Diffuse Medium Research Articles

Investigation of the Gas Permeation Stream through Gas Diffusion Electrodes for CO2 Electrolysis and Possible Links to Selectivity

The electrochemical reduction of CO2 (eCO2R) is one promising attempt to create value added products from excess greenhouse gas with renewable energy. However, to become commercially relevant, some challenges have to be outgrown. To overcome the challenge of mass transport limitations on planar electrodes, Gas-Diffusion-Electrodes (GDE) have been implemented for eCO2R, allowing to reach sufficient reaction rates with the CO2 directly being delivered to the catalyst layer [1]. A major issue in the application of GDEs for eCO2R represents flooding of the mostly carbon based gas diffusion media by the alkaline electrolyte during application. This phenomenon results in a detrimental change of the 3-phase boundary and is accompanied by a loss of activity and a breakdown of performance [2]. A possible approach to avoid flooding of the GDE during eCO2R is to apply a backpressure in order to increase the capillary pressure inside the GDE, which needs to be balanced accurately, since excess backpressure can cause a CO2 crossover stream through the GDE into the electrolyte compartment [3]. In our work we investigate the permeation behavior of GDEs in a customized flow cell and investigate how to influence it via electrode preparation. A deeper understanding of the permeation characteristics of GDEs could lead to a better choice of operation points regarding flooding issues. However, the operation point itself and the preparation of GDEs could impact not only the flooding behavior of the electrode but also selectivity of the reaction. The eCO2R is taking place ~10 µm away from the gas-liquid boundary. The distribution of the two phases inside the GDE is crucial for the reaction pathway [4]. Therefore, we examine possible links of permeation behavior and electrode preparation on selectivity.In detail, our setup contains a customized flow cell in which the pressure in the gas compartment is adjusted with a needle valve and monitored via a pressure transmitter. The gas-crossover stream through the GDE is then registered by collecting the gas transferred to the liquid electrolyte in a measuring cylinder.For electrode preparation, commercial carbon based GDLs (25BC-Sigracet, H23C8-Freudenberg) are pretreated by either spray coating a carbon-ionomer-layer on top of the microporous layer or sputter coating with copper first. In the second step, a galvanostatic deposition of copper is carried out on the pretreated GDLs.The permeation behavior is tested for the non-coated commercial GDLs, the GDLs after the pretreatment step and after deposition of copper without and with current applied, respectively. In our experiments the crossover stream related to backpressure through the GDL H23C8 was lower compared to the crossover stream through GDL 25BC, most likely being linked to differences in the porosity and cracks of the MPL (Figure 1A). However, when comparing identically prepared GDEs based on different GDL types at the same crossover stream, only minor changes in selectivity can be observed (Figure 1B). It was also found that the crossover stream was influenced by the coating of the electrode. While sputter coating (spu) has a minor impact on gas permeation, spray coating (spr) leads to a significant change. These observations could be related to increased electrode wetting after spray- but not after sputter coating. The permeation behavior after galvanic deposition of copper is comparable, independent of the pretreatment procedure. Comparing the selectivity of GDEs with the different pretreatment procedure, a significant change in selectivity can be observed (Figure 1C). In the next steps, it will be crucial to investigate if this selectivity change is related to a different gas-liquid distribution in the GDE or to other factors as the composition of the coating layer to successfully influence operation stability and selectivity.

Probing diffusive media through speckle differencing.

Temporally varying speckle patterns, produced by light-matter interaction encode valuable information about inhomogeneities embedded within a scattering medium. These speckle fluctuations arise either from the tuning of the emission frequency of a laser illuminating a static scattering medium or from the microscopic motion of scatterers within a dynamically scattering medium. In this work, we detect embedded inhomogeneities by probing static and dynamic scattering media with coherent light and leveraging the statistical distribution of temporal speckle differences. In addition, we utilize the insights from the speckle differencing paradigm, to present the first experimental results of detecting inhomogeneities embedded within a scattering medium using bio-inspired neuromorphic sensors. The proposed neuromorphic approach simplifies the optical and electronic design, and significantly reduces data throughput by capturing only the differential information in the form of 1-bit spikes.

Peridynamics modeling of coupled gas convection transport and thermal diffusion in heterogeneous porous media

Peridynamics modeling of coupled gas convection transport and thermal diffusion in heterogeneous porous media

Universal superdiffusion of random walks in media with embedded fractal networks of low diffusivity.

