Search Results (7)

Urban informal green spaces (IGS) represent valuable reservoirs of biodiversity within urban areas and are increasingly recognized as integral components of green infrastructure. They are perceived as temporary ecosystems, and the management of their vegetation is relatively understudied. The development time of spontaneous vegetation on transformed lands is considered to be in the range of decades, which makes it even more necessary to provide managers with better guidelines for such a long period. Two suggested management approaches for these areas involve: (1) retaining vegetation at various stages of succession (non-forest IGS) and (2) protecting advanced developmental stages (forest IGS), with options for balanced intervention or complete non-intervention. However, the differences in biodiversity between these two types in cities across Central Europe remain unknown, as well as whether the predictors of biodiversity at both local and landscape scales are consistent for non-forest and forest IGS. We examined factors such as habitat continuity, landscape structure, soil quality, and human impact to shed light on pathways for enhancing urban floristic diversity. Conducting extensive botanical surveys in existing informal green spaces (IGS) in Warsaw, we derived various parameters, including the total number of species, Shannon-Wiener biodiversity index, hemeroby, urbanity, share of species from distinct ecological groups, and the number of rare and ancient forest plant species. Tracing habitat continuity from the early 20th century using digitized aerial imagery provided a unique long-term perspective on IGS development. We revealed that no management is pivotal for the conservation of select rare and ancient forest species. On the other hand, partial abandonment with occasional maintenance may enrich species diversity across different successional phases. We uncovered the significant influence of landscape structure and human activity on vegetation species composition within IGS. Notably, IGS proximate to extensive forest landscapes displayed a marked abundance of forest species, alongside a greater prevalence of rare species. However, the presence of other vegetation types in the vicinity did not yield similar effects. Our findings indicate that IGS, when left untouched for decades near forested areas, are valuable for urban biodiversity. As cities across the globe seek sustainable paths, this research underscores the importance of properly understanding and integrating IGS into urban ecological planning. Full article

Most structural faults in metal parts can be attributed to fatigue crack propagation. The analysis and prognostics of fatigue crack propagation play essential roles in the health management of mechanical systems. Due to the impacts of different uncertainty factors, the crack propagation process exhibits significant randomness, which causes difficulties in fatigue life prediction. To improve prognostic accuracy, a physics-based Tweedie exponential dispersion process (TEDP) model is proposed via integrating Paris Law and the stochastic process. This TEDP model can capture both the crack growth mechanism and uncertainty. Compared with other existing models, the TEDP taking Wiener process, Gamma process, and inverse process as special cases is more general and flexible in modeling complex degradation paths. The probability density function of the model is derived based on saddle-joint approximation. The unknown parameters are calculated via maximum likelihood estimation. Then, the analytic expressions of the distributions of lifetime and product reliability are presented. Significant findings include that the proposed TEDP model substantially enhances predictive accuracy in lifetime estimations of mechanical systems under varying operational conditions, as demonstrated in a practical case study on fatigue crack data. This model not only provides highly accurate lifetime predictions, but also offers deep insights into the reliability assessments of mechanically stressed components. Full article

The subsea control system, a pivotal element of the subsea production system, plays an essential role in collecting production data and real-time operational monitoring, crucial for the consistent and stable output of offshore oil and gas fields. The increasing demand for secure offshore oil and gas extraction underscores the necessity for advanced reliability modeling and effective maintenance strategies for subsea control systems. Given the enhanced reliability of subsea equipment due to technological advancements, resulting in scarce failure data, traditional reliability modeling methods reliant on historical failure data are becoming inadequate. This paper proposes an innovative reliability modeling technique for subsea control systems that integrates a Wiener degradation model affected by random shocks and utilizes the Copula function to compute the joint reliability of components and their backups. This approach considers the unique challenges of the subsea environment and the complex interplay between components under variable loads, improving model accuracy. This study also examines the effects of imperfect maintenance on degradation paths and introduces a holistic lifecycle cost model for preventive maintenance (PM), optimized against reliability and economic considerations. Numerical simulations on a Subsea Control Module demonstrate the effectiveness of the developed models. Full article

We formulate a general program for describing and analyzing continuous, differential weak, simultaneous measurements of noncommuting observables, which focuses on describing the measuring instrument autonomously, without states. The Kraus operators of such measuring processes are time-ordered products of fundamental differential positive transformations, which generate nonunitary transformation groups that we call instrumental Lie groups. The temporal evolution of the instrument is equivalent to the diffusion of a Kraus-operator distribution function, defined relative to the invariant measure of the instrumental Lie group. This diffusion can be analyzed using Wiener path integration, stochastic differential equations, or a Fokker-Planck-Kolmogorov equation. This way of considering instrument evolution we call the Instrument Manifold Program. We relate the Instrument Manifold Program to state-based stochastic master equations. We then explain how the Instrument Manifold Program can be used to describe instrument evolution in terms of a universal cover that we call the universal instrumental Lie group, which is independent not just of states, but also of Hilbert space. The universal instrument is generically infinite dimensional, in which case the instrument’s evolution is chaotic. Special simultaneous measurements have a finite-dimensional universal instrument, in which case the instrument is considered principal, and it can be analyzed within the differential geometry of the universal instrumental Lie group. Principal instruments belong at the foundation of quantum mechanics. We consider the three most fundamental examples: measurement of a single observable, position and momentum, and the three components of angular momentum. As these measurements are performed continuously, they converge to strong simultaneous measurements. For a single observable, this results in the standard decay of coherence between inequivalent irreducible representations. For the latter two cases, it leads to a collapse within each irreducible representation onto the classical or spherical phase space, with the phase space located at the boundary of these instrumental Lie groups. Full article

