117,500 research outputs found
Transition from order to chaos in the wake of an airfoil
An experimental effort is presented here that examines the nonlinear interaction of multiple frequencies in the forced wake of an airfoil. Wakes with one or two distinct frequencies behave in an ordered manner – being either locked or quasi-periodic. When a third incommensurate frequency is added to the system, the flow demonstrates chaotic behaviour. Previously, the existence of the three-frequency route to chaos has been reported only for closed system flows. It is important to note that this chaotic state is obtained at a low Reynolds number. However, the chaotic flow shows localized characteristics similar to those of high Reynolds number turbulent flows. The degree of chaotic behaviour is verified by applying ideas from nonlinear dynamics (such as Lyapunov exponents and Poincaré sections) to the experimental data, thus relating the basic physics of the system to the concepts of mode interaction and chaos. Significant changes to the vortex configuration in the wake and to the r.m.s. velocity profile occur during the transition from order to chaos
Modified spin-wave theory with ordering vector optimization I: frustrated bosons on the spatially anisotropic triangular lattice
We investigate a system of frustrated hardcore bosons, modeled by an XY
antiferromagnet on the spatially anisotropic triangular lattice, using
Takahashi's modified spin-wave (MSW) theory. In particular we implement
ordering vector optimization on the ordered reference state of MSW theory,
which leads to significant improvement of the theory and accounts for quantum
corrections to the classically ordered state. The MSW results at zero
temperature compare favorably to exact diagonalization (ED) and projected
entangled-pair state (PEPS) calculations. The resulting zero-temperature phase
diagram includes a 1D quasi-ordered phase, a 2D Neel ordered phase, and a 2D
spiraling ordered phase. We have strong indications that the various ordered or
quasi-ordered phases are separated by spin-liquid phases with short-range
correlations, in analogy to what has been predicted for the Heisenberg model on
the same lattice. Within MSW theory we also explore the finite-temperature
phase diagram. We find that the zero-temperature long-range-ordered phases turn
into quasi-ordered phases (up to a Berezinskii-Kosterlitz-Thouless
temperature), while zero-temperature quasi-ordered phases become short-range
correlated at finite temperature. These results show that modified spin-wave
theory is very well suited for describing ordered and quasi-ordered phases of
frustrated XY spins (or, equivalently, of frustrated lattice bosons) both at
zero and finite temperatures. While MSW theory, just as other theoretical
methods, cannot describe spin-liquid phases, its breakdown provides a fast
method for singling out Hamiltonians which may feature these intriguing quantum
phases. We thus suggest a tool for guiding our search for interesting systems
whose properties are necessarily studied with a physical quantum simulator.Comment: 40 pages, 16 figure
Renormalization by Continuous Unitary Transformations: One-Dimensional Spinless Fermions
A renormalization scheme for interacting fermionic systems is presented where
the renormalization is carried out in terms of the fermionic degrees of
freedom. The scheme is based on continuous unitary transformations of the
hamiltonian which stays hermitian throughout the renormalization flow, whereby
any frequency dependence is avoided. The approach is illustrated in detail for
a model of spinless fermions with nearest neighbour repulsion in one dimension.
Even though the fermionic degrees of freedom do not provide an easy starting
point in one dimension very good results are obtained which agree well with the
exact findings based on Bethe ansatz.Comment: 17 pages, figures included some revisions concerning the comparison
to other methods, references update
Pinning and depinning of a classic quasi-one-dimensional Wigner crystal in the presence of a constriction
We studied the dynamics of a quasi-one-dimensional chain-like system of
charged particles at low temperature, interacting through a screened Coulomb
potential in the presence of a local constriction. The response of the system
when an external electric field is applied was investigated. We performed
Langevin molecular dynamics simulations for different values of the driving
force and for different temperatures. We found that the friction together with
the constriction pins the particles up to a critical value of the driving
force. The system can depin \emph{elastically} or \emph{quasi-elastically}
depending on the strength of the constriction. The elastic (quasi-elastic)
depinning is characterized by a critical exponent
(). The dc conductivity is zero in the pinned regime, it has
non-ohmic characteristics after the activation of the motion and then it is
constant. Furthermore, the dependence of the conductivity with temperature and
strength of the constriction was investigated in detail. We found interesting
differences between the single and the multi-chain regimes as the temperature
is increased.Comment: 18 pages, 16 figures, accepted for publication in PR
Well Structured Transition Systems with History
We propose a formal model of concurrent systems in which the history of a
computation is explicitly represented as a collection of events that provide a
view of a sequence of configurations. In our model events generated by
transitions become part of the system configurations leading to operational
semantics with historical data. This model allows us to formalize what is
usually done in symbolic verification algorithms. Indeed, search algorithms
often use meta-information, e.g., names of fired transitions, selected
processes, etc., to reconstruct (error) traces from symbolic state exploration.
