This study presents a detailed numerical analysis of a three-dimensional micro pin fin heat sink incorporating 55 fins arranged in a single channel in four distinct cross-sectional geometries: square, circular, triangular, and pentagonal. A conventional microchannel heat sink (MCHS) without pin fins serves as a baseline for comparison. Water is employed as the working fluid, and simulations are conducted over a laminar flow regime with Reynolds numbers ranging from 500 to 1500. To efficiently capture the thermo-hydrodynamic behavior and reduce computational cost, a representative single flow channel is simulated under symmetrical boundary conditions, and key pin fin parameters such as height and spacing are systematically varied. The cross-sectional hydraulic diameter and spacing are held constant for all cases, with step sizes and non-dimensional spacing ratios sp/hp adjusted to assess their effect on heat sink performance. Results indicate that among all geometries, circular fins exhibit the highest heat transfer enhancement, with the Nusselt number increasing by 60% at Re = 500 and by 90% at Re = 1500 compared to the baseline. However, this improved thermal performance is accompanied by a greater pressure drop relative to the other tested pin fin shapes. Following the circular fins, triangular and square configurations offer progressively lower heat transfer rates, while pentagonal pin fins demonstrate the minimum enhancement. Furthermore, for all fin geometries, increasing the Reynolds number leads to a consistent improvement in heat transfer. Overall, the study provides quantitative insights into the impact of pin fin geometry and arrangement on the thermal and fluid dynamic performance of micro pin fin heat sinks, offering valuable guidelines for the design of advanced cooling solutions in microelectronics.
Decision-theoretic planning is a popular approach to sequential decision making problems, because it treats uncertainty in sensing and acting in a principled way. In single-agent frameworks like MDPs and POMDPs, planning can be carried out by resorting to Q-value functions: an optimal Q-value function Q* is computed in a recursive manner by dynamic programming, and then an optimal policy is extracted from Q*. In this paper we study whether similar Q-value functions can be defined for decentralized POMDP models (Dec-POMDPs), and how policies can be extracted from such value functions. We define two forms of the optimal Q-value function for Dec-POMDPs: one that gives a normative description as the Q-value function of an optimal pure joint policy and another one that is sequentially rational and thus gives a recipe for computation. This computation, however, is infeasible for all but the smallest problems. Therefore, we analyze various approximate Q-value functions that allow for efficient computation. We describe how they relate, and we prove that they all provide an upper bound to the optimal Q-value function Q*. Finally, unifying some previous approaches for solving Dec-POMDPs, we describe a family of algorithms for extracting policies from such Q-value functions, and perform an experimental evaluation on existing test problems, including a new firefighting benchmark problem.
Bastien Baldacci, Philippe Bergault, Olivier Guéant
This paper introduces a novel methodology for the pricing and management of share buyback contracts, overcoming the limitations of traditional optimal control methods, which frequently encounter difficulties with high-dimensional state spaces and the intricacies of selecting appropriate risk penalty or risk aversion parameter. Our methodology applies optimized heuristic strategies to maximize the contract's value. The computation of this value utilizes classical methods typically used for pricing path-dependent options. Additionally, our approach naturally leads to the formulation of a $Δ$-hedging strategy and disentangles therefore the repurchase strategy from the hedging of the payoff.
A bstractWe introduce a new framework for constructing black hole solutions that are holographically dual to strongly coupled field theories with explicitly broken translation invariance. Using a classical gravitational theory with a continuous global symmetry leads to constructions that involve solving ODEs instead of PDEs. We study in detail D = 4 Einstein-Maxwell theory coupled to a complex scalar field with a simple mass term. We construct black holes dual to metallic phases which exhibit a Drude-type peak in the optical conductivity, but there is no evidence of an intermediate scaling that has been reported in other holographic lattice constructions. We also construct black holes dual to insulating phases which exhibit a suppression of spectral weight at low frequencies. We show that the model also admits a novel AdS3 × $ \mathbb{R} $ solution.
