Spectral Actions Research Articles

Shaking-table tests and numerical simulations study of subway stations in loess region

The loess region in China, known for its high seismic activity and the extreme vulnerability of loess to earthquakes, presents a considerable threat to the seismic safety of underground structures, including subway stations. With the Xi'an Aerospace City subway station as the background, a subway station model was designed, and shaking table tests were conducted under various conditions to analyze the seismic damage and dynamic responses in this study. The study reveals the seismic vulnerable areas and dynamic response patterns of the subway station under different spectral earthquake actions. Simultaneously, a three-dimensional numerical modeling analysis accounting for soil-structure interaction, was conducted to explore the displacement response of the structure and soil. Results indicate a noticeable amplification effect on the acceleration of both the structure and the soil under seismic motion. The structure exhibits a suppressive effect on the acceleration amplification of the surrounding soil, diminishing with increasing seismic motion intensity. Different depths show varying differences in acceleration responses between the structure and adjacent soil. Structural strain responses and damage phenomena suggest that the central column is the seismic vulnerable area of the subway station. Additionally, the strain distribution of the structure exhibits a distinct spatial effect. The relative horizontal displacement between the structure and the soil follows certain patterns in the depth direction, with the structure experiencing smaller relative horizontal displacement than the soil under seismic action due to the constraining effect of surrounding soil on its displacement response. The experimental conclusions provide valuable reference points for the seismic design and analysis of subway station structures in loess regions.

Aspects of Aperiodic Order

The theory of aperiodic order expanded and developed significantly since the discovery of quasicrystals, and continues to bring many mathematical disciplines together. The focus of this workshop was on harmonic analysis and spectral theory, dynamical systems and group actions, Schrödinger operators, and their roles in aperiodic order – with links into a full range of problems from number theory to operator theory.

Lifting Bratteli diagrams between Krajewski diagrams: Spectral triples, spectral actions, and AF algebras

In this paper, we present a framework to construct sequences of spectral triples on top of an inductive sequence defining an $AF$-algebra. One aim of this paper is to lift arrows of a Bratteli diagram to arrows between Krajewski diagrams. The spectral actions defining Non-commutative Gauge Field Theories associated to two spectral triples related by these arrows are compared (tensored by a commutative spectral triple to put us in the context of Almost Commutative manifolds). This paper is a follow up of a previous one in which this program was defined and physically illustrated in the framework of the derivation-based differential calculus, but the present paper focuses more on the mathematical structure without trying to study the physical implications.

Spectral actions for q-particles and their asymptotics

For spectral actions consisting of the average number of particles and arising from open systems made of general free q-particles (including Bose, Fermi and classical ones corresponding to q = ±1 and 0, respectively) in thermal equilibrium, we compute the asymptotic expansion with respect to the natural cut-off. We treat both relevant situations relative to massless and non relativistic massive particles, where the natural cut-off is 1/β = k B T and , respectively. We show that the massless situation enjoys less regularity properties than the massive one. We also treat in some detail the relativistic massive case for which the natural cut-off is again 1/β. We then consider the passage to the continuum describing infinitely extended open systems in thermal equilibrium, by also discussing the appearance of condensation phenomena occurring for Bose-like q-particles, q ∈ (0, 1]. We then compare the arising results for the finite volume situation (discrete spectrum) with the corresponding infinite volume one (continuous spectrum).

Second quantization and the spectral action

We consider both the bosonic and fermionic second quantization of spectral triples in the presence of a chemical potential. We show that the von Neumann entropy and the average energy of the Gibbs state defined by the bosonic and fermionic grand partition function can be expressed as spectral actions. It turns out that all spectral action coefficients can be given in terms of the modified Bessel functions. In the fermionic case, we show that the spectral coefficients for the von Neumann entropy, in the limit when the chemical potential μ approaches 0, can be expressed in terms of the Riemann zeta function. This recovers a result of Chamseddine-Connes-van Suijlekom.

Kinetic modeling of the synergistic thermal and spectral actions on the inactivation of Cryptosporidium parvum in water by sunlight

Water contamination with the enteroprotozoan parasite Cryptosporidium is a current challenge worldwide. Solar water disinfection (SODIS) has been proved as a potential alternative for its inactivation, especially at household level in low-income environments. This work presents the first comprehensive kinetic model for the inactivation of Cryptosporidium parvum oocysts by sunlight that, based on the mechanism of the process, is able to describe not only the individual thermal and spectral actions but also their synergy. Model predictions are capable of estimating the required solar exposure to achieve the desired level of disinfection under variable solar spectral irradiance and environmental temperature conditions for different locations worldwide. The thermal contribution can be successfully described by a modified Arrhenius equation while photoinactivation is based on a series-event mechanistic model. The wavelength-dependent spectral effect is modeled by means of the estimation of the C. parvum extinction coefficients and the determination of the quantum yield of the inactivation process. Model predictions show a 3.7% error with respect to experimental results carried out under a wide range of temperature (30 to 45 °C) and UV irradiance (0 to 50 W·m−2). Furthermore, the model was validated in three scenarios in which the spectral distribution radiation was modified using different plastic materials common in SODIS devices, ensuring accurate forecasting of inactivation rates for real conditions.

