Tootfinder

Nine circles of elastic brittle fracture: A series of challenge problems to assess fracture models
Farhad Kamarei, Bo Zheng, John E. Dolbow, Oscar Lopez-Pamies
https://arxiv.org/abs/2507.00266

Nine circles of elastic brittle fracture: A series of challenge problems to assess fracture models
Since the turn of the millennium, capitalizing on modern advances in mathematics and computation, a slew of computational models have been proposed in the literature with the objective of describing the nucleation and propagation of fracture in materials subjected to mechanical, thermal, and/or other types of loads. By and large, each new proposal focuses on a particular aspect of the problem, while ignoring others that have been well-established. This approach has resulted in a plethora of mod…

In-Memory Sorting-Searching with Cayley Tree
Subrata Paul, Sukanta Das, Biplab K Sikdar
https://arxiv.org/abs/2506.19379 https://arxi…

In-Memory Sorting-Searching with Cayley Tree
This work proposes a computing model to reduce the workload of CPU. It relies on the data intensive computation in memory, where the data reside, and effectively realizes an in-memory computing (IMC) platform. Each memory word, with additional logic, acts as a tiny processing element which forms the node of a Cayley tree. The Cayley tree in turn defines the framework for solving the data intensive computational problems. It finds the solutions for in-memory searching, computing the max (min) in…

Belief propagation for networks with loops: The neighborhoods-intersections-based method
Pedro Hack
https://arxiv.org/abs/2506.13791 https://

Belief propagation for networks with loops: The neighborhoods-intersections-based method
In order to diminish the damaging effect of loops on belief propagation (BP), the first explicit version of generalized BP for networks, the KCN-method, was recently introduced. Despite its success, the KCN-method spends computational resources inefficiently. Such inefficiencies can quickly turn the exact application of the method unfeasible, since its time complexity increases exponentially with them. This affects for instance tree networks, for which, despite not offering any accuracy advanta…

Feynman Integral Reduction using Syzygy-Constrained Symbolic Reduction Rules
Sid Smith, Mao Zeng
https://arxiv.org/abs/2507.11140 https://

Feynman Integral Reduction using Syzygy-Constrained Symbolic Reduction Rules
We present a new algorithm for integration-by-parts (IBP) reduction of Feynman integrals with high powers of numerators or propagators, a demanding computational step in evaluating multi-loop scattering amplitudes. The algorithm starts with solving syzygy equations in individual sectors to produce IBP operators that turn seed integrals into IBP equations without artificially raised propagator powers. The IBP operators are expressed in terms of index-shift operators and number operators. We perf…

Joint System Modeling Approach for Fault Simulation of Start-er/Generator and Gas Generator in All-Electric APU
Haotian Mao, Yingqing Guo
https://arxiv.org/abs/2506.10562

Joint System Modeling Approach for Fault Simulation of Start-er/Generator and Gas Generator in All-Electric APU
This paper presents a joint system modeling approach for fault simulation of all-electric auxiliary power unit (APU), integrating starter/generator turn-to-turn short circuit (TTSC) faults with gas generator gas-path faults.To address challenges in electromechanical coupling, simulation precision and computational efficiency balance, we propose a multi-rate continuous-discrete hybrid simulation architecture. This architecture treats the starter/generator as a continuous system with variable ste…