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For jointly assimilating sea‐ice concentration (SIC) and sea‐ice thickness (SIT) observations into a global coupled climate system model consisting of sea‐ice component with multiple sea‐ice categories, we propose a new sea‐ice analysis update scheme in an ensemble assimilation framework and compare it with some previously used schemes. Different from the conventional scheme that often assigns SIC/SIT analysis to multiple sea‐ice categories according to the background ratios and thus directly updates the corresponding variables in model (i.e., direct‐update scheme), the new scheme converts SIC/SIT analysis into ice heating term to adjust the ice enthalpy using model freezing/melting physics and further updates the model sea‐ice state (i.e., enthalpy‐adjusting scheme). It has a capability in particularly adjusting multiple sea‐ice variables in addition to SIC and SIT in a coordinated way, and avoiding the artificial addition or elimination of sea‐ice in analysis that is often adopted in the direct‐update scheme. Evaluated by several sets of experiments assimilating satellite‐derived Arctic sea‐ice observations, the enthalpy‐adjusting scheme performs better than the direct‐update scheme in analysis of the Arctic SIT. Further, 4‐week forecasts after assimilation initialization exhibit slow growth of forecast error. Compared to the direct‐update scheme, the enthalpy‐adjusting scheme initialized forecasts show comparable skills in the SIC but significantly higher skills in the SIT, especially in the Arctic sea‐ice edge areas. These results highlight advantage of the enthalpy‐adjusting scheme that has promise to improve coupled data assimilation and reduce climate prediction uncertainty. Plain Language Summary Effective assimilation of sea‐ice observation is an important task for building coupled data assimilation and prediction system based on the climate system model. For the establishment of coupled sea‐ice assimilation technique, how to ensure the coordination of multiple variables is a crucial issue. Although sea‐ice's ablation and accretion are mainly thermodynamic‐driven and most sea‐ice models focus on describing the enthalpy properties of ice, till now there are few studies to implement enthalpy‐based sea‐ice assimilation in complex climate model due to the difficulty of accurately estimating the enthalpy in observational space and model space. This study proposes an enthalpy‐adjusting scheme that uses sea‐ice concentration/thickness (SIC/SIT) analysis to adjust ice enthalpy and further update the sea‐ice state in model. Compared to the conventional scheme that uses SIC/SIT analysis to directly update the corresponding model variables, the new scheme produces better analysis of the Arctic SIT at the assimilation stage, and also higher subseasonal forecast skill of the Arctic SIT at the forecast stage. The study indicates the obvious superiority of the enthalpy‐adjusting analysis scheme in sea‐ice forecasting and highlights the importance of multivariate coordinated assimilation for improving climate model's forecast performance. Key Points A new sea‐ice analysis update scheme based on enthalpy‐adjusting strategy is developed for coordinated sea‐ice multivariate assimilation The scheme is capable of providing skillful analysis of sea‐ice concentration/thickness (SIC/SIT) in the Arctic The scheme can produce apparently lower error of SIT in subseasonal forecasting of Arctic sea‐ice

Multi-material topology optimization is a practical tool that allows for improved structural designs. However, most studies are presented in the context of continuum topology optimization – few studies focus on truss topology optimization. Moreover, most work in this field has been restricted to linear material behavior with limited volume constraint settings for multiple materials. To address these issues, we propose an efficient multi-material topology optimization formulation considering material nonlinearity. The proposed formulation handles an arbitrary number of candidate materials with flexible material properties, features freely specified material layers, and includes a generalized volume constraint setting. To efficiently handle such arbitrary volume constraints, we derive a design update scheme that performs robust updates of the design variables associated with each volume constraint independently. The derivation is based on the separable feature of the dual problem of the convex approximated primal subproblem with respect to the Lagrange multipliers, and thus the update of design variables in each volume constraint only depends on the corresponding Lagrange multiplier. Through examples in 2D and 3D, using combinations of Ogden-based, bilinear, and linear materials, we demonstrate that the proposed multi-material topology optimization framework with the presented update scheme leads to a design tool that not only finds the optimal topology but also selects the proper type and amount of material. The design update scheme is named ZPR (phonetically, zipper), after the initials of the authors’ last names (Zhang-Paulino-Ramos Jr.).

We present a Matlab implementation for topology optimization of structures subjected to dynamic loads. The code, which we name PolyDyna, is built on top of PolyTop—a Matlab code for static compliance minimization based on polygonal finite elements. To solve the structural dynamics problem, we use the HHT- α method, which is a generalization of the classical Newmark- β method. In order to handle multiple regional volume constraints efficiently, PolyDyna uses a variation of the ZPR design variable update scheme enhanced by a sensitivity separation technique, which enables it to solve non-self-adjoint topology optimization problems. We conduct the sensitivity analysis using the adjoint method with the “discretize-then-differentiate” approach, such that the sensitivity analysis is consistently evaluated on the discretized system (both in space and time). We present several numerical examples, which are explained in detail and summarized in a library of benchmark problems. PolyDyna is intended for educational purposes and the complete Matlab code is provided as electronic supplementary material.

