Open questions in the physics of quasi-one-dimensional metals

2008 ◽  
pp. 463-477 ◽  
Author(s):  
Theodore D. Schultz
Keyword(s):  
One Dimensional ◽  
Open Questions

scholarly journals A comparison of one-dimensional and microscale two-dimensional liquid chromatographic approaches coupled to high resolution mass spectrometry for the analysis of complex samples

2015 ◽  
Vol 7 (18) ◽  
pp. 7697-7706 ◽  
Author(s):  
Juri Leonhardt ◽  
Thorsten Teutenberg ◽  
Jochen Tuerk ◽  
Michael P. Schlüsener ◽  
Thomas A. Ternes ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Liquid Chromatography ◽  
High Resolution ◽  
High Resolution Mass Spectrometry ◽  
Two Dimensional ◽  
Complex Samples ◽  
One Dimensional ◽  
Open Questions ◽  
Liquid Chromatographic ◽  
Resolution Mass

The interest in two-dimensional liquid chromatography separations is growing every year together with the number of open questions on the benefits.

scholarly journals On the Intriguing Search for Good Permutations

2019 ◽  
Vol 14 (1) ◽  
pp. 53-86
Author(s):  
Florian Pausinger
Keyword(s):  
Research Work ◽  
80Th Birthday ◽  
One Dimensional ◽  
Small Discrepancy ◽  
Open Questions ◽  
The Future

AbstractThe intriguing search for permutations that generate generalised van der Corput sequences with exceptionally small discrepancy forms an important part of the research work of Henri Faure. On the occasion of Henri’s 80th birthday we aim to survey (some of) his contributions over the last four decades which considerably improved our understanding of one-dimensional van der Corput sequences and inspired a lot of related work. We recall and compare the different approaches in the search for generalised van der Corput sequences with low discrepancy, i.e., using a single generating permutation versus using a sequence of permutations. Throughout, we collect, sharpen and extend open questions which all stem from the extensive work of Henri and his coworkers and which will hopefully inspire more work in the future.

scholarly journals Control and Optimization of Interfacial Flows Using Adjoint-Based Techniques

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 156
Author(s):  
Alexandru Fikl ◽  
Vincent Le Chenadec ◽  
Taraneh Sayadi
Keyword(s):  
Characteristic Function ◽  
Two Dimensions ◽  
Interfacial Flows ◽  
Volume Of Fluid Method ◽  
Optimal Solutions ◽  
One Dimensional ◽  
Open Questions ◽  
Gradient Computation ◽  
Truncated Newton ◽  
Future Work

The applicability of adjoint-based gradient computation is investigated in the context of interfacial flows. Emphasis is set on the approximation of the transport of a characteristic function in a potential flow by means of an algebraic volume-of-fluid method. A class of optimisation problems with tracking-type functionals is proposed. Continuous (differentiate-then-discretize) and discrete (discretize-then-differentiate) adjoint-based gradient computations are formulated and compared in a one-dimensional configuration, the latter being ultimately used to perform optimisation in two dimensions. The gradient is used in truncated Newton and steepest descent optimisers, and the algorithms are shown to recover optimal solutions. These validations raise a number of open questions, which are finally discussed with directions for future work.

scholarly journals A theory of spectral partitions of metric graphs

2021 ◽  
Vol 60 (2) ◽  
Author(s):  
James B. Kennedy ◽  
Pavel Kurasov ◽  
Corentin Léna ◽  
Delio Mugnolo
Keyword(s):  
Spectral Gaps ◽  
Qualitative Properties ◽  
Metric Graphs ◽  
One Dimensional ◽  
Graph Partitions ◽  
Planar Domains ◽  
Open Questions ◽  
The One ◽  
Abstract Framework ◽  
Special Case

AbstractWe introduce an abstract framework for the study of clustering in metric graphs: after suitably metrising the space of graph partitions, we restrict Laplacians to the clusters thus arising and use their spectral gaps to define several notions of partition energies; this is the graph counterpart of the well-known theory of spectral minimal partitions on planar domains and includes the setting in Band et al. (Commun Math Phys 311:815–838, 2012) as a special case. We focus on the existence of optimisers for a large class of functionals defined on such partitions, but also study their qualitative properties, including stability, regularity, and parameter dependence. We also discuss in detail their interplay with the theory of nodal partitions. Unlike in the case of domains, the one-dimensional setting of metric graphs allows for explicit computation and analytic—rather than numerical—results. Not only do we recover the main assertions in the theory of spectral minimal partitions on domains, as studied in Conti et al. (Calc Var 22:45–72, 2005), Helffer et al. (Ann Inst Henri Poincaré Anal Non Linéaire 26:101–138, 2009), but we can also generalise some of them and answer (the graph counterparts of) a few open questions.

