6,498 research outputs found
Machine learning in solar physics
The application of machine learning in solar physics has the potential to
greatly enhance our understanding of the complex processes that take place in
the atmosphere of the Sun. By using techniques such as deep learning, we are
now in the position to analyze large amounts of data from solar observations
and identify patterns and trends that may not have been apparent using
traditional methods. This can help us improve our understanding of explosive
events like solar flares, which can have a strong effect on the Earth
environment. Predicting hazardous events on Earth becomes crucial for our
technological society. Machine learning can also improve our understanding of
the inner workings of the sun itself by allowing us to go deeper into the data
and to propose more complex models to explain them. Additionally, the use of
machine learning can help to automate the analysis of solar data, reducing the
need for manual labor and increasing the efficiency of research in this field.Comment: 100 pages, 13 figures, 286 references, accepted for publication as a
Living Review in Solar Physics (LRSP
Fast Macroscopic Forcing Method
The macroscopic forcing method (MFM) of Mani and Park and similar methods for
obtaining turbulence closure operators, such as the Green's function-based
approach of Hamba, recover reduced solution operators from repeated direct
numerical simulations (DNS). MFM has been used to quantify RANS-like operators
for homogeneous isotropic turbulence and turbulent channel flows. Standard
algorithms for MFM force each coarse-scale degree of freedom (i.e., degree of
freedom in the RANS space) and conduct a corresponding fine-scale simulation
(i.e., DNS), which is expensive. We combine this method with an approach
recently proposed by Sch\"afer and Owhadi (2023) to recover elliptic integral
operators from a polylogarithmic number of matrix-vector products. The
resulting Fast MFM introduced in this work applies sparse reconstruction to
expose local features in the closure operator and reconstructs this
coarse-grained differential operator in only a few matrix-vector products and
correspondingly, a few MFM simulations. For flows with significant nonlocality,
the algorithm first "peels" long-range effects with dense matrix-vector
products to expose a local operator. We demonstrate the algorithm's performance
for scalar transport in a laminar channel flow and momentum transport in a
turbulent one. For these, we recover eddy diffusivity operators at 1% of the
cost of computing the exact operator via a brute-force approach for the laminar
channel flow problem and 13% for the turbulent one. We observe that we can
reconstruct these operators with an increase in accuracy by about a factor of
100 over randomized low-rank methods. We glean that for problems in which the
RANS space is reducible to one dimension, eddy diffusivity and eddy viscosity
operators can be reconstructed with reasonable accuracy using only a few
simulations, regardless of simulation resolution or degrees of freedom.Comment: 16 pages, 10 figures. S. H. Bryngelson and F. Sch\"afer contributed
equally to this wor
Magnetic field evolution and reconnection in low resistivity plasmas
The mathematics and physics of each of the three aspects of magnetic field
evolution -- topology, energy, and helicity -- is remarkably simple and clear.
When the resistivity is small compared to an imposed evolution, ,
timescale, which means , magnetic field line chaos
dominates the evolution of field-line topology in three-dimensional systems.
