Diffusion System Research Articles

High spatial resolution diffuse optical tomography based on cross-correlation of chaotic light.

A diffuse optical tomography system with chaotic laser is proposed for the three-dimensional optical phantom. The high signal-to-noise ratio is beneficial to improve the spatial resolution of diffuse optical tomography. It is essential to drive the chaotic laser as the incident light into the optical phantom. The transmitted light emitted from phantom as the detection light and a part of the incident light as the reference light to carry out cross-correlation analysis. The high-density source-detector configuration in parallel plate structure is designed for detecting targets in the phantom. The propagation of chaotic laser in the phantom is studied theoretically and experimentally based on the diffusion equation. Image reconstruction is achieved by the cross-correlation analysis of chaotic laser and the Newton-Raphson nonlinear algorithm. The performance of the proposed system has been assessed by reconstruction localization accuracy and contrast-noise-ratio. The results show that the spatial resolution of the proposed system can reach 1.5 mm and the localization error is less than 1 mm.

Spatiotemporal control over self-assembly of supramolecular hydrogels through reaction–diffusion

Supramolecular self-assembly is ubiquitous in living system and is usually controlled to proceed in time and space through sophisticated reaction–diffusion processes, underpinning various vital cellular functions. In this contribution, we demonstrate how spatiotemporal self-assembly of supramolecular hydrogels can be realized through a simple reaction–diffusion-mediated transient transduction of pH signal. In the reaction–diffusion system, a relatively faster diffusion of acid followed by delayed enzymatic production and diffusion of base from the opposite site enables a transient transduction of pH signal in the substrate. By coupling such reaction–diffusion system with pH-sensitive gelators, dynamic supramolecular hydrogels with tunable lifetimes are formed at defined locations. The hydrogel fibers show interesting dynamic growing behaviors under the regulation of transient pH signal, reminiscent of their biological counterpart. We further demonstrate a proof-of-concept application of the developed methodology for dynamic information encoding in a soft substrate. We envision that this work may provide a potent approach to enable transient transduction of various chemical signals for the construction of new colloidal materials with the capability to evolve their structures and functionalities in time and space.

Weak convergence and stability of functional diffusion systems with singularly perturbed regime switching

This paper focuses on a class of functional diffusion systems with singularly perturbed regime switching, where the modulating Markov chain has a large state space and undergoes weak and strong interactions. By using the martingale method and weak convergence, this paper shows that the underlying system will weakly converge to a limit system, which is simpler than the original system. For a class of integro-differential diffusion system with singularly perturbed regime switching, as a class of special functional diffusion system, this paper demonstrates that if the limit system is moment exponentially stable, the original system with singular perturbation is also moment exponentially stable under suitable conditions. This result is interesting since the limit system is always simpler. Finally, an example is given to illustrate this result.

Initial non-invasive in vivo sensing of the lung using time domain diffuse optics

The in vivo diagnosis and monitoring of pulmonary disorders (caused for example by emphysema, Covid-19, immature lung tissue in infants) could be effectively supported by the non-invasive sensing of the lung through light. With this purpose, we investigated the feasibility of probing the lung by means of time-resolved diffuse optics, leveraging the increased depth (a few centimeters) attained by photons collected after prolonged propagation time (a few nanoseconds). We present an initial study that includes measurements performed on 5 healthy volunteers during a breathing protocol, using a time-resolved broadband diffuse optical spectroscopy system. Those measurements were carried out across the spectral range of 600–1100 nm at a source-detector distance of 3 cm, and at 820 nm over a longer distance (7–9 cm). The preliminary analysis of the in vivo data with a simplified homogeneous model revealed a maximum probing depth of 2.6–3.9 cm, suitable for reaching the lung. Furthermore, we observed variations in signal associated with respiration, particularly evident at long photon propagation times. However, challenges stemming from both intra- and inter-subject variability, along with inconsistencies potentially arising from conflicting scattering and absorption effects on the collected signal, hindered a clear interpretation. Aspects that require further investigation for a more comprehensive understanding are outlined.

