature of critical wave functions in Fibonacci systems

We report on a new class of critical states in the energy spectrum of general Fibonacci systems. By introducing a transfer matrix renormalization technique, we prove that the charge distribution of these states spreads over the whole system, showing transport properties characteristic of electronic extended states. Our analytical method is a first step to find out the link between the spatial structure of these critical wave functions and the quasiperiodic order of the underlying lattice.Comment: REVTEX 3.0, 11 pages, 2 figures available upon request. To appear in Phys. Rev. Let

Size constancy in bat biosonar?

Perception and encoding of object size is an important feature of sensory systems. In the visual system object size is encoded by the visual angle (visual aperture) on the retina, but the aperture depends on the distance of the object. As object distance is not unambiguously encoded in the visual system, higher computational mechanisms are needed. This phenomenon is termed "size constancy". It is assumed to reflect an automatic re-scaling of visual aperture with perceived object distance. Recently, it was found that in echolocating bats, the 'sonar aperture', i.e., the range of angles from which sound is reflected from an object back to the bat, is unambiguously perceived and neurally encoded. Moreover, it is well known that object distance is accurately perceived and explicitly encoded in bat sonar. Here, we addressed size constancy in bat biosonar, recruiting virtual-object techniques. Bats of the species Phyllostomus discolor learned to discriminate two simple virtual objects that only differed in sonar aperture. Upon successful discrimination, test trials were randomly interspersed using virtual objects that differed in both aperture and distance. It was tested whether the bats spontaneously assigned absolute width information to these objects by combining distance and aperture. The results showed that while the isolated perceptual cues encoding object width, aperture, and distance were all perceptually well resolved by the bats, the animals did not assign absolute width information to the test objects. This lack of sonar size constancy may result from the bats relying on different modalities to extract size information at different distances. Alternatively, it is conceivable that familiarity with a behaviorally relevant, conspicuous object is required for sonar size constancy, as it has been argued for visual size constancy. Based on the current data, it appears that size constancy is not necessarily an essential feature of sonar perception in bats

Trace and antitrace maps for aperiodic sequences, their extensions and applications

We study aperiodic systems based on substitution rules by means of a transfer-matrix approach. In addition to the well-known trace map, we investigate the so-called `antitrace' map, which is the corresponding map for the difference of the off-diagonal elements of the 2x2 transfer matrix. The antitrace maps are obtained for various binary, ternary and quaternary aperiodic sequences, such as the Fibonacci, Thue-Morse, period-doubling, Rudin-Shapiro sequences, and certain generalizations. For arbitrary substitution rules, we show that not only trace maps, but also antitrace maps exist. The dimension of the our antitrace map is r(r+1)/2, where r denotes the number of basic letters in the aperiodic sequence. Analogous maps for specific matrix elements of the transfer matrix can also be constructed, but the maps for the off-diagonal elements and for the difference of the diagonal elements coincide with the antitrace map. Thus, from the trace and antitrace map, we can determine any physical quantity related to the global transfer matrix of the system. As examples, we employ these dynamical maps to compute the transmission coefficients for optical multilayers, harmonic chains, and electronic systems.Comment: 13 pages, REVTeX, now also includes applications to electronic systems, some references adde

Polymorphic Structures of Alzheimer's β-Amyloid Globulomers

Misfolding and self-assembly of Amyloid-β (Aβ) peptides into amyloid fibrils is pathologically linked to the development of Alzheimer's disease. Polymorphic Aβ structures derived from monomers to intermediate oligomers, protofilaments, and mature fibrils have been often observed in solution. Some aggregates are on-pathway species to amyloid fibrils, while the others are off-pathway species that do not evolve into amyloid fibrils. Both on-pathway and off-pathway species could be biologically relevant species. But, the lack of atomic-level structural information for these Aβ species leads to the difficulty in the understanding of their biological roles in amyloid toxicity and amyloid formation.Here, we model a series of molecular structures of Aβ globulomers assembled by monomer and dimer building blocks using our peptide-packing program and explicit-solvent molecular dynamics (MD) simulations. Structural and energetic analysis shows that although Aβ globulomers could adopt different energetically favorable but structurally heterogeneous conformations in a rugged energy landscape, they are still preferentially organized by dynamic dimeric subunits with a hydrophobic core formed by the C-terminal residues independence of initial peptide packing and organization. Such structural organizations offer high structural stability by maximizing peptide-peptide association and optimizing peptide-water solvation. Moreover, curved surface, compact size, and less populated β-structure in Aβ globulomers make them difficult to convert into other high-order Aβ aggregates and fibrils with dominant β-structure, suggesting that they are likely to be off-pathway species to amyloid fibrils. These Aβ globulomers are compatible with experimental data in overall size, subunit organization, and molecular weight from AFM images and H/D amide exchange NMR.Our computationally modeled Aβ globulomers provide useful insights into structure, dynamics, and polymorphic nature of Aβ globulomers which are completely different from Aβ fibrils, suggesting that these globulomers are likely off-pathway species and explaining the independence of the aggregation kinetics between Aβ globulomers and fibrils

Lipids revert inert Aβ amyloid fibrils to neurotoxic protofibrils that affect learning in mice

Although soluble oligomeric and protofibrillar assemblies of Aβ-amyloid peptide cause synaptotoxicity and potentially contribute to Alzheimer's disease (AD), the role of mature Aβ-fibrils in the amyloid plaques remains controversial. A widely held view in the field suggests that the fibrillization reaction proceeds ‘forward' in a near-irreversible manner from the monomeric Aβ peptide through toxic protofibrillar intermediates, which subsequently mature into biologically inert amyloid fibrils that are found in plaques. Here, we show that natural lipids destabilize and rapidly resolubilize mature Aβ amyloid fibers. Interestingly, the equilibrium is not reversed toward monomeric Aβ but rather toward soluble amyloid protofibrils. We characterized these ‘backward' Aβ protofibrils generated from mature Aβ fibers and compared them with previously identified ‘forward' Aβ protofibrils obtained from the aggregation of fresh Aβ monomers. We find that backward protofibrils are biochemically and biophysically very similar to forward protofibrils: they consist of a wide range of molecular masses, are toxic to primary neurons and cause memory impairment and tau phosphorylation in mouse. In addition, they diffuse rapidly through the brain into areas relevant to AD. Our findings imply that amyloid plaques are potentially major sources of soluble toxic Aβ-aggregates that could readily be activated by exposure to biological lipids

Optics and Quantum Electronics

Contains table of contents for Section 3 and reports on eighteen research projects.Defense Advanced Research Projects Agency/MIT Lincoln Laboratory Contract MDA972-92-J-1038Joint Services Electronics Program Grant DAAH04-95-1-0038National Science Foundation Grant ECS 94-23737U.S. Air Force - Office of Scientific Research Contract F49620-95-1-0221U.S. Navy - Office of Naval Research Grant N00014-95-1-0715MIT Center for Material Science and EngineeringNational Center for Integrated Photonics Technology Contract DMR 94-00334National Center for Integrated Photonics TechnologyU.S. Navy - Office of Naval Research (MFEL) Contract N00014-94-1-0717National Institutes of Health Grant 9-R01-EY11289MIT Lincoln Laboratory Contract BX-5098Electric Power Research Institute Contract RP3170-25ENEC