Chaos has no direct role in the dissipation of energy. A large current density,
, is required for energy dissipation to be on a
comparable time scale to the topological evolution. Nevertheless, chaos plus
Alfv\'en wave damping explain why both timescales tend to be approximately an
order of magnitude longer than the evolution timescale . Magnetic helicity
is injected onto tubes of field lines when boundary flows have vorticity. Chaos
can spread but not destroy magnetic helicity. Resistivity has a negligible
effect on helicity accumulation when . Helicity accumulates within a
tube of field lines until the tube erupts and moves far from its original
location.Comment: arXiv admin note: text overlap with arXiv:2009.08779 by other author
Beam scanning by liquid-crystal biasing in a modified SIW structure
A fixed-frequency beam-scanning 1D antenna based on Liquid Crystals (LCs) is designed for application in 2D scanning with lateral alignment. The 2D array environment imposes full decoupling of adjacent 1D antennas, which often conflicts with the LC requirement of DC biasing: the proposed design accommodates both. The LC medium is placed inside a Substrate Integrated Waveguide (SIW) modified to work as a Groove Gap Waveguide, with radiating slots etched on the upper broad wall, that radiates as a Leaky-Wave Antenna (LWA). This allows effective application of the DC bias voltage needed for tuning the LCs. At the same time, the RF field remains laterally confined, enabling the possibility to lay several antennas in parallel and achieve 2D beam scanning. The design is validated by simulation employing the actual properties of a commercial LC medium
Collective variables between large-scale states in turbulent convection
The dynamics in a confined turbulent convection flow is dominated by multiple
long-lived macroscopic circulation states, which are visited subsequently by
the system in a Markov-type hopping process. In the present work, we analyze
the short transition paths between these subsequent macroscopic system states
by a data-driven learning algorithm that extracts the low-dimensional
transition manifold and the related new coordinates, which we term collective
variables, in the state space of the complex turbulent flow. We therefore
transfer and extend concepts for conformation transitions in stochastic
microscopic systems, such as in the dynamics of macromolecules, to a
deterministic macroscopic flow. Our analysis is based on long-term direct
numerical simulation trajectories of turbulent convection in a closed cubic
cell at a Prandtl number and Rayleigh numbers and
for a time lag of convective free-fall time units. The simulations
resolve vortices and plumes of all physically relevant scales resulting in a
state space spanned by more than 3.5 million degrees of freedom. The transition
dynamics between the large-scale circulation states can be captured by the
transition manifold analysis with only two collective variables which implies a
reduction of the data dimension by a factor of more than a million. Our method
demonstrates that cessations and subsequent reversals of the large-scale flow
are unlikely in the present setup and thus paves the way to the development of
efficient reduced-order models of the macroscopic complex nonlinear dynamical
system.Comment: 24 pages, 12 Figures, 1 tabl
Machine learning approach towards predicting turbulent fluid flow using convolutional neural networks
Using convolutional neural networks, we present a novel method for predicting turbulent fluid flow through an array of obstacles in this thesis. In recent years, machine learning has exploded in popularity due to its ability to create accurate data driven models and the abundance of available data. In an attempt to understand the characteristics of turbulent fluid flow, we utilise a novel convolutional autoencoder neural network to predict the first ten POD modes of turbulent fluid flow. We find
that the model is able to predict the first two POD modes well although and with less accuracy for the remaining eight POD modes. In addition, we find that the
ML-predicted POD modes are accurate enough to be used to reconstruct turbulent flow that adequately captures the large-scale details of the original simulation
Space‐Scale Resolved Surface Fluxes Across a Heterogeneous, Mid‐Latitude Forested Landscape
The Earth\u27s surface is heterogeneous at multiple scales owing to spatial variability in various properties. The atmospheric responses to these heterogeneities through fluxes of energy, water, carbon, and other scalars are scale-dependent and nonlinear. Although these exchanges can be measured using the eddy covariance technique, widely used tower-based measurement approaches suffer from spectral losses in lower frequencies when using typical averaging times. However, spatially resolved measurements such as airborne eddy covariance measurements can detect such larger scale (meso-β, meso-γ) transport. To evaluate the prevalence and magnitude of these flux contributions, we applied wavelet analysis to airborne flux measurements over a heterogeneous mid-latitude forested landscape, interspersed with open water bodies and wetlands. The measurements were made during the Chequamegon Heterogeneous Ecosystem Energy-balance Study Enabled by a High-density Extensive Array of Detectors intensive field campaign. We ask, how do spatial scales of surface-atmosphere fluxes vary over heterogeneous surfaces across the day and across seasons? Measured fluxes were separated into smaller-scale turbulent and larger-scale mesoscale contributions. We found significant mesoscale contributions to sensible and latent heat fluxes through summer to autumn which would not be resolved in single-point tower measurements through traditional time-domain half-hourly Reynolds decomposition. We report scale-resolved flux transitions associated with seasonal and diurnal changes of the heterogeneous study domain. This study adds to our understanding of surface-atmospheric interactions over unstructured heterogeneities and can help inform multi-scale model-data integration of weather and climate models at a sub-grid scale
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Path properties of KPZ models
In this thesis we investigate large deviation and path properties of a few models within the Kardar-Parisi-Zhang (KPZ) universality class.
