Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences最新文献

Climate change and microplastic pollution are two of the most pressing environmental issues of our time. Both have far-reaching effects on ecosystems, human health and global biodiversity. Climate change, driven by the increase in greenhouse gases (GHGs), leads to rising temperatures, altered weather patterns and ocean acidification, which can exacerbate the distribution and effects of microplastics. Microplastics, plastic particles less than 5 mm in size, originate from a variety of sources, including the breakdown of larger plastic debris, microbeads and synthetic fibers. These particles are pervasive in marine, freshwater and terrestrial ecosystems, posing significant risks to wildlife and human health. Emerging research highlights intricate interactions between climate change and microplastics. Elevated temperatures may accelerate plastic degradation, while extreme weather events can enhance microplastic transport and distribution across environments. These dynamics may disrupt critical processes like carbon sequestration, potentially affecting global carbon cycles. Understanding the interplay between these two environmental stressors is crucial for developing effective mitigation and adaptation strategies. This review aims to synthesize current knowledge on the link between climate change and microplastics, highlight key mechanisms and pathways, and identify gaps in the existing research, providing a comprehensive overview of their potential synergistic effects, while, simultaneously, offering recommendations for future research and policy development.This article is part of the Theo Murphy meeting issue 'Sedimentology of plastics: state of the art and future directions'.

Plastic pollution in the ocean is a global environmental issue, with buoyant debris accumulating at the surface and posing long-term ecological threats. Although sediments are the ultimate sink for plastics, a mismatch between observed surface concentrations and estimated inputs implies the understanding of vertical sedimentation mechanisms and rates are inaccurate. Here, we present a coupled fragmentation-sedimentation model that quantitatively predicts the vertical transport and long-term fate of buoyant plastic debris and microplastics (MPs, less than 5 mm). Using a representative 10 mm polyethylene (PE) particle, we show that fragmentation into small MPs is essential for their incorporation into marine snow aggregates (MSAs) and subsequent settling. Even after 100 yr, ca. 10% of the initial plastic mass still remains at the surface providing a continual source of small MPs to ocean surface waters. This study provides the first mechanistic framework linking large plastic degradation to size selective sedimentation, demonstrating that plastic pollution will persist at our ocean surfaces for over a century even if inputs cease. Our findings highlight the need for mitigation strategies beyond input reduction and ocean clean-up, addressing the long-term removal of existing ocean plastics.This article is part of the Theo Murphy meeting issue 'Sedimentology of plastics: state of the art and future directions'.

Quantum [Formula: see text]-qubit states that are totally symmetric under the permutation of qubits are essential ingredients of important algorithms and applications in quantum information. Consequently, there is significant interest in developing methods to prepare and manipulate Dicke states, which form a basis for the subspace of fully symmetric states. Two simple protocols for transforming Dicke states are considered. An algebraic characterization of the operations that these protocols induce is obtained in terms of the Weyl algebra [Formula: see text] and [Formula: see text]. Fixed points under the application of the combination of both protocols are explicitly determined. Connections with the binary Hamming scheme, the Hadamard transform and Krawtchouk polynomials are highlighted.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.

In this paper, we extend the notions of complex C-R-calculus and complex Hermite polynomials to the bicomplex setting and compare the bicomplex polyanalytic function theory with the classical complex case. Specifically, we introduce two kinds of bicomplex Hermite polynomials and present some of their basic properties, such as the Rodrigues formula and generating functions. We also define three bicomplex Landau operators and calculate their action on the bicomplex Hermite polynomials of the first kind.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.

We consider pretty good state transfer in coined quantum walks between antipodal vertices on the hypercube [Formula: see text]. When [Formula: see text] is a prime, this was proven to occur in the arc-reversal walk with Grover coins. We extend this result by constructing weighted Grover coins that enable pretty good state transfer on every [Formula: see text]. Our coins are real and require modification of the weight on only one arc per vertex. We also generalize our approach and establish a sufficient condition for pretty good state transfer to occur on other graphs.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.

Variational quantum algorithms (VQAs) are promising hybrid quantum-classical methods designed to leverage the computational advantages of quantum computing while mitigating the limitations of current noisy intermediate-scale quantum (NISQ) hardware. Although VQAs have been demonstrated as proofs of concept, their practical utility in solving real-world problems-and whether quantum-inspired classical algorithms can match their performance-remains an open question. We present a novel application of the variational quantum linear solver (VQLS) and its classical neural quantum states-based counterpart, the variational neural linear solver (VNLS), as key components within a minimum map Newton solver for a complementarity-based rigid-body contact model. We demonstrate using the VNLS that our solver accurately simulates the dynamics of rigid spherical bodies during collision events. These results suggest that quantum and quantum-inspired linear algebra algorithms can serve as viable alternatives to standard linear algebra solvers for modelling certain physical systems.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.

Discriminating between quantum states and channels is an important task in the field of quantum computation and quantum information theory. Metrics and statistical distances form the tools for various approaches proposed for this task. We analyse existing results to compare properties, main purpose, computability and advantages and disadvantages of each approach.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.

Quantum Gaussian channels are fundamental models for communication and information processing in continuous-variable quantum systems. This work addresses both foundational aspects and physical implementation pathways for these channels. Firstly, we provide a rigorous, unified framework by formally proving the equivalence of three principal definitions of quantum Gaussian channels prevalent in the literature. Secondly, we investigate the physical realization of these channels using linear optics, a key platform in photonics. The central research contributions are (i) a new characterization of Gaussian channels in terms of their ampliations, (ii) a precise characterization of the specific pairs of matrices [Formula: see text] that correspond to Gaussian channels physically implementable via linear optical multiport interferometers, (iii) answering the questions posed by Parthasarathy (Parthasarathy KR. 2015 Symplectic dilations, Gaussian states and Gaussian channels. Indian J. Pure Appl. Math. 46, 419-439. (doi:10.1007/s13226-015-0144-5)) and (iv) a discussion on some common misunderstandings in the literature. This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.

We study Grover's quantum walk on a new class of graphs, termed segmented complete graphs, which combine high symmetry with detailed spectral properties. Using these graphs, we implement Grover's search algorithm and investigate its performance, focussing on the relationship between graph volume, optimal search time and success probabilities. Our results generalize classical findings for directed weighted graphs and provide new insights into enhancing quantum search algorithms on complex graph structures.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.

Motivated by the product formula of the Chebyshev polynomials of the second kind [Formula: see text], we newly introduce the partial Chebyshev polynomials [Formula: see text] and [Formula: see text] and derive their basic properties, relations to the classical Chebyshev polynomials and new factorization formulas for [Formula: see text]. To calculate the quadratic embedding constant (QEC) of a fan graph [Formula: see text], we derive a new polynomial [Formula: see text], which is factorized by the partial Chebyshev polynomial [Formula: see text]. We prove that [Formula: see text] is given in terms of the minimal zero of [Formula: see text] and obtain the explicit value of [Formula: see text] for an even [Formula: see text] and its reasonable estimate for an odd [Formula: see text].This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.