Antimicrobial susceptibility of bacterial clinical specimens isolated from Al-Sader Teaching Hospital in Basra-Iraq

Antibiotic resistance is a global health concern that requires multiple efforts to establish proper preventive and curative programs. This study aimed to assess the antibiotic susceptibility profiles of commonly isolated bacteria at Al-Sader Teaching Hospital, Basra-Iraq. A total of 234 clinical specimens were collected from urine, skin infections, and blood. The bacterial isolates were initially identified using standard microbiological methods, and the identification of the four most common isolates was confirmed by PCR technique using species-specific primers (malB for Escherichia coli, rpoB for Klebsiella pneumonia, OprL for Pseudomonas aeruginosa, and mecA for methicillin resistant Staphylococcus aureus). The identified bacteria were subjected to disc diffusion and VITEK2 system to test the antibiotic susceptibility. E. coli was the most prevalent in urine (51.25%), followed by S. aureus (15%), while S. aureus (31.25%) and P. aeruginosa (30.20%) were more prevalent in skin infections. S. aureus (31.57%) and E. coli (26.31%) were predominant in the blood samples. The Antibiotic susceptibility pattern of Gram-negative isolates revealed high resistance to Cefoxitin (90%), Aztreonam (87%), Ceftriaxone (87%), Piperacillin/tazobactam (85%), and Amoxicillin/clavulanic acid (85%). S. aureus showed high resistance to Cefoxitin (93%), Oxacillin (89.58), and Methicillin (91%), whereas, the highest sensitivity was recorded for Colistin (100%), Rifampin (93%), Amikacin (87%), and Meropenem (76%). A high level of multidrug-resistance strains was detected among Gram negative bacteria (76%) and S. aureus (56%). The current study provides valuable insights into the distribution of pathogenic bacteria and their antibiotic resistance patterns in different clinical samples, contributing to improved treatment strategies and infection control measures.

Sliding mode control for the stabilization of fractional heat equations subject to boundary uncertainty

By adopting the sliding mode control (SMC) and the generalized Lyapunov method, the boundary feedback stabilization issue is studied for the fractional diffusion system subject to boundary control matched disturbance. The classical sliding surface and the fractional integral sliding function are constructed and sliding mode controllers are designed respectively to realize the Mittag-Leffler (M-L) stabilization of the considered system. The controller based on the newly-introduced fractional integral sliding function not only helps to relax the constraints on the disturbance but also realizes the same stabilization effect as that of the classical one. The well-posedness result of the solution is also obtained for discontinuous fractional heat equations. Besides, a numerical experiment validates the theoretical outcomes.

A reaction–diffusion vector-borne disease model with incubation period in almost periodic environments

To study the multiple effects of seasonal fluctuations, spatial heterogeneity and extrinsic incubation period on vector-borne disease transmission, a nonlocal almost periodic reaction–diffusion model of vector-borne diseases is proposed and studied. We first give a characterization of the upper Lyapunov exponent λ∗ for a class of linear almost periodic reaction–diffusion systems with time delay, and provide a numerical scheme to compute it. Then we show that λ∗ is a threshold value determining the uniform persistence and extinction of our model. Specifically, the disease will die out when λ∗<0, while the disease is uniformly persistent when λ∗>0. Some numerical simulations finally are presented to verify our theoretical results, and to investigate the effects of diffusion rates, extrinsic incubation period and spatial heterogeneity on disease transmission.

