Finite Difference Method in Fluid Potential Function and Velocity Calculation

There is no deterministic solution for many fluid problems but by applying analytical solutions many of them are approximated. In this study an implicit finite difference method presented which solves the potential function and further expanded to drive out the velocity components in 2D-space by applying a point-by-point swiping approach. The results showed the rotational behavior of both potential function as well as velocity components while encountering central obstacle.

Cosmological scenario in κ(R,T) gravity

In this paper, we investigate the cosmic acceleration and the behavior of dark energy (DE) in the structure of the recently proposed [Formula: see text] gravity theory [G. R. P. Teruel, [Formula: see text] gravity, Eur. Phys. J. C 78 (2018) 660]. In this study, we obtained some fascinating cosmological features that are coherent with observational evidences and the touchstone [Formula: see text]CDM model. To find the deterministic solution, we consider a periodic deceleration parameter [Formula: see text], where [Formula: see text] [M. Shen and L. Zhao, Oscillating quintom model with time periodic varying deceleration parameter, Chin. Phys. Lett. 31 (2014) 010401], which predicts the decelerating and accelerating phases of the universe. The Equation of State (EoS) parameter also supports the idea of DE, which is the dominant component and it is responsible for the universe’s accelerated expansion. Here, we also construct cosmographic parameters, like, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and studied their evolution in spatially flat [Formula: see text] gravity. We find that these observations are sufficient in comparison with the universe’s physical and kinematic properties and also consistent with ongoing (OHD[Formula: see text][Formula: see text][Formula: see text]JLA) observation. Next, we apply the geometric diagnostics, the state-finder ([Formula: see text]) in [Formula: see text] gravity to discriminate from the [Formula: see text]CDM model. We found that our model lies in quintessence and the Chaplygin Gas region. Finally, the model approaches [Formula: see text]CDM at the present epoch of the universe.

Harmonic Passive Motion Paradigm

Humans can robustly interact with external dynamics that are not yet fully understood. This work presents a hierarchical architecture of semi-autonomous controllers that can control the redundant kinematics of the limbs during dynamic interaction, even with delays comparable to the nervous system. The postural optimisation is performed via a non-linear mapping of the system kineto-static properties, and it allows independent control of the end-effector trajectories and the arms stiffness. The proposed architecture is tested in a physical simulator in the absence of gravity, presence of gravity, and with gravity plus a viscous force field. The data indicates that the architecture can generalise the motor strategies to different environmental conditions. The experiments also verify the existence of a deterministic solution to the task-separation principle. The architecture is also compatible with Optimal Feedback Control and the Passive Motion Paradigm. The existence of a deterministic mapping implies that this task could be encoded in neural networks capable of generalisation of motion strategies to affine tasks.

On the Value of Community Association for Microgrid Development: Learnings from Multiple Deterministic and Stochastic Planning Designs

The reliability of the power grid is a constant problem faced by those who operate, plan and study power systems. An alternative approach to this problem, and others related to the integration of renewable energy sources, is the microgrid. This research seeks to quantify the potential benefits of urban community microgrids, based on the development of planning models with deterministic and stochastic optimization approaches. The models ensure that supply meets demand whilst assuring the minimum cost of investment and operation. To verify their effectiveness, the planning of hundreds of microgrids was set in the city of Santiago de Chile. The most important results highlight the value of community association, such as: a reduction in investment cost of up to 35%, when community microgrids are planned with a desired level of reliability, compared to single residential household microgrids. This reduction is due to the diversity of energy consumption, which can represent around 20%, on average, of cost reduction, and to the Economies of Scale (EoS) present in the aggregation microgrid asset capacity, which can represent close to 15% of the additional reduction in investment costs. The stochastic planning approach also ensures that a community can prepare for different fault scenarios in the power grid. Furthermore, it was found that for approximately 90% of the planned microgrids with reliability requirements, the deterministic solution for the worst three fault scenarios is equivalent to the solution of the stochastic planning problem.

Machine Learning Prediction and Reliability Analysis Applied to Subsea Spool and Jumper Design

In subsea pipelines projects, the design of rigid spool and jumper can be a challenging and time-consuming task. The selected spool layout for connecting the pipelines to the subsea structures, including the number of bends and leg lengths, must offer the flexibility to accommodate the pipeline thermal expansion, the pipe-lay target box and misalignments associated with the post-lay survey metrology and spool fabrication. The analysis results are considerably affected by many uncertainties involved. Consequently, a very large amount of calculations is required to assess the full combination of uncertainties and to capture the worst-case scenario. Rather than applying the deterministic solution, this paper uses machine learning prediction to significantly improve the efficiency of the design process. In addition, thanks to the fast predictive model using machine learning algorithms, the uncertainty quantification and propagation analysis using probabilistic statistical method becomes feasible in terms of CPU time and can be incorporated into the design process to evaluate the reliability of the outputs. The latter allows us to perform a systematic probabilistic design by considering a certain level of acceptance on the probability of failure, for example as per DNVGL design code. The machine learning predictive modelling and the reliability analysis based upon the probability distribution of the uncertainties are introduced and explained in this paper. Some project examples are shown to highlight the method’s comprehensive nature and efficient characteristics.