Effect of DNA conformation on facilitated diffusion

2013 ◽  
Vol 41 (2) ◽  
pp. 582-588 ◽  
Author(s):  
Chris A. Brackley ◽  
Mike E. Cates ◽  
Davide Marenduzzo
Keyword(s):  
Three Dimensional ◽  
Bulk Diffusion ◽  
Dna Looping ◽  
Dna Conformation ◽  
Standard Theory ◽  
Facilitated Diffusion ◽  
One Dimensional ◽  
Open Questions ◽  
Dna Backbone ◽  
Do So

Within a living cell, site-specific DNA-binding proteins need to search the whole genome to find a target of ~10–20 bp. That they find the target, and do so quickly, is vital for the correct functioning of the DNA, and of the cell as a whole. The current understanding is that this search is performed via facilitated diffusion, i.e. by combining three-dimensional bulk diffusion within the cytoplasm or nucleoplasm, with one-dimensional diffusion along the DNA backbone, to which the protein binds non-specifically. After reviewing the standard theory of facilitated diffusion, we discuss in the present article the still rather rare direct computer simulations of this process, focusing on the three-dimensional part of the search, and the effect of DNA looping and the general DNA conformation on its efficiency. We close by highlighting some open questions in this field.

Reachability Problems for One-Dimensional Piecewise Affine Maps

2018 ◽  
Vol 29 (04) ◽  
pp. 529-549 ◽  
Author(s):  
Olivier Bournez ◽  
Oleksiy Kurganskyy ◽  
Igor Potapov
Keyword(s):  
Open Problem ◽  
Reference Model ◽  
Base System ◽  
Topological Properties ◽  
Reachability Problem ◽  
New Techniques ◽  
One Dimensional ◽  
Piecewise Affine ◽  
Affine Maps ◽  
Open Questions

Piecewise affine maps (PAMs) are frequently used as a reference model to discuss the frontier between known and open questions about the decidability for reachability questions. In particular, the reachability problem for one-dimensional PAM is still an open problem, even if restricted to only two intervals. As the main contribution of this paper we introduce new techniques for solving reachability problems based on [Formula: see text]-adic norms and weights as well as showing decidability for two classes of maps. Then we show the connections between topological properties for PAM’s orbits, reachability problems and representation of numbers in a rational base system. Finally we construct an example where the distribution properties of well studied sequences can be significantly disrupted by taking fractional parts after regular shifts. The study of such sequences could help with understanding similar sequences generated in PAMs or in well known Mahler’s [Formula: see text] problem.

scholarly journals Electrodynamics of Bechgaard Salts: Optical Properties of One-Dimensional Metals

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Martin Dressel
Keyword(s):  
Collective Mode ◽  
Density Wave ◽  
Spin Density Wave ◽  
Low Frequency ◽  
Current Status ◽  
Excitation Spectra ◽  
Bechgaard Salts ◽  
One Dimensional ◽  
Open Questions ◽  
Liquid Behavior

The electrodynamic properties of the quasi-one-dimensional organic conductors (TMTSF)2X are discussed, with particular emphasis on important deviations from the simple Drude model, the transition from a Luttinger-liquid to a Fermi-liquid behavior at the dimensional crossover when pressure is applied or temperature reduced, indications of a pseudogap as well as a low-frequency collective mode. Superconductivity and spin-density-wave ground states breaking the symmetry and gaps should occur in the excitation spectra. The previous literature is summarized and the current status of our understanding presented. Novel THz experiments on (TMTSF)2PF6 and (TMTSF)2ClO4 not only shine light into some of the open questions, but also pose new ones.

scholarly journals Bifurcation currents and equidistribution in parameter space

2014 ◽  
Author(s):  
Romain Dujardin
Keyword(s):  
Dynamical Systems ◽  
Parameter Space ◽  
Rational Maps ◽  
Parameter Spaces ◽  
One Dimensional ◽  
Open Questions ◽  
Higher Dimensional ◽  
Möbius Group ◽  
Positive Currents

This chapter reviews the use of techniques of positive currents for the study of parameter spaces of one-dimensional holomorphic dynamical systems (rational mappings on P¹ or subgroups of the Möbius group PSL(2,C)). The topics covered include the construction of bifurcation currents and the characterization of their supports, the equidistribution properties of dynamically defined subvarieties of the parameter space. Emphasis will be placed as much as possible on the similarities between methods of higher-dimensional dynamics, of the study of families of rational maps, and that of Möbius subgroups. The chapter also states a number of open questions to foster further developments of this theory.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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