Twisted moiré conductive thermal metasurface

Extensive investigations on the moiré magic angle in twisted bilayer graphene have unlocked the emerging field—twistronics. Recently, its optics analogue, namely opto-twistronics, further expands the potential universal applicability of twistronics. However, since heat diffusion neither possesses the dispersion like photons nor carries the band structure as electrons, the real magic angle in electrons or photons is ill-defined for heat diffusion, making it elusive to understand or design any thermal analogue of magic angle. Here, we introduce and experimentally validate the twisted thermotics in a twisted diffusion system by judiciously tailoring thermal coupling, in which twisting an analog thermal magic angle would result in the function switching from cloaking to concentration. Our work provides insights for the tunable heat diffusion control, and opens up an unexpected branch for twistronics -- twisted thermotics, paving the way towards field manipulation in twisted configurations including but not limited to fluids.

Gastro-entero-pancreatic neuroendocrine neoplasms (GEP-NENs) - Current literature review of diagnostics and therapy. What has changed in the management?

&lt;b&gt;Introduction:&lt;/b&gt; Gastro-entero-pancreatic neuroendocrine neoplasms (GEP-NENs) are malignancies originating from cells of the diffuse endocrine system. They are rare and localize in the upper and lower parts of the gastrointestinal tract and in the pancreas. Despite such a varied location, GEP-NENs are considered a common group of neoplasms due to the fact of their similar morphology and ability to secrete peptide hormones and biologically active amines. They are associated with clinical manifestations specific to the substances produced by a particular neoplasm. The classification of GEP-NENs is constantly systematized and updated based on their differentiation and grading. The development of available diagnostic and treatment methods for these tumors has made significant progress over the past 10 years and is still ongoing.&lt;b&gt;Aim:&lt;/b&gt; In the following paper, we review the diagnostics and treatment of GEP-NENs, taking into account the latest molecular, immunological, or gene-based methods. Imaging methods using markers for receptors allow for high diagnostic sensitivity&lt;b&gt;Methods:&lt;/b&gt; Medical databases were searched for the latest information. The authors also sought confirmation of the content of a particular publication in another publications, so as to present the most reliable information possible.&lt;b&gt;Results:&lt;/b&gt; Research results revealed that the diagnostics and treatment of GEP-NENs have significantly advanced in recent years. Surgical interventions, especially minimally invasive techniques, have shown efficacy in treating GEP-NENs, with specific therapies such as somatostatin analogs, chemotherapy, and peptide receptor radionuclide therapy demonstrating promising outcomes. The evolution of diagnostic methods, including imaging techniques and biomarker testing, has contributed to improved patient care and prognosis.&lt;b&gt;Conclusions:&lt;/b&gt; The increasing incidence of GEP-NENs is attributed to enhanced diagnostic capabilities rather than a rise in population prevalence. The study emphasizes the importance of ongoing research to identify specific markers for early detection and targeted therapies to further enhance the effectiveness of treating these rare and heterogeneous malignancies. The findings suggest a positive trajectory in the management of GEP-NENs, with future prospects focused on personalized and targeted treatment approaches.

Intermittent boundary control for fixed-time stability of reaction–diffusion systems

This work is a pilot effort to investigate the fixed-time stability (FxTS) of reaction–diffusion systems under aperiodically intermittent boundary control (AIBC). The average control rate and a new Lyapunov function are proposed to overcome the challenges of handling the FxTS of reaction–diffusion systems with AIBC. Moreover, the proposed method is applicable to the study of finite-time stability and exponential stability of reaction–diffusion systems under AIBC. Based on the Wirtinger’s inequality and the Lyapunov method, a FxTS criterion for a reaction–diffusion system with AIBC is given. Finally, two examples are discussed along with the simulated results to verify the effectiveness of the proposed method.

Numerical analysis of light-controlled drug delivery systems

In this paper, we solve a non-linear reaction–diffusion system with Dirichlet–Neumann mixed boundary conditions using a finite difference method (FDM) in space and the implicit midpoint method in time. This type of system appears, e.g., in the mathematical modeling of light-controlled drug delivery. One of the key results of this paper is the proof that the method has superconvergence second-order in space in a discrete H1-norm and optimal second-order convergence in time in a discrete L2-norm. Our result relies on the direct analysis of a suitable error equation, avoiding the classic construction of consistency plus stability implies convergence. One advantage of such an analysis technique is the establishment of the method’s non-linear stability in an elegant way. Numerical examples support the theoretical convergence result.