Advances on hormone-like activity of Panax ginseng and ginsenosides.

Traditional Chinese medicine (TCM) has been paid much attentions due to the prevention and treatment of steroid hormone disorders. Ginseng, the root of Panax ginseng C. A. Meyer (Araliaceae), is one of the most valuable herbs in complementary and alternative medicines around the world. A series of dammarane triterpenoid saponins, also known as phytosteroids, were reported as the primary ingredients of Ginseng, and indicated broad spectral pharmacological actions, including anti-cancer, anti-inflammation and anti-fatigue. The skeletons of the dammarane triterpenoid aglycone are structurally similar to the steroid hormones. Both in vitro and in vivo studies showed that Ginseng and its active ingredients have beneficial hormone-like role in hormonal disorders. This review thus summarizes the structural similarities between hormones and dammarane ginsenosides and integrates the analogous effect of Ginseng and ginsenosides on prevention and treatment of hormonal disorders published in recent twenty years (1998-2018). The review may provide convenience for anticipate structure-function relationship between saponins structure and hormone-like effect.

Kinetic modeling of the synergistic thermal and spectral actions on the inactivation of viruses in water by sunlight

Sunlight can be an effective tool for inactivating pathogens in water disinfection processes. In clear water, photoinactivation of viruses is driven by the absorption of UVB radiation and it is more efficient at shorter wavelengths. Moreover, the temperature can significantly improve the efficiency of the process. To date, no kinetic model has been reported that describes the simultaneous thermal and spectral effects that occur during the solar inactivation of viruses. This work presents a novel comprehensive kinetic model for the solar inactivation of MS2 coliphage as a function of the water temperature, irradiance, and spectral distribution of the incident radiation. The model is based on a combination of the modified Arrhenius equation, a wavelength-dependent first-order inactivation model with the quantum yield, and thermal parameters estimated from laboratory data. Model predictions have a 9% error with respect to experiments in the temperature range from 30 to 50 °C and UV irradiance range from 15 to 50 W/m2. Moreover, the model was validated in three scenarios using different plastic materials that modify the spectral range of the radiation reaching the water, confirming an accurate prediction of inactivation rates for real solar disinfection systems worldwide using containers made of any material.

Quantum gravity signatures in the Unruh effect

We study quantum gravity signatures emerging from phenomenologically motivated multiscale models, spectral actions, and Causal Set Theory within the detector approach to the Unruh effect. We show that while the Unruh temperature is unaffected, Lorentz-invariant corrections to the two-point function leave a characteristic fingerprint in the induced emission rate of the accelerated detector. Generically, quantum gravity models exhibiting dynamical dimensional reduction exhibit a suppression of the Unruh rate at high energy while the rate is enhanced in Kaluza-Klein theories with compact extra dimensions. We quantify this behavior by introducing the "Unruh dimension" as the effective spacetime dimension seen by the Unruh effect and show that it is related, though not identical, to the spectral dimension used to characterize spacetime in quantum gravity. We comment on the physical origins of these effects and their relevance for black hole evaporation.

Spectral action models of gravity on packed swiss cheese cosmology

We present a model of (modified) gravity on spacetimes with fractal structure based on packing of spheres, which are (Euclidean) variants of the packed swiss cheese cosmology models. As the action functional for gravity we consider the spectral action of noncommutative geometry, and we compute its expansion on a space obtained as an Apollonian packing of three-dimensional spheres inside a four-dimensional ball. Using information from the zeta function of the Dirac operator of the spectral triple, we compute the leading terms in the asymptotic expansion of the spectral action. They consist of a zeta regularization of the divergent sum of the leading terms of the spectral actions of the individual spheres in the packing. This accounts for the contribution of points 1 and 3 in the dimension spectrum (as in the case of a 3-sphere). There is an additional term coming from the residue at the additional point in the real dimension spectrum that corresponds to the packing constant, as well as a series of fluctuations coming from log-periodic oscillations, created by the points of the dimension spectrum that are off the real line. These terms detect the fractality of the residue set of the sphere packing. We show that the presence of fractality influences the shape of the slow-roll potential for inflation, obtained from the spectral action. We also discuss the effect of truncating the fractal structure at a certain scale related to the energy scale in the spectral action.

