Realizations of Causal Manifolds by Quantum Fields

Quantum mechanical operators and quantum fields are interpreted as realizations of timespace manifolds. Such causal manifolds are parametrized by the classes of the positive unitary operations in all complex operations, i.e. by the homogenous spaces \D(n)=\GL(\C^n_\R)/\U(n) with $n=1$ for mechanics and $n=2$ for relativistic fields. The rank $n$ gives the number of both the discrete and continuous invariants used in the harmonic analysis, i.e. two characteristic masses in the relativistic case. 'Canonical' field theories with the familiar divergencies are inappropriate realizations of the real 4-dimensional causal manifold \D(2). Faithful timespace realizations do not lead to divergencies. In general they are reducible, but nondecomposable - in addition to representations with eigenvectors (states, particle) they incorporate principal vectors without a particle (eigenvector) basis as exemplified by the Coulomb field.Comment: 36 pages, latex, macros include

Quantum dynamics with short-time trajectories and minimal adaptive basis sets

Methods for solving the time-dependent Schrödinger equation via basis set expansion of the wave function can generally be categorized as having either static (time-independent) or dynamic (time-dependent) basis functions. We have recently introduced an alternative simulation approach which represents a middle road between these two extremes, employing dynamic (classical-like) trajectories to create a static basis set of Gaussian wavepackets in regions of phase-space relevant to future propagation of the wave function [J. Chem. Theory Comput., 11, 8 (2015)]. Here, we propose and test a modification of our methodology which aims to reduce the size of basis sets generated in our original scheme. In particular, we employ short-time classical trajectories to continuously generate new basis functions for short-time quantum propagation of the wave function; to avoid the continued growth of the basis set describing the time-dependent wave function, we employ Matching Pursuit to periodically minimize the number of basis functions required to accurately describe the wave function. Overall, this approach generates a basis set which is adapted to evolution of the wave function while also being as small as possible. In applications to challenging benchmark problems, namely a 4-dimensional model of photoexcited pyrazine and three different double-well tunnelling problems, we find that our new scheme enables accurate wave function propagation with basis sets which are around an order-of-magnitude smaller than our original trajectory-guided basis set methodology, highlighting the benefits of adaptive strategies for wave function propagation

Linear compression behaviour of oil palm empty fruit bunches

Received: January 29th, 2021 ; Accepted: April 8th, 2021 ; Published: May 20th, 2021 ; Correspondence: [email protected] study describes the mechanical behaviour of oil palm empty fruit bunches (EFB) as a promising product for pyrolysis production. The EFB samples mixture of moisture content 6.3 ± 0.3 (% d.b.) were grouped into different fraction sizes of 10, 20, 40 and 100 mm. The initial pressing height of each fraction size was measured at 60 mm and compressed at a maximum force of 4,500 N and speed of 10 mm min-1 to obtain the force-deformation dependencies using the universal compression machine and pressing vessel of diameter 60 mm with a plunger. Deformation, deformation energy, volume energy and strain were calculated. While deformation decreased with fraction sizes, deformation energy increased. The deformation energies at fraction sizes from 10 mm to 100 mm indicated energy savings of approximately 23%. The optimal fraction size in relation to energy efficiency was observed at 10 mm. The tangent model accurately described the mechanical behaviour of the EFB samples mixture. The results provide useful information for the design of optimal technology for processing EFB for energy purposes

On the identity of the identity operator in nonadiabatic linearized semiclassical dynamics

Simulating the nonadiabatic dynamics of condensed-phase systems continues to pose a significant challenge for quantum dynamics methods. Approaches based on sampling classical trajectories within the mapping formalism, such as the linearized semiclassical initial value representation (LSC-IVR), can be used to approximate quantum correlation functions in dissipative environments. Such semiclassical methods however commonly fail in quantitatively predicting the electronic-state populations in the long-time limit. Here we present a suggestion to minimize this difficulty by splitting the problem into two parts, one of which involves the identity, and treating this operator by quantum-mechanical principles rather than with classical approximations. This strategy is applied to numerical simulations of spin-boson model systems, showing its potential to drastically improve the performance of LSC-IVR and related methods with no change to the equations of motion or the algorithm in general, but rather by simply using different functional forms of the observables

Real null coframes in general relativity and GPS type coordinates

Based on work of Derrick, Coll, and Morales, we define a `symmetric' null coframe with {\it four real null covectors}. We show that this coframe is closely related to the GPS type coordinates recently introduced by Rovelli.Comment: Latex script, 9 pages, 4 figures; references added to work of Derrick, Coll, and Morales, 1 new figur

Sampling minimal, adaptive basis sets for multidimensional, nuclear quantum dynamics using simple, semi-classical trajectories

