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Concept# Island of stability

Summary

In nuclear physics, the island of stability is a predicted set of isotopes of superheavy elements that may have considerably longer half-lives than known isotopes of these elements. It is predicted to appear as an "island" in the chart of nuclides, separated from known stable and long-lived primordial radionuclides. Its theoretical existence is attributed to stabilizing effects of predicted "magic numbers" of protons and neutrons in the superheavy mass region.
Several predictions have been made regarding the exact location of the island of stability, though it is generally thought to center near copernicium and flerovium isotopes in the vicinity of the predicted closed neutron shell at N = 184. These models strongly suggest that the closed shell will confer further stability towards fission and alpha decay. While these effects are expected to be greatest near atomic number Z = 114 and N = 184, the region of increased stability is expected to encompass several neighboring elements, and there may also be additional islands of stability around heavier nuclei that are doubly magic (having magic numbers of both protons and neutrons). Estimates of the stability of the nuclides within the island are usually around a half-life of minutes or days; some estimates predict half-lives of millions of years.
Although the nuclear shell model predicting magic numbers has existed since the 1940s, the existence of long-lived superheavy nuclides has not been definitively demonstrated. Like the rest of the superheavy elements, the nuclides within the island of stability have never been found in nature; thus, they must be created artificially in a nuclear reaction to be studied. Scientists have not found a way to carry out such a reaction, for it is likely that new types of reactions will be needed to populate nuclei near the center of the island. Nevertheless, the successful synthesis of superheavy elements up to Z = 118 (oganesson) with up to 177 neutrons demonstrates a slight stabilizing effect around elements 110 to 114 that may continue in unknown isotopes, consistent with the existence of the island of stability.

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Superheavy element

Superheavy elements, also known as transactinide elements, transactinides, or super-heavy elements, are the chemical elements with atomic number greater than 103. The superheavy elements are those beyond the actinides in the periodic table; the last actinide is lawrencium (atomic number 103). By definition, superheavy elements are also transuranium elements, i.e., having atomic numbers greater than that of uranium (92). Depending on the definition of group 3 adopted by authors, lawrencium may also be included to complete the 6d series.

Island of stability

In nuclear physics, the island of stability is a predicted set of isotopes of superheavy elements that may have considerably longer half-lives than known isotopes of these elements. It is predicted to appear as an "island" in the chart of nuclides, separated from known stable and long-lived primordial radionuclides. Its theoretical existence is attributed to stabilizing effects of predicted "magic numbers" of protons and neutrons in the superheavy mass region.

Electron shell

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Delphine Lorraine Perle Blondel

Over the past decade, methods to culture stem cells in three dimensions have opened up a plethora of new opportunities for basic and translational research in the life sciences. In particular, the use of natural extracellular matrix (ECM) surrogates, such as mouse tumour-derived Matrigel, unleashed the possibility to recapitulate complex multicellular behaviours in vitro, culminating in the successful derivation of miniaturized organs, termed organoids. While organoids hold tremendous potential as model systems in basic biology, the translational potential of these systems is hampered by their strict dependency on animal-derived matrices that suffer from batch-to-batch variability, potential immunogenicity, and ethical concerns. Recent efforts in engineering covalently crosslinked synthetic hydrogels have attempted to substitute these ill-defined organoid culture systems. However, although these bio-artificial matrices have shown significant potential for 3D organoid culture, their stability and their inherent elastic nature hamper organoid development. Indeed, the native ECM, just like Matrigel, is a highly viscoelastic and dynamic 3D milieu that can relax in response to tissue-induced stress by breaking and subsequently rearranging its network, thus permitting cellular remodelling without compromising the macroscopic stability of the material over time. Therefore, there is a need to develop the next generation of synthetic organoid culture matrices, exhibiting in vivo-like stress-relaxation properties.
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In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point argument. Unlike the unperturbed case, a noteworthy difficulty here arises from the possible non-unitarity of the semigroup generating the corresponding linear evolution. We then show that the equation is Hamiltonian and we establish several stability/instability results for its standing waves. Our analysis relies on a detailed study of the spectral properties of the linearization of the equation, and on the well-known 'slope condition' for orbital stability. (C) 2019 Elsevier Inc. All rights reserved.

2019