Diffusion in composite media with high contrasts between diffusion coefficients in fractal sets of inclusions and in their embedding matrices is modeled by lattice random walks (RWs) with probabilities p<1 of hops from fractal sites and 1 from matrix sites. Superdiffusion is predicted in time intervals that depend on p and with diffusion exponents that depend on the dimensions of matrix (E) and fractal (D_{F}) as ν=1/(2+D_{F}-E). This contrasts with the nonuniversal subdiffusion of RWs confined to fractal media. Simulations with four fractals show the anomaly at several time decades for p≲10^{-3} and the crossover to the asymptotic normal diffusion. These results show that superdiffusion can be observed in isotropic RWs with finite moments of hop length distributions and allow the estimation of the dimension of the inclusion set from the diffusion exponent. However, displacements within single trajectories have normal scaling, which shows transient ergodicity breaking.

On the Doublet Flux Ratio of Mg ii Resonance Lines in and Around Galaxies

Observations of metallic doublet emission lines, particularly Mg ii λ λ2796, 2803, provide crucial information for understanding galaxies and their circumgalactic medium. This study explores the effects of resonant scattering on the Mg ii doublet lines and the stellar continuum in spherical and cylindrical geometries. Our findings show that under certain circumstances, resonance scattering can cause an increase in the doublet flux ratio and the escaping flux of the lines beyond what is expected in optically thin spherical media. As expected, the doublet ratio is consistently lower than the intrinsic ratio when the scattering medium is spherically symmetric and dusty. However, if the scattering medium has a disk shape, such as face-on disk galaxies, and is viewed face-on, the doublet ratio is predicted to be higher than 2. It is also shown that doublet ratios as low as those observed in compact star-forming galaxies cannot be explained solely by pure dust attenuation of intrinsic Mg ii emission lines in spherical models unless dust opacity deviates markedly from that expected based on the dust-to-Mg+ gas ratio of our Galaxy. The importance of the continuum-pumped emission lines and expanding media is discussed to understand observational aspects, including doublet flux ratios, which can be lower than 1.5 or higher than 2, as well as symmetric or asymmetric line profiles. It is also discussed that the diffuse warm neutral medium may be an important source of Mg ii emission. These results provide insight into the complexity of the shape and orientation of distant, spatially unresolved galaxies.

Radiative and mechanical energies in galaxies

Context. Atomic and molecular lines emitted from galaxies are fundamental tracers of the medium responsible for the emission and contain valuable information regarding the energy budget and the strength of the different feedback mechanisms. Aims. The goal of this work is to provide a new framework for the interpretation of atomic and molecular lines originating from extragalactic sources and a robust method to deduce the mechanical and radiative energy budget from a set of observations. Methods. Atomic and molecular lines detected in a given object are assumed to result from the combination of distributions of shocks and photo-dissociation regions (PDRs) within the observational beam. The emission of individual structures is computed using the Paris-Durham shock code and the Meudon PDR code over a wide range of parameters. The total emission is then calculated assuming probability distribution functions for shocks and PDRs. A distance between the observational dataset and the model is finally defined based on the ratios of the observed to the predicted intensities. Results. As a test case scenario, we consider the radio galaxy 3C 326 N. The dataset is composed of 12 rotational and ro-vibrational lines of H2 and the fine structure lines of C+ and O. Our interpretative framework shows that both shocks and PDRs are required to explain the line fluxes. Surprisingly, viable solutions are obtained at low density only (nH &lt; 100 cm−3), indicating that most of the emission originates from diffuse interstellar matter. The optimal solution, obtained for nH = 10 cm−3, corresponds to a distribution of low-velocity shocks (between 5 and 20 km s−1) propagating in PDR environments illuminated by a UV radiation field ten times larger than that in the solar neighborhood. This solution implies that at least 4% of the total mass carried by the PDRs is shocked. The H2 0-0 S(0) 28 μm, [CII] 158 μm, and [OI] 63 μm lines originate from the PDR components, while all the other H2 lines are mostly emitted by shocks. The total solid angles sustained by PDRs and shocks imply that the radiative and mechanical energies reprocessed by these structures are LUV = 6.3 × 109 L⊙ and LK = 3.9 × 108 L⊙, respectively, in remarkable agreement with the values of the IR luminosity deduced from the fit of the spectral energy distribution (SED) of 3C 326 N, and consistent with a small fraction of the active galactic nuclei (AGN) jet kinetic power dissipated in the interstellar medium (≈1%). Conclusions. This work shows that the radiative and mechanical energy budget of galaxies can be derived from the sole observations of atomic and molecular lines. It reveals the unexpected importance of the diffuse medium for 3C 326 N, in contrast to previous studies. A last-minute comparison of the model to new JWST data obtained in 3C 326 N shows a striking agreement and demonstrates the ability of the model to make accurate predictions. This framework opens new prospects for the prediction and interpretation of extragalactic observations, in particular in the context of JWST observations.