The other interesting point of the proposed model is related to a possible new
application of the theory of well-structured transition systems (wsts). In our
setting wsts theory can be applied to formally extend the class of properties
that can be verified using coverability to take into consideration (ordered and
unordered) historical data. This can be done by using different types of
representation of collections of events and by combining them with wsts by
using closure properties of well-quasi orderings.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
Equilibrium properties of the lattice system with SALR interaction potential on a square lattice: quasi-chemical approximation versus Monte Carlo simulation
The lattice system with competing interactions that models biological objects
(colloids, ensembles of protein molecules, etc.) is considered. This system is
the lattice fluid on a square lattice with attractive interaction between
nearest neighbours and repulsive interaction between next-next-nearest
neighbours. The geometric order parameter is introduced for describing the
ordered phases in this system. The critical value of the order parameter is
estimated and the phase diagram of the system is constructed. The simple
quasi-chemical approximation (QChA) is proposed for the system under
consideration. The data of Monte Carlo simulation of equilibrium properties of
the model are compared with the results of QChA. It is shown that QChA provides
reasonable semiquantitative results for the systems studied and can be used as
the basis for next order approximations.Comment: 10 pages, 8 figure
Magnetic ordering of weakly coupled frustrated quantum spin chains
The ordering temperature of a quasi-one-dimensional system, consisting of
weakly interacting quantum spin-1/2 chains with antiferromagnetic
spin-frustrating couplings (or zig-zag ladder) is calculated. The results show
that a quantum critical point between two phases of the one-dimensional
subsystem plays a crucial role. If the one-dimensional subsystem is in the
antiferromagnetic-like phase in the ground state, similar to the phase of a
spin chain without frustration, weak couplings yield magnetic ordering of the
Neel type. For intra-chain spin-frustrating interactions larger than the
critical one (at which the quantum phase transition takes place), the
quasi-one-dimensional spin system manifests a spiral magnetic incommensurate
ordering. The obtained results of our quantum theory are compared with the
quasi-classical approximations. The calculated features of magnetic ordering
are expected to be generic for weakly coupled quantum spin chains with gapless
excitations and spin-frustrating nearest and next-nearest neighbor
interactions.Comment: 6 pages, 2 figure
Electronic properties of the pseudogap system (TaSe4)2I
The room temperature ``metallic'' properties of the quasi-one-dimensional
charge density wave system (TaSe4)2I differ markedly from those expected of
either a Fermi or a Luttinger Liquid. We discuss evidence for the simplest
possible explanation of the observed behavior of (TaSe4)2I in its conducting
phase - namely the existence of large quasi-static fluctuations of structural
order, which however remain of finite extent above the charge density wave
transition temperature. These fluctuations produce a pseudogap in the density
of states. We compute the temperature dependence of the optical and DC
conductivities of (TaSe4)2I in its conducting phase, the nature of its core
hole spectra, and the NMR relaxation rate. Predictions for these quantities are
made on the basis of a Lee, Rice and Anderson model. This model represents the
simplest theory of a pseudogap, and gives satisfactory agreement with
experiment in the cases where comparisons can be made. In contrast, the
predictions of a strongly correlated (Luttinger Liquid) model appear to to
contradict the data. The chief remaining discrepancy is that the gap appearing
in transport quantities is less than that observed in photoemission. We discuss
some possibilities for resolving this issue.Comment: 41 pages latex, 11 ps figures, uses IOP macro
- …