Identification with an anti-system party undermines diffuse political support: The case of Alternative for Germany and trust in the Federal Constitutional Court

The rise of the far right is increasingly raising the question of whether partisanship can have negative consequences for democracy. While issues such as partisan bias and affective polarization have been extensively researched, little is known about the relationship between identification with anti-system parties and diffuse system support. I address this gap by introducing a novel indicator and utilising the GESIS panel dataset, which tracks the rise of a new party, ”Alternative for Germany” (AfD) from 2013, when the party was founded, to 2017, when the AfD, now transformed into a right-wing populist and anti-system party, entered the federal parliament for the first time. Employing a panel fixed effects design, I demonstrate that identification with ”Alternative for Germany” reduces trust in the Federal Constitutional Court by a considerable margin. These findings are robust across various alternative specifications, suggesting that the effects of anti-system party identification should not be dismissed.

Arrhenius law for interacting diffusive systems.

Finding the mean time it takes for a particle to escape from a metastable state due to thermal fluctuations is a fundamental problem in physics, chemistry, and biology. Here, we consider the escape rate of interacting diffusive particles, from a deep potential trap within the framework of the macroscopic fluctuation theory-a nonequilibrium hydrodynamic theory. For systems without excluded volume, our investigation reveals adherence to the well-established Arrhenius law. However, in the presence of excluded volume, a universality class emerges, fundamentally altering the escape rate. Remarkably, the modified escape rate within this universality class is independent of the interactions at play. The universality class, demonstrating the importance of excluded volume effects, may bring insights to the interpretation of escape processes in the realm of chemical physics.

A variational PDNet network using a learning reaction–diffusion equation

Due to their high performance in modeling and forecasting a large amount of real-world complex phenomena, deep convolutional neural networks have received a great deal of attention over the past ten years. It has been extensively utilized in several recent vision problems, such as image denoising and deblurring. By incorporating recent developments in learning-based nonlinear diffusion models and highlighting the connection between partial differential equations (PDEs) and networks, especially residual networks, we propose a flexible learning reaction–diffusion system with spatially computed convolution kernels. This trained PDE is employed to prevent the low-level features from deteriorating, which is needed for tasks involving denoising. In fact, we introduce an improved network architecture for a denoising network entitled VPDNet through an optimal control problem. More precisely, the network architecture is governed by an explicit Euler discretization of a reaction–diffusion system. We give the main algorithm to identify the kernel parameters using the Alternating Direction Method of Multipliers (ADMM) combined with a Primal–Dual algorithm. Finally, numerical simulations are provided with appropriate comparisons to demonstrate the efficiency of the elaborated network.

Global existence for nonlocal quasilinear diffusion systems in nonisotropic nondivergence form

AbstractWe consider the quasilinear diffusion problem of for an open set , , for , and any . Here, denotes an operator which may involve the distributional Riesz fractional gradient of order , with , the classical gradient or/and nonlocal derivatives , with . We show global existence results for various quasilinear diffusion systems in nondivergence form for linear elliptic operators , including classical elliptic systems, anisotropic fractional equations and systems, and anisotropic local and nonlocal operators of the following type: for coercive, invertible matrices and suitable vectorial functions .