Plasticization-assisted slow crack growth modeling of high-density polyethylene

The existing crack layer model can theoretically predict the slow crack growth behavior of high-density polyethylene. However, it can only be applied to oxidative environments causing chemical degradation. Most oil and gas field components, such as pressurized pipes, are subjected to hydrocarbon exposures, leading to a plasticized material response, i.e., shear yielding instead of crazing. Therefore, the effect of such sorptive media diffusion on the slow crack growth behavior and lifespans tf should be understood. In this work and for the first time, a novel crack layer model is developed that can simulate the diffusion-assisted slow crack growth behavior of plasticized high-density polyethylene. The proposed model was validated by comparing its prediction with experimental results and by conducting a sensitivity study on several input parameters. Using the proposed model, the reported plasticization results were reconstructed successfully including the SCG rate with R2 = 0.95. This study expands the applicability of the crack layer model for the reliability assessment of polyethylene pipes under various environmental conditions, including plasticizers.

Aiming the water transport issues of anion exchange membrane fuel cells by introducing hydrophobic carbon nanotube diffusion layer

The gas diffusion layer (GDL) enhances the transport efficiency of reaction gases and facilitates the removal of accumulated liquid water, thereby improving water management in anion exchange membrane fuel cells (AEMFCs). Carbon nanotubes (CNTs) are recognized as one of the promising materials to optimize mass transport within GDLs. In this study, we successfully synthesized an abundance of CNTs on the surface of commercial gas diffusion media. The as-prepared CNT layer exhibits exceptionally high hydrophobic properties and forms a hierarchically hydrophobic structure combined with the gas diffusion media, effectively enhancing the mass transfer of the membrane electrode assembly (MEA) and reducing ohmic impedance. Under supersaturation conditions, the power density of the MEA containing CNTs reaches 1031.7 mW/cm2, significantly higher than the 760.64 mW/cm2 observed for the commercial GDL. Further testing demonstrates that the MEA containing CNTs exhibits a limiting current density of 2507.4 mA/cm2, which is much superior to the benchmark MEA with the commercial GDL (1591 mA/cm2). Electrochemical impedance spectroscopy analysis reveals that the mass transfer resistance of MEAs with CNTs is lower than that of MEAs with the commercial GDL. More importantly, the phase-field modeling is performed to simulate the transport of the liquid water in the hierarchical GDL.

Diffusion in biological media: a comprehensive numerical-analytical study via surface analysis and diffusivities calculation

The study of diffusion in biological materials is crucial for fields like food science, engineering, and pharmaceuticals. Research that combines numerical and analytical methods is needed to better understand diffusive phenomena across various dimensions and under variable boundary conditions within food matrices. This study aims to bridge this gap by examining the diffusion of substances through biological materials analytically and numerically, calculating diffusivity and conducting surface analysis. The research proposes a process for sweetening Bing-type cherries (Prunus avium) using sucrose/xylitol solutions and a staining technique utilising erythrosine and red gardenia at varying concentrations (119, 238 and 357 ppm) and temperatures (40, 50 and 60 °C). Given the fruit's epidermis resistance, the effective diffusivities of skin were inferior to those in flesh. Temperature and concentration synergise in enhancing diffusion coefficients and dye penetration within the food matrix (357 ppm and 60 °C). Red gardenia displayed significant temperature-dependent variation (p = 0.001), whereas erythrosine dye remained stable by temperature changes (p > 0.05). Gardenia's effective diffusivities in cherry flesh and skin, at 357 ppm and 60 °C, 3.89E−08 and 6.61E−09 m2/s, respectively, significantly differed from those obtained at lower temperatures and concentrations. The results highlight the temperature-concentration impacts on mass transfer calculations for food colouring processes and preservation methodologies.