Neutron Star Measurements Neutron stars are one of the densest manifestations of matter in the universe. Yagi and Yunes (p. 365) examined the moment of inertia of neutron stars, which determines how fast they can spin, and the quadrupole moment and tidal Love number, which determine how much they can be deformed. The findings suggest that these three quantities obey universal relationships that are independent of the internal structure of the stars, implying that measurements of one of the three could accurately predict the other two. The relation of inertia, Love number, and quadrupole moment is independent of neutron and quark stars’ internal structure. Neutron stars and quark stars are not only characterized by their mass and radius but also by how fast they spin, through their moment of inertia, and how much they can be deformed, through their Love number and quadrupole moment. These depend sensitively on the star’s internal structure and thus on unknown nuclear physics. We find universal relations between the moment of inertia, the Love number, and the quadrupole moment that are independent of the neutron and quark star’s internal structure. These can be used to learn about neutron star deformability through observations of the moment of inertia, break degeneracies in gravitational wave detection to measure spin in binary inspirals, distinguish neutron stars from quark stars, and test general relativity in a nuclear structure–independent fashion.
By investigating nonfungible tokens (NFTs), we provide the first systematic study of retail investor behavior through asset bubbles. Given that NFTs are recorded in public blockchains, we are able to track investor behavior over time, leading to the identification of numerous price run-ups and crashes. Our study reveals that agent-level variables, such as investor sophistication, heterogeneity, and wash trading, in addition to aggregate variables, such as volatility, price acceleration, and turnover, significantly predict bubble formation and price crashes. We find that sophisticated investors consistently outperform others and exhibit characteristics consistent with superior information and skills, supporting the narrative surrounding asset pricing bubbles.
This paper develops a coupled model for day-ahead electricity prices and average daily temperature which allows to model quanto weather and energy derivatives. These products have gained on popularity as they enable to hedge against both volumetric and price risks. Electricity day-ahead prices and average daily temperatures are modelled through non homogeneous Ornstein-Uhlenbeck processes driven by a Brownian motion and a Normal Inverse Gaussian Lévy process, which allows to include dependence between them. A Conditional Least Square method is developed to estimate the different parameters of the model and used on real data. Then, explicit and semi-explicit formulas are obtained for derivatives including quanto options and compared with Monte Carlo simulations. Last, we develop explicit formulas to hedge statically single and double sided quanto options by a portfolio of electricity options and temperature options (CDD or HDD).
The technical virtual power plant (TVPP) is a promising paradigm to facilitate the integration of distributed energy resources (DERs) while incorporating operational constraints of both DERs and networks. Due to the volatility and limited predictability of DER generation and electric loads, the output capability of the TVPP is uncertain. In this regard, this paper proposes the robust capability curve (RCC) of the TVPP, which explicitly characterizes the allowable range of the scheduled power output that is executable for the TVPP under uncertainties. Implementing the RCC can secure the scheduling of the TVPP against unexpected fluctuations of operating conditions when the TVPP participates in the transmission-level dispatch. Mathematically, the RCC is the first-stage feasible set of an adjustable robust optimization problem. An uncertainty set model incorporating the variable correlation and uncertainty budget is employed, which makes the robustness and conservatism of the RCC adjustable. A novel methodology is proposed to estimate the RCC by the convex hull of several points on its perimeter. These perimeter points are obtained by solving a series of multi scenario-optimal power flow problems with worst-case uncertainty realizations identified based on a linearized network configuration. Case studies based on the IEEE-13 test feeder validate the effectiveness of the RCC to ensure the scheduling feasibility while hedging against uncertainties. The computational efficiency of the proposed RCC estimation method is also verified based on larger-scale test systems.
By making use of the concept of basic (or q-) calculus, various families of q-extensions of starlike functions of order α in the open unit disk U were introduced and studied from many different viewpoints and perspectives. In this paper, we first investigate the relationship between various known classes of q-starlike functions that are associated with the Janowski functions. We then introduce and study a new subclass of q-starlike functions that involves the Janowski functions. We also derive several properties of such families of q-starlike functions with negative coefficients including (for example) distortion theorems.