1,538 research outputs found
Finite Extinction Time for Non-Linear Absorption-Diffusion Equations
In this thesis, we develop a numerical method in order to approximate the solutions of one-dimensional, non-linear absorption-diffusion equations. We test our method for accuracy against a linear diffusion equation with a solution that can be written in closed form. We then test various types of diffusion and absorption terms to determine which ones produce extinction in finite time. We also develop a numerical method to computationally solve diffusion-free equations. We compare the numerical solutions of the one-dimensional, non-linear absorption-diffusion equation and the diffusion-free equation and we find that for the cases tested, the numerical absorption-diffusion solutions are always less than the numerical diffusion-free solutions. Furthermore, we find this is true for the cases tested when there is finite and infinite extinction time. We also look at the open problem where we have slow diffusion and weak absorption but, their combined effect is strong. Our results provide some insight into the answer of this problem
An Analytical Model of Nanometer Scale Viscoelastic Properties of Polymer Surfaces Measured Using an Atomic Force Microscope
The United States Air Force and the Department of Defense is increasingly interested in nanomaterials. To study these materials, one needs to measure the mechanics of materials on the nanoscale. Over the past few decades the atomic force microscope (AFM) has been used in various methods to establish local surface properties at the nanoscale. In particular, surface elasticity measurements are crucial to understanding nanoscale surface properties. Problems arise, however, when measuring soft surfaces such as polymers and biological specimens, because these materials have a more complex viscoelastic response. This research focuses on modeling an AFM dynamic nanoindentation experiment intended to characterize near-surface viscoelastic material parameters. The experiment uses an AFM in dynamic contact mode with a polymer surface to gather frequency dependent amplitude and phase data. A three-dimensional, dynamic viscoelastic model of the AFM and surface interaction is developed and then analytically solved in the linear approximation under appropriate physical assumptions based on the physics of the AFM experimental setup. As an illustrative application, the analytical solution is coupled with experimental data from a polystyrene material to ascertain surface material properties at the nanoscale. Our solution allows the direct calculation of the storage and loss modulus from experimental data
The Complexity of Approximately Counting Retractions
Let be a graph that contains an induced subgraph . A retraction from
to is a homomorphism from to that is the identity function on
. Retractions are very well-studied: Given , the complexity of deciding
whether there is a retraction from an input graph to is completely
classified, in the sense that it is known for which this problem is
tractable (assuming ). Similarly, the complexity of
(exactly) counting retractions from to is classified (assuming
). However, almost nothing is known about
approximately counting retractions. Our first contribution is to give a
complete trichotomy for approximately counting retractions to graphs of girth
at least . Our second contribution is to locate the retraction counting
problem for each in the complexity landscape of related approximate
counting problems. Interestingly, our results are in contrast to the situation
in the exact counting context. We show that the problem of approximately
counting retractions is separated both from the problem of approximately
counting homomorphisms and from the problem of approximately counting list
homomorphisms --- whereas for exact counting all three of these problems are
interreducible. We also show that the number of retractions is at least as hard
to approximate as both the number of surjective homomorphisms and the number of
compactions. In contrast, exactly counting compactions is the hardest of all of
these exact counting problems
Influence of surface states on the conductance spectra for Co adsorbed on Cu(111)
We calculate the conductance spectra of a Co atom adsorbed on Cu(111), considering the Co 3d orbitals within a correlated multiple configurations model interacting through the substrate band with the Co 4s orbital, which is treated in a mean-field-like approximation. By symmetry, only the dz2 orbital couples with the s orbital through the Cu bands, and the interference between both conduction channels introduces a zero-bias anomaly in the conductance spectra. We find that, while the Kondo resonance is mainly determined by the interaction of the Co d orbitals with the bulk states of the Cu(111) surface, a proper description of the contribution given by the coupling with the localized surface states to the Anderson widths is crucial to describe the interference line shape. We find that the coupling of the Co 4s orbital with the Shockley surface states is responsible for two main features observed in the measured conductance spectra, the dip shape around the Fermi energy and the resonance structure at the surface state low band edge.Fil: Tacca, Marcos Sebastian. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - Santa Fe. Instituto de FĂsica del Litoral. Universidad Nacional del Litoral. Instituto de FĂsica del Litoral; Argentina. Universitat Ulm. Faculty Of Natural Sciences; AlemaniaFil: Jacob, T.. Universitat Ulm. Faculty Of Natural Sciences; AlemaniaFil: Goldberg, Edith Catalina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - Santa Fe. Instituto de FĂsica del Litoral. Universidad Nacional del Litoral. Instituto de FĂsica del Litoral; Argentin