Laboratory infrared spectra and fragmentation chemistry of sulfur allotropes

Sulfur is one of six life-essential elements, but its path from interstellar clouds to planets and their atmospheres is not well known. Astronomical observations in dense clouds have so far been able to trace only 1 percent of cosmic sulfur, in the form of gas phase molecules and volatile ices, with the missing sulfur expected to be locked in a currently unidentified form. The high sulfur abundances inferred in icy and rocky solar system bodies indicate that an efficient pathway must exist from volatile atomic sulfur in the diffuse interstellar medium to some form of refractory sulfur. One hypothesis is the formation of sulfur allotropes, particularly of the stable S8. However, experimental information about sulfur allotropes under astrochemically relevant conditions, needed to constrain their abundance, is lacking. Here, we report the laboratory far-infrared spectra of sulfur allotropes and examine their fragmentation pathways. The spectra, including that of cold, isolated S8 with three bands at 53.5, 41.3 and 21.1 µm, form a benchmark for computational modelling, which show a near-perfect match with the experiments. The experimental fragmentation pathways of sulfur allotropes, key information for astrochemical formation/destruction models, evidence a facile fragmentation of S8. These findings suggest the presence of sulfur allotropes distributions in interstellar space or in the atmosphere of planets, dependent on the environmental conditions.

Enhance Ethanol Sensing Performance of Fe-Doped Tetragonal SnO2 Films on Glass Substrate with a Proposed Mathematical Model for Diffusion in Porous Media.

This research enhances ethanol sensing with Fe-doped tetragonal SnO2 films on glass, improving gas sensor reliability and sensitivity. The primary objective was to improve the sensitivity and operational efficiency of SnO2 sensors through Fe doping. The SnO2 sensors were synthesized using a flexible and adaptable method that allows for precise doping control, with energy-dispersive X-ray spectroscopy (EDX) confirming homogeneous Fe distribution within the SnO2 matrix. A morphological analysis showed a surface structure ideal for gas sensing. The results demonstrated significant improvement in ethanol response (1 to 20 ppm) and lower temperatures compared to undoped SnO2 sensors. The Fe-doped sensors exhibited higher sensitivity, enabling the detection of low ethanol concentrations and showing rapid response and recovery times. These findings suggest that Fe doping enhances the interaction between ethanol molecules and the sensor surface, improving performance. A mathematical model based on diffusion in porous media was employed to further analyze and optimize sensor performance. The model considers the diffusion of ethanol molecules through the porous SnO2 matrix, considering factors such as surface morphology and doping concentration. Additionally, the choice of electrode material plays a crucial role in extending the sensor's lifespan, highlighting the importance of material selection in sensor design.

Development of optimized resveratrol/piperine-loaded phytosomal nanocomplex for isoproterenol-induced myocardial infarction treatment

Cardiovascular disease is a significant and ever-growing concern, causing high morbidity and mortality worldwide. Conventional therapy is often very precarious and requires long-term usage. Several phytochemicals, including Resveratrol (RSV) and Piperine (PIP), possess significant cardioprotection and may be restrained in clinical settings due to inadequate pharmacokinetic properties. Therefore, this study strives to develop an optimized RSV phytosomes (RSVP) and RSV phytosomes co-loaded with PIP (RPP) via solvent evaporation method using Box-Behnken design to enhance the pharmacokinetic properties in isoproterenol-induced myocardial infarction (MI). The optimized particle size (20.976 ± 0.39 and 176.53 ± 0.88 nm), zeta potential (−33.33 ± 1.5 and −48.7 ± 1.6 mV), drug content (84.57 ± 0.9 and 87.16 ± 0.6%), and %EE (70.56 ± 0.7 and 67.60 ± 0.57%) of the prepared RSVP and RPP, respectively demonstrated enhanced solubility and control release in diffusion media. The oral administration of optimized RSVP and RPP in myocardial infarction-induced rats exhibited significant (p < 0.001) improvement in heart rate, ECG, biomarker, anti-oxidant levels, and no inflammation than pure RSV. The pharmacokinetic assessment on healthy Wistar rats exhibited prolonged circulation (>24 h) of RSVP and RPP compared to free drug/s. The enhanced ability of RSVP and RPP to penetrate bio-membranes and enter the systemic circulation renders them a more promising strategy for mitigating MI.

