224 research outputs found
The role of fully coupled ice sheet basal processes in quaternary glacial cycles
Bed conditions such as meltwater pressurization and unconsolidated sediment cover
(soft versus hard bedded) strongly impact ice sheet sliding velocities. How the
dynamical processes governing these conditions affect glacial cycle scale ice sheet
evolution has been little studied. The influence of subglacial hydrology and glacial
sediment production and transport is therefore largely unknown. Here I present a
glaciological model Glacial Systems Model (GSM) with the to-date most complete
representations of fully coupled subglacial hydrology and sediment production and
transport for the glacial cycle continental scale context. I compare the influence of
of several types of subglacial hydrology drainage systems on millennial scale
variability and examine the role dynamical sediment processes potentially played
in the mid-Pleistocene Transition (MPT) from 41 to 100 kyr glacial cycles.
Subglacial hydrology has long been inferred to play a role in glacial dynamics at
decadal and shorter scales. However, it remains unclear whether subglacial
hydrology has a critical role in ice sheet evolution on greater than centennial
time-scales. It is also unclear which drainage system is most appropriate for the
continental/glacial cycle scale. Here I compare the dynamical role of three
subglacial hydrology systems most dominant in the literature in the context of
surge behaviour for an idealized Hudson Strait scale ice stream. I find that
subglacial hydrology is an important system inductance for realistic ice stream
surging and that the three formulations all exhibit similar surge behaviour. Even a
detail as fundamental as mass conserving transport of subglacial water is not
necessary for simulating a full range of surge frequency and amplitude. However,
one difference is apparent: the combined positive and negative feedbacks of the
linked-cavity system yields longer duration surges and a broader range of effective
pressures than its poro-elastic and leaky-bucket counterparts.
The MPT from 41 kyr to 100 kyr glacial cycles was one of the largest changes in
the Earth system over the past million years. A change from a low to high friction
base under the North American Ice Complex through the removal of pre-glacial
regolith has been hypothesized to play a critical role in the transition to longer
and stronger glaciations. However, this hypothesis requires constraint on
pre-glacial regolith cover as well as mechanistic constraints on whether the
appropriate amount of regolith can be removed from the required regions to enable
MPT occurrence at the right time. This is the first study to test the regolith
hypothesis for a realistic 3D North American ice sheet that treats regolith removal
as a system internal process instead of a forced soft to hard transition.
The fully coupled climate, ice, subglacial hydrology, and sediment physics capture
the progression of Pleistocene glacial cycles within parametric and observational
uncertainty. Incorporating the constraint from estimates for the present day
sediment distribution, Quaternary erosion, and Atlantic Quaternary sediment
volume suggests the mean Pliocene regolith thickness was 40 m or less. Given this
constraint, I compare the simulated soft to hard bed transitions with the timing
inferred for the MPT. The combined constraint, bedrock erosion, and sediment
transport poses a challenge to the Regolith Hypothesis: denudation occurs well in
advance of the MPT and the hard bedded area stays largely constant by 1.5 Ma.
