International Centre for Theoretical Sciences

<title>Abstract</title> Water (H$_2$O), one of the most consequential compounds in the Solar System, governs the structure and dynamics of icy planets, the terrestrial water cycle, and through the pressure-induced transition from hydrogen to ionic bonding, it exhibits marked changes over the pressure range of planetary interiors. While many materials are expected to favour simple, densely packed lattices with increasing compression, as observed in water ice-X, others %such as the complex hP4 phase of sodium exhibit unexpected structural complexity at extreme pressures. Here we report experimental evidence that water ice undergoes a transformation from ice-X to a less symmetric structure above 222(12) GPa. Synchrotron X-ray diffraction reveals a distortion of the cubic lattice consistent with either \textit{Pbcm} or \textit{P}4$_2$\textit{/nnm} symmetry, the former being strongly favorable by \textit{ab initio} calculations. This transition marks the onset of a new regime of structural complexity in high-pressure H$_2$O, redefining the upper stability limit of ice-X.

Complex systems with nonreciprocal interactions are often stratified into layers. Ecosystems are a prime example, where species at one trophic level grow by consuming those at another. Yet the dynamical consequences of such stratified nonreciprocity—where the correlation between growth and consumption differs across trophic levels—remain unexplored. Here, using an ecological model with three trophic levels, we reveal an emergent asymmetry: nonreciprocal interactions between consumers and predators (top and middle level) destabilize ecosystems far more readily than non-reciprocity between consumers and resources (middle and bottom level). We analytically derive the phase diagram for the model and show that its stability boundary is controlled by energy flow across trophic levels. Because energy flows upward—from resources to predators—diversity is progressively lower at higher trophic levels, which we show explains the asymmetry. Lowering energy flow efficiency flips the asymmetry toward resources and remarkably expands the stable region of the phase diagram, suggesting that the famous “10% energy transfer” seen in natural ecosystems might promote stability. More broadly, our findings show that the location of nonreciprocity within a complex network, not merely its magnitude, determines stability.

The Banda Arc serves as a natural laboratory for continent-arc collision studies. We present a new 3D shear-wave velocity model from ambient noise tomography that captures the Banda Basin, the Banda Arc and the surrounding regions. Our velocity model

Ribbons are a subset of polymerized networks that occupy an intermediate space between polymers and surfaces. We perform extensive numerical simulations to understand how to interpolate the statistical properties of ribbons across the two limits by studying their behavior as a function of their widths and bending rigidities, taking into consideration both ideal and self-avoiding ribbons. We map out a two-dimensional phase diagram of the morphology of ideal ribbons, and uncover the onset of a crumpling transition for ribbons of sufficiently large width. We also discuss the onset width above which a ribbon behaves effectively as a surface. Finally, we suggest scaling laws and functional forms that properly link and interpolate the shape of self-avoiding polymers to that of self-avoiding surfaces.

Introduction:Osteonecrosis (ON) refers to the death of bone cells caused by a disruption in blood flow. Multiple-site osteonecrosis (MSON) is a rare condition characterized by concurrent or sequential involvement of three or more separate anatomic sites approximately 3% of ON patients. Avascular necrosis (AVN) is commonly associated with high-dose or long-term corticosteroid use, and several reports suggest that high-dose corticosteroid use is the primary risk factor for developing MSON. The ideal management of ON in a young individual remains a subject of debate. Review of literature supports Core decompression (CD) as an effective treatment option in the pre-collapse stage of ON in small to medium-sized lesions according to Ficat and Arlet Stage I and II. In the advanced stages of the disease (i.e., Stages III and IV), arthroplasty is required when joint preservation is not possible.Case Report:A 27-year-old female presented with pain in the right ankle and left shoulder. The patient was on corticosteroids. Suspected MSON by examination was later confirmed using magnetic resonance imaging. CD and bone marrow aspiration concentrate application sequentially in all affected joints in three sessions with a 2-month gap. Alendronate 70 mg once a week was advised. Tensor fascia lata muscle pedicle bone grafting was performed on both hips following two years post-primary surgery due to the continued progression of the disease.Conclusion:Therefore, young adults experiencing pain or a limited range of motion in their shoulder and ankle joints, particularly if they have a history of steroid use and no other known causes, should be checked for MSON. CD, Bone marrow aspirate concentrate application, and alendronate have decreased the rate of progression of the disease in all joints except in the hips. Tensor fascia lata muscle pedicle grafting decreased progression in the hips.

Abstract Fabrication of diverse and complex 2D molecular architectures using surface‐confined supramolecular coordination chemistry has been continuously attracting considerable attention for years. Here, the on‐surface synthesis of 2D coordination networks exhibiting both crystalline and vitreous phases employing the same constituents is reported. Robust and flexible bimolecular 2D coordination networks, structurally analogous to 2D bilayer silica films on Ru(0001) and graphene, are achieved by iron‐directed self‐assembly of indigo and 1,3,5‐tris[4‐(pyridin‐4‐yl)phenyl]benzene (ext‐TPyB) or 1,3,5‐tris(pyridyl)benzene (TPyB) linkers on Au(111). The crystalline phase features honeycombed nanopores, displaying long‐range order with local defects that can be attributed to variations in coordination nodes and shape flexibility of the ext‐TPyB (/ TPyB) ligand. The vitreous phase evolves upon annealing the honeycomb network to higher temperatures and exhibits reticulated polygons similar to Zachariasen's 2D random network theory. The size of the polygons follows a lognormal distribution, with the probability density function showing an almost linear behavior as characteristic of the structure of glass. The results enrich avenues toward the fabrication and understanding of novel nanostructured condensed matter systems, such as 2D crystalline and vitreous structures, as well as provide the unique possibility to understand structurally bulk glasses.

ABSTRACTThe Korteweg–de‐Vries (KdV) equation is of fundamental importance in a wide range of subjects with generalization to multi‐component systems relevant for multi‐species fluids and cold atomic mixtures. We present a general framework in which a family of multi‐component KdV (mcKdV) equations naturally arises from a broader mathematical structure under reasonable assumptions on the nature of the nonlinear couplings. In particular, we derive a universal form for such a system of coupled KdV‐type equations that is parameterized by non‐zero real numbers and two symmetric functions of those numbers. Second, we show that physically relevant setups such as multi‐component nonlinear Schrödinger equations (mcNLS), under scaling and perturbative treatment, reduce to such a mcKdV equation for a specific choice of the symmetric functions. The reduction from mcNLS to mcKdV requires one to be in a suitable parameter regime where the associated sound speeds of mcNLS are repeated. Hence, we connect the assumptions made in the derivation of the mcKdV system to physically interpretable assumptions for the mcNLS equation. Lastly, our approach provides a systematic foundation for facilitating a natural emergence of multi‐component partial differential equations starting from a general mathematical structure.