A novel strategy to improve the corrosion resistance of SiCf/SiC composites in high-temperature combustion environments by cooperation of self-healing SiBCN and high-stability Yb2Si2O7

How to improve the resistance to water-oxygen-salt corrosion of SiCf/SiC composites is vital to their long-term service in the advanced aero-engines or gas turbines. SiCf/SiC-SiBCN-Yb2Si2O7 (SSY) self-healing composites were exposed to combustion environments at 1200–1350 °C for a long time up to 100 h. The dissolution of solid Yb2Si2O7 into low-viscosity glassy oxides derived mainly from oxidation of SiBCN leads to the formation of stable Yb2Si2O7-contianing multi-phase silicate which can inhibit the diffusion of corrosive media and alleviate corrosive damage of composites. After corrosion in H2O/O2/Na2SO4 at 1200 °C and 1350 °C, the strength retention rates of SSY are 96 % and 88 %, respectively, (6.4 ± 0.9)% higher than those of SiCf/SiC-SiBCN (SS), due to the good cooperative protective effect of SiBCN-Yb2Si2O7. However, the insufficient dissolution of Yb2Si2O7 causes the formation of plenty of solid/liquid interfaces conductive to the diffusion of corrosive media in H2O/O2 at 1200 °C and 1350 °C. As a result, the retention rates of flexural strengths of SSY are 100 % and 91 %, respectively, (2.5 ± 0.5)% lower than those of SS.

Antibacterial and Biofilm Removal Strategies Based on Micro/Nanomotors in the Biomedical Field.

Bacterial infection, which can trigger varieties of diseases and tens of thousands of deaths each year, poses serious threats to human health. Particularly, the new dilemma caused by biofilms is gradually becoming a severe and tough problem in the biomedical field. Thus, the strategies to address these problems are considered an urgent task at present. Micro/nanomotors (MNMs), also named micro/nanoscale robots, are mostly driven by chemical energy or external field, exhibiting strong diffusion and self-propulsion in the liquid media, which has the potential for antibacterial applications. In particular, when MNMs are assembled in swarms, they become robust and efficient for biofilm removal. However, there is a lack of comprehensive review discussing the progress in this aspect. Bearing it in mind and based on our own research experience in this regard, the studies on MNMs driven by different mechanisms orchestrated for antibacterial activity and biofilm removal are timely and concisely summarized and discussed in this work, aiming to show the advantages of MNMs brought to this field. In addition, an outlook was proposed, hoping to provide the fundamental guidance for future development in this area.

Shocks in the warm neutral medium. II. Origin of neutral carbon at high pressure

Ultraviolet lines of neutral carbon observed in absorption in the local diffuse interstellar medium (ISM) have long revealed that a substantial fraction of the mass of the gas lies at a thermal pressure one to three orders of magnitude above that of the bulk of the ISM. In this paper, we propose that this enigmatic component originates from shocks propagating at intermediate ($V_S &gt; 30$ and high velocities ($V_S in the warm neutral medium (WNM). Shock waves irradiated by the standard interstellar radiation field (ISRF) are modelled using the Paris-Durham shock code designed to follow the dynamical, thermal, and chemical evolutions of shocks with velocities up to 500 Each observed line of sight is decomposed into a high-pressure component and a low-pressure component. The column density of carbon at high pressure is confronted with the model predictions to derive the number of shocks along the line of sight and their total dissipation rate. Phase transition shocks spontaneously lead to the presence of high-pressure gas in the diffuse ISM and are found to naturally produce neutral carbon with excitation conditions and line widths in remarkable agreement with the observations. The amounts of neutral carbon at high pressure detected over a sample of 89 lines of sight imply a dissipation rate of mechanical energy with a median of sim $3 and a dispersion of about a factor of three. This distribution of the dissipation rate weakly depends on the detailed characteristics of shocks as long as they propagate at velocities between 30 and 200 in a medium with a pre-shock density of $ and a transverse magnetic field of $B_0 3$ mu G. We not only show that this solution is consistent with a scenario of shocks driven by supernova remnants (SNRs) but also that this scenario is in fact unavoidable. Any line of sight in the observational sample is bound to intercept SNRs, which are mostly distributed in the spiral arms of the Milky Way and expanding in the diffuse ionised and neutral phases of the Galaxy. Surprisingly, the range of dissipation rate derived here, in events that probably drive turbulence in the WNM, is found to be comparable to the distribution of the kinetic energy transfer rate of the turbulent cascade derived from the observations of CO in the cold neutral medium (CNM). This work reveals a possible direct tracer of the mechanisms by which mechanical energy is injected into the ISM. It also suggests that a still unknown connection exists between the amount of energy dissipated during the injection process in the WNM and that used to feed interstellar turbulence and the turbulent cascade observed in the CNM.