Unsupervised Distillation of Syntactic Information from Contextualized Word Representations
Contextualized word representations, such as ELMo and BERT, were shown to
perform well on various semantic and syntactic tasks. In this work, we tackle
the task of unsupervised disentanglement between semantics and structure in
neural language representations: we aim to learn a transformation of the
contextualized vectors, that discards the lexical semantics, but keeps the
structural information. To this end, we automatically generate groups of
sentences which are structurally similar but semantically different, and use
metric-learning approach to learn a transformation that emphasizes the
structural component that is encoded in the vectors. We demonstrate that our
transformation clusters vectors in space by structural properties, rather than
by lexical semantics. Finally, we demonstrate the utility of our distilled
representations by showing that they outperform the original contextualized
representations in a few-shot parsing setting.Comment: Accepted in BlackboxNLP@EMNLP202
Multiorbital electronic correlation effects of Co adatoms on graphene: An ionic Hamiltonian approach
In the present work, we propose an ionic Hamiltonian for describing the interaction of graphene with an adsorbed Co atom. In this approach, the electronic correlation effects, related to the many d orbitals involved in the interaction, are taken into account by selecting appropriate electronic configurations of the adsorbed atom. The Hamiltonian parameters are calculated considering the localized and extended features of the atom-surface interacting system. The physical quantities of interest are calculated by using a Green functions formalism, solved by means of the equations of motion method closed up to a second order in the atom-band coupling term. The charge and spin fluctuations in the adsorbed Co atom are inferred from density functional theory calculations and assuming that the lower energy configurations obey Hund's rules. The calculated spectral densities and the occurrence probabilities of the different atomic configurations are analyzed as a function of the Co energy level positions and the surface temperature. In addition, the conductance spectra are calculated by using the Keldysh formalism and compared with existing measurements. We analyze the behavior, under variable bias and gate potentials, of resonancelike features in the conductance spectra which can be related to transitions between atomic configurations of low occurrence probability.Fil: Tacca, Marcos Sebastian. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - Santa Fe. Instituto de FĂsica del Litoral. Universidad Nacional del Litoral. Instituto de FĂsica del Litoral; ArgentinaFil: Jacob, T.. Universitat Ulm. Faculty of Natural Sciences; AlemaniaFil: Goldberg, Edith Catalina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - Santa Fe. Instituto de FĂsica del Litoral. Universidad Nacional del Litoral. Instituto de FĂsica del Litoral; Argentin
Quantum control of Rydberg atoms for mesoscopic-scale quantum state and circuit preparation
Individually trapped Rydberg atoms show significant promise as a platform for
scalable quantum simulation and for development of programmable quantum
computers. In particular, the Rydberg blockade effect can be used to facilitate
both fast qubit-qubit interactions and long coherence times via low-lying
electronic states encoding the physical qubits. To bring existing
Rydberg-atom-based platforms a step closer to fault-tolerant quantum
computation, we demonstrate high-fidelity state and circuit preparation in a
system of five atoms. We specifically show that quantum control can be used to
reliably generate fully connected cluster states and to simulate the
error-correction encoding circuit based on the 'Perfect Quantum Error
Correcting Code' by Laflamme et al. [Phys. Rev. Lett. 77, 198 (1996)]. Our
results make these ideas and their implementation directly accessible to
experiments and demonstrate a promising level of noise tolerance with respect
to experimental errors. With this approach, we motivate the application of
quantum control in small subsystems in combination with the standard gate-based
quantum circuits for direct and high-fidelity implementation of few-qubit
modules
Counting Homomorphisms to -minor-free Graphs, modulo 2
We study the problem of computing the parity of the number of homomorphisms
from an input graph to a fixed graph . Faben and Jerrum [ToC'15]
introduced an explicit criterion on the graph and conjectured that, if
satisfied, the problem is solvable in polynomial time and, otherwise, the
problem is complete for the complexity class of parity
problems. We verify their conjecture for all graphs that exclude the
complete graph on vertices as a minor. Further, we rule out the existence
of a subexponential-time algorithm for the -complete cases,
assuming the randomised Exponential Time Hypothesis. Our proofs introduce a
novel method of deriving hardness from globally defined substructures of the
fixed graph . Using this, we subsume all prior progress towards resolving
the conjecture (Faben and Jerrum [ToC'15]; G\"obel, Goldberg and Richerby
[ToCT'14,'16]). As special cases, our machinery also yields a proof of the
conjecture for graphs with maximum degree at most , as well as a full
classification for the problem of counting list homomorphisms, modulo
- …