Results 71 to 80 of about 39,805 (286)

Pseudo-differential Operators on Fractals

, 2011
We define and study pseudo-differential operators on a class of fractals that include the post-critically finite self-similar sets and Sierpinski carpets. Using the sub-Gaussian estimates of the heat operator we prove that our operators have kernels that decay and, in the constant coefficient case, are smooth off the diagonal.
Ionescu, Marius, Rogers, Luke G., Strichartz, Robert S.   +2 more
openaire   +2 more sources

Dirac and magnetic Schrödinger operators on fractals

Journal of Functional Analysis, 2013
In this paper we define (local) Dirac operators and magnetic Schr dinger Hamiltonians on fractals and prove their (essential) self-adjointness. To do so we use the concept of 1-forms and derivations associated with Dirichlet forms as introduced by Cipriani and Sauvageot, and further studied by the authors jointly with R ckner, Ionescu and Rogers. For
Hinz, Michael, Teplyaev, Alexander
openaire   +3 more sources

Sub‐Unit‐Cell Logic Governs Transport in TPMS Architectures

Advanced Science, EarlyView.
ABSTRACT Next‐generation energy, thermal, and chemical systems require architectures capable of highly efficient transport across multiple length scales. Triply periodic minimal surfaces (TPMS), first conceptualized in 1865, offer inherently scalable geometries with exceptional transport potential, yet mechanistic links between topology and performance
Haozhang Zhong, Yipei He, Jiaxuan Wang, Chenyi Qian, Gerd E Schröder‐Turk, Raj Das, Junye Shi, Qi Tang, Zheda Ning, Wenjue Yi, Chuanwei Li, Jiangping Chen, Zeyao Chen, Binbin Yu, Jian LU, Jianfeng Gu, Ma Qian   +16 more
wiley   +1 more source

Elastic Scattering by Deterministic and Random Fractals: Self-Affinity of the Diffraction Spectrum

, 1996
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the Cantor set and ...
B. B. Mandelbrot, B. Dubuc, C. Allain, C. Allain, C. Allain, C. Iemmi, C. Kittel, D. Berger, D.A. Hamburger, D.A. Hamburger, Daniel A. Hamburger-Lidar, H.D. Bale, J. Guojun, J. Teixeira, J. Uozumi, J.K. Kjems, J.M. Ziman, J.R. Taylor, K. Jarrendahl, K.M. Watson, M. Barnsley, M. Born, M.S. Child, M.V. Berry, P. Pfeifer, P. Pfeifer, P.-z. Wong, P.-z. Wong, P.T. Callaghan, P.W. Schmidt, R.B Gerber, R.B. Gerber, R.G. Newton, S. Silver, T. Vicsek, T.A. Witten, Jr., V.V. Konotop, X. Sun   +37 more
core   +1 more source

A General and Efficient Framework for the Rapid Design of Miniaturized, Wideband, and High‐Bit RIS

Advanced Electronic Materials, EarlyView.
A general and efficient framework is proposed for the rapid design of high‐performance reconfigurable intelligent surfaces (RISs). This framework integrates advanced antenna design techniques and incorporates various load types, quantities, and values to achieve the design of high‐performance RISs.
Jun Wei Zhang, Zheng Xing Wang, Wanwan Cao, Zhen Jie Qi, Li Jie Wu, Han Qing Yang, Qun Yan Zhou, Si Ran Wang, Hui Dong Li, Jun Yan Dai, Jiang Luo, Jun Wei Wu, Jia Nan Zhang, Zhen Zhang, Qiang Cheng   +14 more
wiley   +1 more source

Fractional Systems and Fractional Bogoliubov Hierarchy Equations

, 2005
We consider the fractional generalizations of the phase volume, volume element and Poisson brackets. These generalizations lead us to the fractional analog of the phase space.
A. A. Vlasov, A. Isihara, B. A. Dubrovin, B. Mandelbrot, D. Ya. Petrina, I. P. Kornfeld, J. C. Collins, K. P. Gurov, M. Schroeder, N. Bogolybow, N. N. Bogoliubov, N. N. Bogoliubov, N. N. Bogoliubov, P. Debye, S. G. Samko, T. F. Nonnenmacher, V. E. Tarasov, V. E. Tarasov, V. E. Tarasov, Vasily E. Tarasov   +19 more
core   +1 more source

Deciphering Intricacies in Directional CO2 Conversion From Electrolysis to CO2 Batteries

Advanced Energy Materials, EarlyView.
This review will delve into the inherent connections and distinctions of CO2‐directed conversion in ECO2RR and CO2 batteries, in terms of product types, catalyst selection, catalytic mechanisms, and electrochemical performances, while proposing a benchmarking framework for the evaluation of CO2 batteries and innovative CO2 battery configurations for ...
Changfan Xu, Huaping Zhao, Lizhuang Chen, Weidong Shi, Guosheng Shao, Yong Lei   +5 more
wiley   +1 more source

Assessment of the influence of electromagnetic noise radiation in the WiFi range on the emotional state of the operator

Системный анализ и прикладная информатика
Experimental studies of electroencephalograms of an operator located in conditions of electromagnetic noise radiation in the WiFi range were carried out.
A. V. Sidorenko, M. A. Saladukha
doaj   +1 more source

CrossMatAgent: AI‐Assisted Design of Manufacturable Metamaterial Patterns via Multi‐Agent Generative Framework

Advanced Intelligent Discovery, EarlyView.
CrossMatAgent is a multi‐agent framework that combines large language models and diffusion‐based generative AI to automate metamaterial design. By coordinating task‐specific agents—such as describer, architect, and builder—it transforms user‐provided image prompts into high‐fidelity, printable lattice patterns.
Jie Tian, Martin Taylor Sobczak, Dhanush Patil, Jixin Hou, Lin Pang, Arunachalam Ramanathan, Libin Yang, Xianyan Chen, Yuval Golan, Xiaoming Zhai, Hongyue Sun, Kenan Song, Xianqiao Wang   +12 more
wiley   +1 more source

Laplace Operators on Fractals and Related Functional Equations

, 2012
We give an overview over the application of functional equations, namely the classical Poincar\'e and renewal equations, to the study of the spectrum of Laplace operators on self-similar fractals.
Akkermans E, Akkermans E Benichou O Dunne G Teplyaev A Voituriez R, Bajorin N, Barlow M T, Barlow M T, Barlow M T, Barlow M T Bass R F, Bellissard J, Bellissard J, Boas R P Jr, de Gennes P G, Derfel G, Derfel G, Dunne G V, Dunne G V, Elizalde E, Elizalde E, Elizalde E, Erëmenko A È, Erëmenko A È, Falconer K J, Falconer K J, Federer H, Feller W, Fritz Vogl, Fukushima M, Fukushima M, Gilkey P B, Gilkey P B, Gregory Derfel, Grigor’yan A, Hamilton D H, Hardy G H, He C Q, Jorgenson J, Kajino N, Kigami J, Kirillov A A, Kirsten K, Kumagai T, Kusuoka S, Lapidus M L, Lapidus M L, Lapidus M L van Frankenhuysen M, Levin G M, Lindstrøm T, Mandelbrot B B, Metz V, Milnor J, Molčanov S A, Molčanov S A, Naimark K, Naimark K, Peter J Grabner, Poincaré H, Poincaré H, Sabot C, Schweitzer G, Seeley R T, Shima T Elworthy K D Ikeda N, Simon B, Steinhurst B Teplyaev A, Strichartz R S, Tenenbaum G, Teplyaev A, Triebel H, Valiron G, Valiron G, Yosida K   +68 more
core   +1 more source