Spectral dimensions from the spectral action

The generalized spectral dimension ${D}_{S}(T)$ provides a powerful tool for comparing different approaches to quantum gravity. In this work, we apply this formalism to the classical spectral actions obtained within the framework of almost-commutative geometry. Analyzing the propagation of spin-0, spin-1 and spin-2 fields, we show that a nontrivial spectral dimension arises already at the classical level. The effective field theory interpretation of the spectral action yields plateau structures interpolating between a fixed spin-independent ${D}_{S}(T)={d}_{S}$ for short and ${D}_{S}(T)=4$ for long diffusion times $T$. Going beyond effective field theory the spectral dimension is completely dominated by the high-momentum properties of the spectral action, yielding ${D}_{S}(T)=0$ for all spins. Our results support earlier claims that high-energy bosons do not propagate.

Spectral Gap Actions and Invariant States

We define spectral gap actions of discrete groups on von Neumann algebras and study their relations with invariant states. We will show that a finitely generated ICC group Γ is inner amenable if and only if there exist more than one inner invariant states on the group von Neumann algebra L(Γ). Moreover, a countable discrete group Γ has property (T) if and only if for any action α of Γ on a von Neumann algebra N, every α-invariant state on N is a weak-*-limit of a net of normal α-invariant states.

Spectral action for a one-parameter family of Dirac operators on $\bm{ SU}\textbf {(2)}$SU(2) and $\bm{SU}\textbf {(3)}$SU(3)

The one-parameter family of Dirac operators containing the Levi-Civita, cubic, and the trivial Dirac operators on a compact Lie group is analyzed. The spectra for the one-parameter family of Dirac Laplacians on SU(2) and SU(3) are computed by considering a diagonally embedded Casimir operator. Then the asymptotic expansions of the spectral actions for SU(2) and SU(3) are computed, using the Poisson summation formula and the two-dimensional Euler-Maclaurin formula, respectively. The inflation potential and slow-roll parameters for the corresponding pure gravity inflationary theory are generated, using the full asymptotic expansion of the spectral action on SU(2).

Global and local aspects of spectral actions

The principal object in noncommutative geometry is the spectral triple consisting of an algebra , a Hilbert space and a Dirac operator . Field theories are incorporated in this approach by the spectral action principle, which sets the field theory action to , where f is a real function such that the trace exists and Λ is a cutoff scale. In the low-energy (weak-field) limit, the spectral action reproduces reasonably well the known physics including the standard model. However, not much is known about the spectral action beyond the low-energy approximation. In this paper, after an extensive introduction to spectral triples and spectral actions, we study various expansions of the spectral actions (exemplified by the heat kernel). We derive the convergence criteria. For a commutative spectral triple, we compute the heat kernel on the torus up to the second order in gauge connection and consider limiting cases.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.

Intracavity changes in the field statistics of Raman fiber lasers

We present an experiment in which intracavity optical power spectra of a Raman fiber laser are precisely measured both in the forward and in the backward propagation directions near the cavity mirrors. The statistical properties of the intracavity Stokes field are found to be very different before and after reflection on the cavity mirrors. The influence of both the dispersion and the spectral filtering actions of fiber Bragg grating mirrors are discussed.

A molecular logic gate for the highly selective recognition of pyrophosphate with a hypocrellin A-Zn(ii) complex

Pyrophosphate (PPi) participates in many biological and chemical processes such as energy transduction so that investigations on its role and detection have become very significant. In this contribution, we have developed a molecular logic gate for the recognition of PPi with a fluorescent hypocrellin A-zinc(II) complex (HA-Zn(2+)), and the outputs of which correspond to the fluorescence emission ratio at 604 nm and wavelength shift relative to 629 nm. The emission at 604 nm is the intrinsic fluorescence of HA, which can be effectively quenched by Zn(2+) with a new emission at 629 nm owing to the formation of the HA-Zn(2+) complex. It was found, however, that the new emission at 629 nm is highly selectively quenched with the addition of PPi, recovering the emission at 604 nm, and the recovery ratio is linearly correlated with PPi in the range of 1.8 × 10(-5) mol L(-1) to 2.4 × 10(-4) mol L(-1). ATP, UTP, CTP, GTP, GDP and GMP cannot demonstrate the same spectral actions as PPi. Since the inputs of PPi and the phosphate anions obtain different logical outputs, the designed logic gates have good selectivity and can distinguish PPi from the other anions.