Methods for the study of nuclear quantum dynamics can be categorised by the nature of the basis set expansion they employ. The wavefunction can be expanded in a static set of time-independent basis functions, the time evolution being described solely via the expansion coefficients. Alternatively, basis functions can be propagated in time, along with the coefficients, via equations of motion for their parameters. Time-independent basis sets are plagued by exponential scaling, while the equations of motion for time-dependent basis functions are challenging to integrate and, if not derived variationally, can violate energy conservation laws. This work presents a novel basis set sampling method which represents a compromise between these two categories. A set of sampling trajectories, evolving on the potential energy surface of the system, are used to place basis functions in regions of phase space, relevant to wavefunction propagation. These functions then act as a time-independent basis set, the wavefunction being evolved via exact, variational equations of motion for the expansion coefficients. This approach is applied to a challenging quantum dynamics benchmark, namely the relaxation dynamics of photoexcited pyrazine, and yields highly encouraging results. In order to address divergence from exact dynamics at longer timescales, which is attributed to the classical sampling trajectories being a sound approximation to quantum propagation of the wavefunction only in the short-time limit, a modification of this method is proposed. Shorter iterations of trajectory sampling and wavefunction propagation are used, linked by a minimisation algorithm that continuously optimises the basis set, preventing unfavourable scaling. This adaptive sampling approach is again applied to the pyrazine benchmark with a significant increase in performance and accuracy. Highly encouraging results are also obtained for a quantum tunnelling benchmark system, which are improved upon even further, and at little extra cost, by the use of path integral sampling trajectories

Simplicial quantum dynamics

Present-day quantum field theory can be regularized by a decomposition into quantum simplices. This replaces the infinite-dimensional Hilbert space by a high-dimensional spinor space and singular canonical Lie groups by regular spin groups. It radically changes the uncertainty principle for small distances. Gaugeons, including the gravitational, are represented as bound fermion-pairs, and space-time curvature as a singular organized limit of quantum non-commutativity. Keywords: Quantum logic, quantum set theory, quantum gravity, quantum topology, simplicial quantization.Comment: 25 pages. 1 table. Conference of the International Association for Relativistic Dynamics, Taiwan, 201

Clinical presentation and management of acromegaly in elderly patients

Background and aim: Acromegaly is a rare disease with a peak of incidence in early adulthood. However, enhanced awareness of this disease, combined with wide availability of magnetic resonance imaging (MRI), has increased the diagnosis of forms with mild presentation, especially in elderly patients. Moreover, due to increased life expectancy and proactive individualized treatment, patients with early-onset acromegaly are today aging. The aim of our study was to describe our cohort of elderly patients with acromegaly. Materials and methods: This is a cross-sectional retrospective study of 96 outpatients. Clinical, endocrine, treatment, and follow-up data were collected using the electronic database of the University Hospital of Padova, Italy. Results: We diagnosed acromegaly in 13 patients, aged 6565\ua0years, presenting with relatively small adenomas and low IGF-1 secretion. Among them, 11 patients were initially treated with medical therapy and half normalized hormonal levels after 6\ua0months without undergoing neurosurgery (TNS). Remission was achieved after TNS in three out of four patients (primary TNS in two); ten patients presented controlled acromegaly at the last visit. Acromegaly-related comorbidities (colon polyps, thyroid cancer, adrenal incidentaloma, hypertension, and bone disease) were more prevalent in patients who had an early diagnosis (31 patients, characterized by a longer follow-up of 24\ua0years) than in those diagnosed aged 6565\ua0years (5\ua0years of follow-up). Conclusions: Elderly acromegalic patients are not uncommon. Primary medical therapy is a reasonable option and is effectively used, while the rate of surgical success is not reduced. A careful cost-benefit balance is suggested. Disease-specific comorbidities are more prevalent in acromegalic patients with a longer follow-up rather than in those diagnosed aged 6565\ua0years

Towards the development of Bacillus subtilis as a cell factory for membrane proteins and protein complexes

Background: The Gram-positive bacterium Bacillus subtilis is an important producer of high quality industrial enzymes and a few eukaryotic proteins. Most of these proteins are secreted into the growth medium, but successful examples of cytoplasmic protein production are also known. Therefore, one may anticipate that the high protein production potential of B. subtilis can be exploited for protein complexes and membrane proteins to facilitate their functional and structural analysis. The high quality of proteins produced with B. subtilis results from the action of cellular quality control systems that efficiently remove misfolded or incompletely synthesized proteins. Paradoxically, cellular quality control systems also represent bottlenecks for the production of various heterologous proteins at significant concentrations. Conclusion: While inactivation of quality control systems has the potential to improve protein production yields, this could be achieved at the expense of product quality. Mechanisms underlying degradation of secretory proteins are nowadays well understood and often controllable. It will therefore be a major challenge for future research to identify and modulate quality control systems of B. subtilis that limit the production of high quality protein complexes and membrane proteins, and to enhance those systems that facilitate assembly of these proteins.