Game with a random second player and its application to the problem of optimal fare choice

The choice of the optimal strategy for a significant number of applied problems can be formalized as a game theory problem, even in conditions of incomplete information. The article deals with a hierarchical game with a random second player, in which the first player chooses a deterministic solution, and the second player is represented by a set of decision makers. The strategies of the players that ensure the Stackelberg equilibrium are studied. The strategy of the second player is formalized as a probabilistic solution to an optimization problem with an objective function depending on a continuously distributed random parameter. In many cases, the choice of optimal strategies takes place in conditions when there are many decision makers, and each of them chooses a decision based on his (her) criterion. The mathematical formalization of such problems leads to the study of probabilistic solutions to problems with an objective function depending on a random parameter. In particular, probabilistic solutions are used for mathematical describing the passenger's choice of a mode of transport. The problem of optimal fare choice for a new route based on a probabilistic model of passenger preferences is considered. In this formalization, the carrier that sets the fare is treated as the first player; the set of passengers is treated as the second player. The second player's strategy is formalized as a probabilistic solution to an optimization problem with a random objective function. A model example is considered.

Text Indexing for Regular Expression Matching

Finding substrings of a text T that match a regular expression p is a fundamental problem. Despite being the subject of extensive research, no solution with a time complexity significantly better than O(|T||p|) has been found. Backurs and Indyk in FOCS 2016 established conditional lower bounds for the algorithmic problem based on the Strong Exponential Time Hypothesis that helps explain this difficulty. A natural question is whether we can improve the time complexity for matching the regular expression by preprocessing the text T? We show that conditioned on the Online Matrix–Vector Multiplication (OMv) conjecture, even with arbitrary polynomial preprocessing time, a regular expression query on a text cannot be answered in strongly sublinear time, i.e., O(|T|1−ε) for any ε>0. Furthermore, if we extend the OMv conjecture to a plausible conjecture regarding Boolean matrix multiplication with polynomial preprocessing time, which we call Online Matrix–Matrix Multiplication (OMM), we can strengthen this hardness result to there being no solution with a query time that is O(|T|3/2−ε). These results hold for alphabet sizes three or greater. We then provide data structures that answer queries in O(|T||p|τ) time where τ∈[1,|T|] is fixed at construction. These include a solution that works for all regular expressions with Expτ·|T| preprocessing time and space. For patterns containing only ‘concatenation’ and ‘or’ operators (the same type used in the hardness result), we provide (1) a deterministic solution which requires Expτ·|T|log2|T| preprocessing time and space, and (2) when |p|≤|T|z for z=2o(log|T|), a randomized solution with amortized query time which answers queries correctly with high probability, requiring Expτ·|T|2Ωlog|T| preprocessing time and space.

التدفق النقدي الاحتمالي, نموذج مونتكارلو و سلوك مدراء مشاريع التشييد فى السودان

Construction industry in the Sudan has experienced a high or disastrous economical, financial, political and social environment during the last decade and respondents and their organizations had committed to deliver projects within deterministic costs. Inevitably, project stakeholders had been challenged by the effect of overall disastrous project risks. The research checked whether respondents were capable to manage those issues and risks efficiently and effectively. The research highlighted the effect of overall risks on a default project employing Monte Carlo simulation. 80 % of the respondents had overestimated their achievements when compared to actual projects outputs. In fact, the average respondent employed only 11 % of the researched tools and techniques, while none of the tools or techniques usage was rated as good, excellent or outstanding. It was proofed that adopting optimistic or the most likely estimates is a deterministic solution to both the project and the organization. Finally, it is recommended to train respondents and company chief executive officers in handle construction cost risks.

Heat diffusion in a channel under white noise modeling of turbulence

<abstract><p>A passive scalar equation for the heat diffusion and transport in an infinite channel is studied. The velocity field is white noise in time, modelling phenomenologically a turbulent fluid. Under the driving effect of a heat source, the phenomenon of eddy dissipation is investigated: the solution is close, in a weak sense, to the stationary deterministic solution of the heat equation with augmented diffusion coefficients.</p></abstract>

Robust Maximum Coverage Facility Location Problem with Drones Considering Uncertainties in Battery Availability and Consumption

Given a set of a spatially distributed demand for a specific commodity, potential facility locations, and drones, an agency is tasked with locating a pre-specified number of facilities and assigning drones to them to serve the demand while respecting drone range constraints. The agency seeks to maximize the demand served while considering uncertainties in initial battery availability and battery consumption. The facilities have a limited supply of the commodity being distributed and also act as a launching site for drones. Drones undertake one-to-one trips (from located facility to demand location and back) until their available battery energy is exhausted. This paper extends the work done by Chauhan et al. and presents an integer linear programming formulation to maximize coverage using a robust optimization framework. The uncertainty in initial battery availability and battery consumption is modeled using a penalty-based approach and gamma robustness, respectively. A novel robust three-stage heuristic (R3SH) is developed which provides objective values which are within 7% of the average solution reported by MIP solver with a median reduction in computational time of 97% on average. Monte Carlo simulation based testing is performed to assess the value of adding robustness to the deterministic problem. The robust model provides higher and more reliable estimates of actual coverage under uncertainty. The average maximum coverage difference between the robust optimization solution and the deterministic solution is 8.1% across all scenarios.