Observation of non-Hermitian skin effect in thermal diffusion

The paradigm shift of Hermitian systems into the non-Hermitian regime profoundly modifies inherent property of the topological systems, leading to various unprecedented effects such as the non-Hermitian skin effect (NHSE). In the past decade, the NHSE has been demonstrated in quantum, optical and acoustic systems. Beside those wave systems, the NHSE in diffusive systems has not yet been observed, despite recent abundant advances in the study of topological thermal diffusion. In this work, we design a thermal diffusion lattice based on a modified Su-Schrieffer-Heeger model and demonstrate the diffusive NHSE. In the proposed model, the asymmetric temperature field coupling inside each unit cell can be judiciously realized by appropriate configurations of structural parameters. We find that the temperature fields trend to concentrate toward the target boundary which is robust against initial excitation conditions. We thus experimentally demonstrated the NHSE in thermal diffusion and verified its robustness against various defects. Our work provides a platform for exploration of non-Hermitian physics in the diffusive systems, which has important applications in efficient heat collection, highly sensitive thermal sensing and others.

Global asymptotic stability of endemic equilibria and stability of traveling waves for a diffusive SIR epidemic model with logistic growth

AbstractThis paper deals with the asymptotic behavior of solutions for the diffusive epidemic model with logistic growth. In the first part, we consider the initial boundary value problem on the bounded domain and derive the stabilization of the solutions of the reaction–diffusion system to a constant equilibrium. In the second part, we consider the initial value problem on $${\mathbb {R}},$$ R , and derive the stability of forced waves under certain perturbations of a class of initial data.

Multi-wavelength multi-distance diffuse correlation spectroscopy system for assessment of premature infants' cerebral hemodynamics.

Infants born at an extremely low gestational age (ELGA, < 29 weeks) are at an increased risk of intraventricular hemorrhage (IVH), and there is a need for standalone, safe, easy-to-use tools for monitoring cerebral hemodynamics. We have built a multi-wavelength multi-distance diffuse correlation spectroscopy device (MW-MD-DCS), which utilizes time-multiplexed, long-coherence lasers at 785, 808, and 853 nm, to simultaneously quantify the index of cerebral blood flow (CBFi) and the hemoglobin oxygen saturation (SO2). We show characterization data on liquid phantoms and demonstrate the system performance on the forearm of healthy adults, as well as clinical data obtained on two preterm infants.

Weakly nonlinear analysis of a two-species non-local advection–diffusion system

Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection–diffusion model with nonlocal advection terms describing the species movements generated by inter-species interactions. We use linear analysis to assess the stability of the constant steady state, then weakly nonlinear analysis to recover the shape and stability of non-homogeneous solutions. Since the system arises from a conservation law, the resulting amplitude equations consist of a Ginzburg–Landau equation coupled with an equation for the zero mode. In particular, this means that supercritical branches from the Ginzburg–Landau equation need not be stable. Indeed, we find that, depending on the parameters, bifurcations can be subcritical (always unstable), stable supercritical, or unstable supercritical. We show numerically that, when small amplitude patterns are unstable, the system exhibits large amplitude patterns and hysteresis, even in supercritical regimes. Finally, we construct bifurcation diagrams by combining our analysis with a previous study of the minimizers of the associated energy functional. Through this approach we reveal parameter regions in which stable small amplitude patterns coexist with strongly modulated solutions.

Limitations and generalizations of the first order kinetics reaction expression for modeling diffusion-driven exchange: Implications on NMR exchange measurements.

The study and modeling of water exchange in complex media using different applications of diffusion and relaxation magnetic resonance (MR) have been of interest in recent years. Most models attempt to describe this process using a first order kinetics expression, which is appropriate to describe chemical exchange; however, it may not be suitable to describe diffusion-driven exchange since it has no direct relationship to diffusion dynamics of water molecules. In this paper, these limitations are addressed through a more general exchange expression that does consider such important properties. This exchange fraction expression features a multi-exponential recovery at short times and a mono-exponential decay at long times, both of which are not captured by the first order kinetics expression. Furthermore, simplified exchange expressions containing partial information of the analyzed system's diffusion and relaxation processes and geometry are proposed, which can potentially be employed in already established estimation protocols. Finally, exchange fractions estimated from simulated MR data and derived here were compared, showing qualitative similarities but quantitative differences, suggesting that the features of the derived exchange fraction in this paper can be partially recovered by employing an existing estimation framework.