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1. Locomotion of a multi-link non-holonomic snake robot with passive joints

   Dear, T; Buchanan, B; Abrajan-Guerrero, R; Kelly, SD; Travers, M; Choset, H (April 2020, The international journal of robotics research)

   Abstract Conventional approaches in prescribing controls for locomoting robots assume control over all input degrees of freedom (DOFs). Many robots, such as those with non-holonomic constraints, may not require or even allow for direct command over all DOFs. In particular, a snake robot with more than three links with non-holonomic constraints cannot achieve arbitrary configurations in all of its joints while simultaneously locomoting. For such a system, we assume partial command over a subset of the joints, and allow the rest to evolve according to kinematic chained and dynamic models. Different combinations of actuated and passive joints, as well as joints with dynamic elements such as torsional springs, can drastically change the coupling interactions and stable oscillations of joints. We use tools from nonlinear analysis to understand emergent oscillation modes of various robot configurations and connect them to overall locomotion using geometric mechanics and feedback control for robots that may not fully utilize all available inputs. We also experimentally verify observations and motion planning results on a physical non-holonomic snake robot 

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2. Charge-transfer-enhanced d – d emission in antiferromagnetic NiPS3

   https://doi.org/10.1063/5.0107065  

   Tan, Qishuo; Luo, Weijun; Li, Tianshu; Cao, Jun; Kitadai, Hikari; Wang, Xingzhi; Ling, Xi (November 2022, Applied Physics Reviews)

   The d electron plays a significant role in determining and controlling the properties of magnetic materials. However, the d electron transitions, especially d–d emission, have rarely been observed in magnetic materials due to the forbidden selection rules. Here, we report an observation of d–d emission in antiferromagnetic nickel phosphorus trisulfides (NiPS3) and its strong enhancement by stacking it with monolayer tungsten disulfide (WS2). We attribute the observation of the strong d–d emission enhancement to the charge transfer between NiPS3 and WS2 in the type-I heterostructure. The d–d emission peak splits into two peaks, D1 and D2, at low temperature below 150 K, from where an energy splitting due to the trigonal crystal field is measured as 105 meV. Moreover, we find that the d–d emissions in NiPS3 are nonpolarized lights, showing no dependence on the zigzag antiferromagnetic configuration. These results reveal rich fundamental information on the electronic and optical properties of emerging van der Waals antiferromagnetic NiPS3. 

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3. On the optimal arrangement of 2 d lines in ℂ d

   https://doi.org/10.1093/imaiai/iaaf008  

   Fallon, Kean; Iverson, Joseph W (March 2025, Information and Inference: A Journal of the IMA)

   Abstract We show the optimal coherence of $2d$ lines in $$\mathbb{C}^{d}$$ is given by the Welch bound whenever a skew Hadamard matrix of order $d+1$ exists. Our proof uses a variant of Hadamard matrix doubling that converts any equiangular tight frame of size $$\tfrac{d-1}{2} \times d$$ into another one of size $$d \times 2d$$. Among $$d \leq 160$$, this produces equiangular tight frames of new sizes when $d = 11$, $35$, $39$, $43$, $47$, $59$, $67$, $71$, $83$, $95$, $103$, $107$, $111$, $119$, $123$, $127$, $131$, $143$, $151$ and $155$. 

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4. Substorm‐Time Ground d B / d t Variations Controlled by Interplanetary Shock Impact Angles: A Statistical Study

   https://doi.org/10.1029/2023SW003767  

   Oliveira, Denny M; Weygand, James M; Coxon, John C; Zesta, Eftyhia (March 2024, Space Weather)

   Abstract In this study, we investigate the effects caused by interplanetary (IP) shock impact angles on the subsequent grounddB/dtvariations during substorms. IP shock impact angles have been revealed as a major factor controlling the subsequent geomagnetic activity, meaning that shocks with small inclinations with the Sun‐Earth line are more likely to trigger higher geomagnetic activity resulting from nearly symmetric magnetospheric compressions. Such field variations are linked to the generation of geomagnetically induced currents (GICs), which couple to artificial conductors on the ground leading to deleterious consequences. We use a sub‐set of a shock data base with 237 events observed in the solar wind at L1 upstream of the Earth, and large arrays of ground magnetometers at stations located in North America and Greenland. The spherical elementary current system methodology is applied to the geomagnetic field data, and field‐aligned‐like currents in the ionosphere are derived. Then, such currents are inverted back to the ground anddB/dtvariations are computed. Geographic maps are built with these field variations as a function of shock impact angles. The main findings of this investigation are: (a) typicaldB/dtvariations (5–10 nT/s) are caused by shocks with moderate inclinations; (b) the more frontal the shock impact, the more intense and the more spatially defined the ionospheric current amplitudes; and (c) nearly frontal shocks trigger more intensedB/dtvariations with larger equatorward latitudinal expansions. Therefore, the findings of this work provide new insights for GIC forecasting focusing on nearly frontal shock impacts on the magnetosphere. 

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5. On the Convolution Inequality f ≥ f ⋆ f

   https://doi.org/10.1093/imrn/rnaa350  

   Carlen, Eric A; Jauslin, Ian; Lieb, Elliott H; Loss, Michael P (January 2021, International Mathematics Research Notices)

   null (Ed.)

   Abstract We consider the inequality $$f \geqslant f\star f$$ for real functions in $$L^1({\mathbb{R}}^d)$$ where $$f\star f$$ denotes the convolution of $$f$$ with itself. We show that all such functions $$f$$ are nonnegative, which is not the case for the same inequality in $L^p$ for any $$1 < p \leqslant 2$$, for which the convolution is defined. We also show that all solutions in $$L^1({\mathbb{R}}^d)$$ satisfy $$\int _{{\mathbb{R}}^{\textrm{d}}}f(x)\ \textrm{d}x \leqslant \tfrac 12$$. Moreover, if $$\int _{{\mathbb{R}}^{\textrm{d}}}f(x)\ \textrm{d}x = \tfrac 12$$, then $$f$$ must decay fairly slowly: $$\int _{{\mathbb{R}}^{\textrm{d}}}|x| f(x)\ \textrm{d}x = \infty $$, and this is sharp since for all $r< 1$, there are solutions with $$\int _{{\mathbb{R}}^{\textrm{d}}}f(x)\ \textrm{d}x = \tfrac 12$$ and $$\int _{{\mathbb{R}}^{\textrm{d}}}|x|^r f(x)\ \textrm{d}x <\infty $$. However, if $$\int _{{\mathbb{R}}^{\textrm{d}}}f(x)\ \textrm{d}x =: a < \tfrac 12$$, the decay at infinity can be much more rapid: we show that for all $$a<\tfrac 12$$, there are solutions such that for some $$\varepsilon>0$$, $$\int _{{\mathbb{R}}^{\textrm{d}}}e^{\varepsilon |x|}f(x)\ \textrm{d}x < \infty $$. 

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