A numerical scheme of new class is presented for computing unsteady swirling flows in nozzles and pipes based on equations for a compressible inviscid gas. The main advantage of such schemes is that they are efficient as applied to unsteady multiscale problems. A scheme of this type is constructed using Godunov’s well-known approach, according to which fluxes on faces of mesh cells (volumes) are computed by solving auxiliary one-dimensional problems near each face and by approximating conservation laws. An analysis of the current solution near the face is used to switch between explicit and implicit flux computation algorithms. The scheme is unconditionally stable, and it does not generate spurious oscillations. The performance of the scheme is demonstrated by computing unsteady swirling flows in nozzles and pipes. The features of the formulation of problems of this type are investigated, and variants of correct problem formulation are proposed. The properties of solutions of the swirling flow problem with a central body covering part of the axis of symmetry in the computational domain are studied.

Samples from a high-dimensional first-order auto-regressive process generated by an independently and identically distributed random innovation sequence are observed by a sender which can communicate only finitely many bits per unit time to a receiver. The receiver seeks to form an estimate of the process value at every time instant in real-time. We consider a time-slotted communication model in a slow-sampling regime where multiple communication slots occur between two sampling instants. We propose a successive update scheme which uses communication between sampling instants to refine estimates of the latest sample and study the following question: Is it better to collect communication of multiple slots to send better refined estimates, making the receiver wait more for every refinement, or to be fast but loose and send new information in every communication opportunity? We show that the fast but loose successive update scheme with ideal spherical codes is universally optimal asymptotically for a large dimension. However, most practical quantization codes for fixed dimensions do not meet the ideal performance required for this optimality, and they typically will have a bias in the form of a fixed additive error. Interestingly, our analysis shows that the fast but loose scheme is not an optimal choice in the presence of such errors, and a judiciously chosen frequency of updates outperforms it.

A numerical method is presented for Runge-Kutta discretization of unconstrained optimal control problems. First, general Runge-Kutta discretization is carried out to obtain a finitedimensional approximation of the continous-time optimal control problem. Then a recent optimization technique, the inexact restoration (IR) method, due to Martinez and coworkers [E. G. Birgin and J. M. Martinez, J. Optim. Theory Appl., 127 (2005), pp. 229-247; J. M. Martinez and E. A. Pilotta, J. Optim. Theory Appl, 104 (2000), pp. 135-163; J. M. Martinez, J. Optim. Theory Appl, 111 (2001), pp. 39-58], is applied to the discretized problem to find an approximate solution. It is proved that, for optimal control problems, a key sufficiency condition for convergence of the IR method is readily satisfied. Under reasonable assumptions, the IR method for optimal control problems is shown to converge to a solution of the discretized problem. Convergence of a solution of the discretized problem to a solution of the continuous-time problem is also shown. It turns out that optimality phase equations of the IR method emanate from an associated Hamiltonian system, and so general Runge-Kutta discretization induces a symplectic partitioned Runge-Kutta scheme. A computational algorithm is described, and numerical experiments are made to demonstrate the working of the method for optimal control of the van der Pol system, employing the three-stage (order 6) Gauss-Legendre discretization.

This paper introduces the problematics deriving from the adoption of asynchronous update schemes in CA models. Several cellular automata update schemes and a tentative classification of such schemes are introduced and discussed. In order to analyze the effects of the different update schemes, a class of simple CA—called One neighbor binary cellular automata (1nCA)—is then introduced. An overview of the general features of 1nCA is described, then the effects of six different updates schemes on all the class of 1nCA are described.

There is much interest within the mathematical biology and statistical physics community in converting stochastic agent-based models for random walkers into a partial differential equation description for the average agent density. Here a collection of noninteracting biased random walkers on a one-dimensional lattice is considered. The usual master equation approach requires that two continuum limits, involving three parameters, namely step length, time step and the random walk bias, approach zero in a specific way. We are interested in the case where the two limits are not consistent. New results are obtained using a Fokker–Planck equation and the results are highly dependent on the simulation update schemes. The theoretical results are confirmed with examples. These findings provide insight into the importance of updating schemes to an accurate macroscopic description of stochastic local movement rules in agent-based models when the lattice spacing represents a physical object such as cell diameter.

This chapter contains sections titled: Introduction MRTD Basics MRTD Update Scheme Scaling MRTD References

A methodology is presented for evaluating the performance of database update schemes in a distributive environment. The methodology makes use of the history of how data are used in the database. Parameters such as update-to-retrieval ratio and average file size can be set based on the actual characterization of a system. The analysis is specifically directed toward the support of derived data within the relational model. Because concurrency is a major problem in a distributive system, the support of derived data is analyzed with respect to three distributive concurrency control techniques: master/slave, distributed, and synchronized.< >