The KPZ equation is the central object in the KPZ universality class. It is a stochastic PDE describing various objects in statistical mechanics such as random interface growth, directed polymers, interacting particle systems. In the first project we study one point upper tail large deviations of the KPZ equation (t,x) started from narrow wedge initial data. We obtain precise expression of the upper tail LDP in the long time regime for the KPZ equation. We then extend our techniques and methods to obtain upper tail LDP for the asymmetric exclusion process model, which is a prelimit of the KPZ equation.
In the next direction, we investigate temporal path properties of the KPZ equation. We show that the upper and lower law of iterated logarithms for the rescaled KPZ temporal process occurs at a scale (log log )²/³ and (log log )¹/³ respectively. We also compute the exact Hausdorff dimension of the upper level sets of the solution, i.e., the set of times when the rescaled solution exceeds (log log )²/³. This has relevance from the point of view of fractal geometry of the KPZ equation.
We next study superdiffusivity and localization features of the (1+1)-dimensional continuum directed random polymer whose free energy is given by the KPZ equation. We show that for a point-to-point polymer of length and any ⋲ (0,1), the point on the path which is distance away from the origin stays within a (1) stochastic window around a random point _, that depends on the environment. This provides an affirmative case of the folklore `favorite region' conjecture. Furthermore, the quenched density of the point when centered around _, converges in law to an explicit random density function as → ∞ without any scaling. The limiting random density is proportional to ^{-(x)} where (x) is a two-sided 3D Bessel process with diffusion coefficient 2. Our proof techniques also allow us to prove properties of the KPZ equation such as ergodicity and limiting Bessel behaviors around the maximum. In a follow up project, we show that the annealed law of polymer of length , upon ²/³ superdiffusive scaling, is tight (as → ∞) in the space of ([0,1]) valued random variables. On the other hand, as → 0, under diffusive scaling, we show that the annealed law of the polymer converges to Brownian bridge.
In the final part of this thesis, we focus on an integrable discrete half-space variant of the CDRP, called half-space log-gamma polymer.We consider the point-to-point log-gamma polymer of length 2 in a half-space with i.i.d.Gamma⁻¹(2) distributed bulk weights and i.i.d. Gamma⁻¹(+) distributed boundary weights for > 0 and > -. We establish the KPZ exponents (1/3 fluctuation and 2/3 transversal) for this model when ≥ 0. In particular, in this regime, we show that after appropriate centering, the free energy process with spatial coordinate scaled by ²/³ and fluctuations scaled by ¹/³ is tight.
The primary technical contribution of our work is to construct the half-space log-gamma Gibbsian line ensemble and develop a toolbox for extracting tightness and absolute continuity results from minimal information about the top curve of such half-space line ensembles. This is the first study of half-space line ensembles. The ≥ 0 regime correspond to a polymer measure which is not pinned at the boundary. In a companion work, we investigate the < 0 setting. We show that in this case, the endpoint of the point-to-line polymer stays within (1) window of the diagonal. We also show that the limiting quenched endpoint distribution of the polymer around the diagonal is given by a random probability mass function proportional to the exponential of a random walk with log-gamma type increments
2023-2024 Boise State University Undergraduate Catalog
This catalog is primarily for and directed at students. However, it serves many audiences, such as high school counselors, academic advisors, and the public. In this catalog you will find an overview of Boise State University and information on admission, registration, grades, tuition and fees, financial aid, housing, student services, and other important policies and procedures. However, most of this catalog is devoted to describing the various programs and courses offered at Boise State
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