The canonical commutation relation, $[Q,P]=i\hslash$, stands at the foundation of quantum theory and the original Hilbert space. The interpretation of P and Q as observables has always relied on the analogies that exist between the unitary transformations of Hilbert space and the canonical (also known as contact) transformations of classical phase space. Now that the theory of quantum measurement is essentially complete (this took a while), it is possible to revisit the canonical commutation relation in a way that sets the foundation of quantum theory not on unitary transformations but on positive transformations. This paper shows how the concept of simultaneous measurement leads to a fundamental differential geometric problem whose solution shows us the following. The simultaneous P and Q measurement (SPQM) defines a universal measuring instrument, which takes the shape of a seven-dimensional manifold, a universal covering group we call the instrumental Weyl-Heisenberg ($\mathrm{IWH}$) group. The group $\mathrm{IWH}$ connects the identity to classical phase space in unexpected ways that are significant enough that the positive-operator-valued measure (POVM) offers a complete alternative to energy quantization. Five of the dimensions define processes that can be easily recognized and understood. The other two dimensions, the normalization and phase in the center of the $\mathrm{IWH}$ group, are less familiar. The normalization, in particular, requires special handling in order to describe and understand the SPQM instrument. Full article

Using torus gauge fixing, Hahn in 2008 wrote down an expression for a Chern-Simons path integral to compute the Wilson Loop observable, using the Chern-Simons action \(S_{CS}^\kappa\), \(\kappa\) is some parameter. Instead of making sense of the path integral over the space of \(\mathfrak{g}\)-valued smooth 1-forms on \(S^2 \times S^1\), we use the Segal Bargmann transform to define the path integral over \(B_i\), the space of \(\mathfrak{g}\)-valued holomorphic functions over \(\mathbb{C}^2 \times \mathbb{C}^{i-1}\). This approach was first used by us in 2011. The main tool used is Abstract Wiener measure and applying analytic continuation to the Wiener integral. Using the above approach, we will show that the Chern-Simons path integral can be written as a linear functional defined on \(C(B_1^{\times^4} \times B_2^{\times^2}, \mathbb{C})\) and this linear functional is similar to the Chern-Simons linear functional defined by us in 2011, for the Chern-Simons path integral in the case of \(\mathbb{R}^3\). We will define the Wilson Loop observable using this linear functional and explicitly compute it, and the expression is dependent on the parameter \(\kappa\). The second half of the article concentrates on taking \(\kappa\) goes to infinity for the Wilson Loop observable, to obtain link invariants. As an application, we will compute the Wilson Loop observable in the case of \(SU(N)\) and \(SO(N)\). In these cases, the Wilson Loop observable reduces to a state model. We will show that the state models satisfy a Jones type skein relation in the case of \(SU(N)\) and a Conway type skein relation in the case of \(SO(N)\). By imposing quantization condition on the charge of the link \(L\), we will show that the state models are invariant under the Reidemeister Moves and hence the Wilson Loop observables indeed define a framed link invariant. This approach follows that used in an article written by us in 2012, for the case of \(\mathbb{R}^3\). Full article

This work advances the modeling of bondonic effects on graphenic and honeycomb structures, with an original two-fold generalization: (i) by employing the fourth order path integral bondonic formalism in considering the high order derivatives of the Wiener topological potential of those 1D systems; and (ii) by modeling a class of honeycomb defective structures starting from graphene, the carbon-based reference case, and then generalizing the treatment to Si (silicene), Ge (germanene), Sn (stannene) by using the fermionic two-degenerate statistical states function in terms of electronegativity. The honeycomb nanostructures present η-sized Stone-Wales topological defects, the isomeric dislocation dipoles originally called by authors Stone-Wales wave or SWw. For these defective nanoribbons the bondonic formalism foresees a specific phase-transition whose critical behavior shows typical bondonic fast critical time and bonding energies. The quantum transition of the ideal-to-defect structural transformations is fully described by computing the caloric capacities for nanostructures triggered by η-sized topological isomerisations. Present model may be easily applied to hetero-combinations of Group-IV elements like C-Si, C-Ge, C-Sn, Si-Ge, Si-Sn, Ge-Sn. Full article