Furthermore, I examine the sensitivity of glacial cycle evolution to the initial
thickness of the regolith in the absence of erosion. Surprisingly, thicker regolith
does not delay the transition but produces large glacial cycles in the early
Pleistocene even extending the length of some. This is due to the effect from
higher topography on ice sheet mass balance. Therefore, I suggest that the
regolith removal mechanism is not singularly responsible for the MPT, but that
the MPT results from changes in many aspects of the systems. One of these
aspects which remains under-studied in the literature is the long term evolution of
glacierized beds over the Pleistocene
Mixed Chebyshev and Legendre polynomials differentiation matrices for solving initial-boundary value problems
A new form of basis functions structures has been constructed. These basis functions constitute a mix of Chebyshev polynomials and Legendre polynomials. The main purpose of these structures is to present several forms of differentiation matrices. These matrices were built from the perspective of pseudospectral approximation. Also, an investigation of the error analysis for the proposed expansion has been done. Then, we showed the presented matrices' efficiency and accuracy with several test functions. Consequently, the correctness of our matrices is demonstrated by solving ordinary differential equations and some initial boundary value problems. Finally, some comparisons between the presented approximations, exact solutions, and other methods ensured the efficiency and accuracy of the proposed matrices
Chaos control and numerical solution of time-varying fractional Newton-Leipnik system using fractional Atangana-Baleanu derivatives
Nonlinear fractional differential equations and chaotic systems can be modeled with variable-order differential operators. We propose a generalized numerical scheme to simulate variable-order fractional differential operators. Fractional calculus' fundamental theorem and Lagrange polynomial interpolation are used. Two methods, Atangana-Baleanu-Caputo and Atangana-Seda derivatives, were used to solve a chaotic Newton-Leipnik system problem with fractional operators. Our scheme examined the existence and uniqueness of the solution. We analyze the model qualitatively using its equivalent integral through an iterative convergence sequence. This novel method is illustrated with numerical examples. Simulated and analytical results agree. We contribute to real-world mathematical applications. Finally, we applied a numerical successive approximation method to solve the fractional model
Kernel Functions and New Applications of an Accurate Technique
In this article, some general reproducing kernel Sobolev spaces was constructed. We find the general functions in these reproducing kernel Sobolev spaces. Many higher order boundary value problems can be investigated by these special functions
A reproducing kernel method for solving singularly perturbed delay parabolic partial differential equations
In this article, we put forward an efficient method on the foundation of a few reproducing kernel spaces(RK-spaces) and the collocation method to seek the solution of delay parabolic partial differential equations(PDEs) with singular perturbation. The approximated solution to the equations is formulated and proved the exact solution is uniformly convergent by the solution. Furthermore, the partial differentiation of the approximated solution is also proved the partial derivatives of the exact solution is uniformly convergent by the solution. Meanwhile, we show that the accuracy of our method is in the order of T/n where T is the final time and n is the number of spatial (and time) discretization in the domain of interests. Three numerical examples are put forward to demonstrate the effectiveness of our presented scheme
Fitted mesh method for singularly perturbed fourth order differential equation of convection diffusion type with integral boundary condition
This article focuses on a class of fourth-order singularly perturbed convection diffusion equations (SPCDE) with integral boundary conditions (IBC). A numerical method based on a finite difference scheme using Shishkin mesh is presented. The proposed method is close to the first-order convergent. The discrete norm yields an error estimate and theoretical estimations are tested by numerical experiments
Event-triggered robust control for multi-player nonzero-sum games with input constraints and mismatched uncertainties
In this article, an event-triggered robust control (ETRC) method is investigated for multi-player nonzero-sum games of continuous-time input constrained nonlinear systems with mismatched uncertainties. By constructing an auxiliary system and designing an appropriate value function, the robust control problem of input constrained nonlinear systems is transformed into an optimal regulation problem. Then, a critic neural network (NN) is adopted to approximate the value function of each player for solving the event-triggered coupled Hamilton-Jacobi equation and obtaining control laws. Based on a designed event-triggering condition, control laws are updated when events occur only. Thus, both computational burden and communication bandwidth are reduced. We prove that the weight approximation errors of critic NNs and the closed-loop uncertain multi-player system states are all uniformly ultimately bounded thanks to the Lyapunov's direct method. Finally, two examples are provided to demonstrate the effectiveness of the developed ETRC method
Differential Models, Numerical Simulations and Applications
This Special Issue includes 12 high-quality articles containing original research findings in the fields of differential and integro-differential models, numerical methods and efficient algorithms for parameter estimation in inverse problems, with applications to biology, biomedicine, land degradation, traffic flows problems, and manufacturing systems
A pseudo-spectral method based on reproducing kernel for solving the time-fractional diffusion-wave equation
In this paper, we focus on the development and study of the finite difference/pseudo-spectral method to obtain an approximate solution for the time-fractional diffusion-wave equation in a reproducing kernel Hilbert space. Moreover, we make use of the theory of reproducing kernels to establish certain reproducing kernel functions in the aforementioned reproducing kernel Hilbert space. Furthermore, we give an approximation to the time-fractional derivative term by applying the finite difference scheme by our proposed method. Over and above, we present an appropriate technique to derive the numerical solution of the given equation by utilizing a pseudo-spectral method based on the reproducing kernel. Then, we provide two numerical examples to support the accuracy and efficiency of our proposed method. Finally, we apply numerical experiments to calculate the quality of our approximation by employing discrete error norms. © 2022, The Author(s)
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