Phase-lag and diffusion in porous thermoelastic micropolar media with initial pressure and rotational forces affected by modified Ohm’s law and gravity

Phase-lag and diffusion in porous thermoelastic micropolar media with initial pressure and rotational forces affected by modified Ohm’s law and gravity

Darboux and generalized Darboux transformations for the fractional integrable derivative nonlinear Schrödinger equation

Analytical methods provide crucial mathematical insights into the stable solitary waves hidden in nonlinear phenomena. The nonlinear Schrödinger (NLS) equation is one of the most important typical integrable soliton models. From a mathematical perspective, the essence of the celebrated derivative NLS (DNLS) equation’s difference from the classical NLS equation lies in its cubic potential being differentiated once by the spatial variable and multiplied by the imaginary unit, which leads to the former having some characteristics that the latter cannot have. This paper extends the DNLS equation to the fractional integrable case with conformable derivative operators, and uses Darboux transformations (DTs) and generalized DT (GDT) to solve it exactly. Specifically, Lax pairs generating the fractional DNLS equation are first given. Based on the given Lax pairs, then the n-fold DTs and GDT for the fractional DNLS equation are derived. Some special exact solutions of the fractional DNLS equation are further obtained by employing the derived n-fold DTs and GDT. Finally, several novel space–time structures and dynamical evolutions of the obtained exact solutions are analyzed. This paper reveals through the DT and GDT methods that the double power-law fractional orders in the exact solutions of the fractional DNLS equation can be used to dominate the variable velocity propagation and anomalous diffusion in fractional dimensional media at different geometric scales.

Time-fractional fabric to quantify non-Fickian diffusion in porous media: New vision from previous studies

The diffusion kinetics of different substances in porous media is a priori described by the second Fick's law of diffusion. Herein, we demonstrate that such a description sometimes yields erratic results. In contrast, the time-fractional diffusion equation is found to reflect the diffusion kinetics in the case of Fick's law failure. The analytic solutions of the time-fractional diffusion equation are based on the Mittag–Leffler function. At large times, it is shown that the utilization of the approximation of the Mittag–Leffler function for the large values of its argument for the description of the experimental data gives almost the same results as those obtained using the Mittag–Leffler function itself. The time-fractional diffusion is applied on a phenomenological basis. Nevertheless, we speculate that the deviations from Fick's law may be governed by strong adsorption of the diffusing species inside the small micropores of a porous material.

Bayesian inference methodology to characterize the dust emissivity at far-infrared and submillimeter frequencies

ABSTRACT We present a Bayesian inference method to characterize the dust emission properties using the well-known dust-${\rm H\,{\small I}}$ correlation in the diffuse interstellar medium at Planck frequencies $\nu \ge 217$ GHz. We use the Galactic ${\rm H\,{\small I}}$ map from the Galactic All-Sky Survey (GASS) as a template to trace the Galactic dust emission. We jointly infer the pixel-dependent dust emissivity and the zero level present in the Planck intensity maps. We use the Hamiltonian Monte Carlo technique to sample the high-dimensional parameter space ($D \sim 10^3$). We demonstrate that the methodology leads to unbiased recovery of dust emissivity per pixel and the zero level when applied to realistic Planck sky simulations over a 6300 $\rm {deg}^2$ area around the Southern Galactic pole. As an application on data, we analyse the Planck intensity map at 353 GHz to jointly infer the pixel-dependent dust emissivity at $N_{\rm side}=32$ resolution (1.8° pixel size) and the global offset. We find that the spatially varying dust emissivity has a mean of 0.031 MJy sr$^{-1}$$(10^{20} \, \mathrm{cm^{-2}})^{-1}$ and $1\sigma$ standard deviation of 0.007 MJy sr$^{-1}$$(10^{20} \, \mathrm{cm^{-2}})^{-1}$. The mean dust emissivity increases monotonically with increasing mean ${\rm H\,{\small I}}$ column density. We find that the inferred global offset is consistent with the expected level of cosmic infrared background (CIB) monopole added to the Planck data at 353 GHz. This method is useful in studying the line-of-sight variations of dust spectral energy distribution in the multiphase interstellar medium.

Anomalous and ultraslow diffusion of a particle driven by power-law-correlated and distributed-order noises

We study the generalised Langevin equation (GLE) approach to anomalous diffusion for a harmonic oscillator and a free particle driven by different forms of internal noises, such as power-law-correlated and distributed-order noises that fulfil generalised versions of the fluctuation-dissipation theorem. The mean squared displacement and the normalised displacement correlation function are derived for the different forms of the friction memory kernel. The corresponding overdamped GLEs for these cases are also investigated. It is shown that such models can be used to describe anomalous diffusion in complex media, giving rise to subdiffusion, superdiffusion, ultraslow diffusion, strong anomaly, and other complex diffusive behaviours.