Allometric scaling laws of metabolism

One of the most pervasive laws in biology is the allometric scaling, whereby a biological variable Y is related to the mass M of the organism by a power law, Y=Y₀M^b, where b is the so-called allometric exponent. The origin of these power laws is still a matter of dispute mainly because biological laws, in general, do not follow from physical ones in a simple manner. In this work, we review the interspecific allometry of metabolic rates, where recent progress in the understanding of the interplay between geometrical, physical and biological constraints has been achieved.

For many years, it was a universal belief that the basal metabolic rate (BMR) of all organisms is described by Kleiber's law (allometric exponent b=3/4). A few years ago, a theoretical basis for this law was proposed, based on a resource distribution network common to all organisms. Nevertheless, the 3/4-law has been questioned recently. First, there is an ongoing debate as to whether the empirical value of b is 3/4 or 2/3, or even nonuniversal. Second, some mathematical and conceptual errors were found these network models, weakening the proposed theoretical arguments. Another pertinent observation is that the maximal aerobically sustained metabolic rate of endotherms scales with an exponent larger than that of BMR. Here we present a critical discussion of the theoretical models proposed to explain the scaling of metabolic rates, and compare the predicted exponents with a review of the experimental literature. Our main conclusion is that although there is not a universal exponent, it should be possible to develop a unified theory for the common origin of the allometric scaling laws of metabolism.     

Analytic calculation of scaling dimensions: Tricritical hard squares and critical hard hexagons

The finite-size corrections, central chargesc, and scaling dimensionsx of tricritical hard squares and critical hard hexagons are calculated analytically. This is achieved by solving the special functional equation or inversion identity satisfied by the commuting row transfer matrices of these lattice models at criticality. The results are expressed in terms of Rogers dilogarithms. For tricritical hard squares we obtainc=7/10,x=3/40, 1/5, 7/8, 6/5 and for hard hexagons we obtainc=4/5,x=2/15, 4/5, 17/15, 4/3, 9/5, in accord with the predictions of conformal and modular invariance.     

A theoretical extraction scheme of transport information based on exclusion models

In order to explore how to extract more transport information from current fluctuation,a theoretical extraction scheme is presented in a single barrier structure based on exclusion models,which include counter-flows model and tunnel model.The first four cumulants of these two exclusion models are computed in a single barrier structure,and their characteristics are obtained.A scheme with the help of the first three cumulants is devised to check a transport process to follow the counter-flows model,the tunnel model or neither of them.Time series generated by Monte Carlo techniques is adopted to validate the abstraction procedure,and the result is reasonable.     

Dynamical properties of a dissipative discontinuous map: A scaling investigation

The effects of dissipation on the scaling properties of nonlinear discontinuous maps are investigated by analyzing the behavior of the average squared action 〈I²〉$〈I^2〉$ as a function of the n-th iteration of the map as well as the parameters K and γ  , controlling nonlinearity and dissipation, respectively. We concentrate our efforts to study the case where the nonlinearity is large; i.e., K?1$K?1$. In this regime and for large initial action _I0?K$I_0?K$, we prove that dissipation produces an exponential decay for the average action 〈I〉$〈I〉$. Also, for _I0≅0$I_0\cong 0$, we describe the behavior of 〈I²〉$〈I^2〉$ using a scaling function and analytically obtain critical exponents which are used to overlap different curves of 〈I²〉$〈I^2〉$ onto a universal plot. We complete our study with the analysis of the scaling properties of the deviation around the average action ω.     

Mathematical models to characterize early epidemic growth: A review

There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014–2015 Ebola epidemic in West Africa.     

Numerical models in simulating wire-plate electrostatic precipitators: A review

This paper attempts to review the most important works on numerical simulation of processes in electrostatic precipitators published so far. Only the wire-plate configuration is considered, although the discharge electrode may have different geometries: smooth cylinder, barbed wire of different shape or helical electrode. Different mathematical models and numerical algorithms for gas flow, electric field, corona discharge and particle transport have been compared. The discussion is focused on coupling between different phenomena. A continuous progress has been shown from early works published about 30 years ago, which dealt with much idealized models of the problem, to recent publications, where the numerical predictions show close agreement with the experimental data.     

Matrix models of RNA folding with external interactions: A review

The matrix model of (simplified) RNA folding with an external linear interaction in the action of the partition function is reviewed. The important results for structure combinatorics of the model are discussed and analysed in terms of the already existing models.     

Stimulation of bone repair with ultrasound: A review of the possible mechanic effects

In vivo and in vitro studies have demonstrated the positive role that ultrasound can play in the enhancement of fracture healing or in the reactivation of a failed healing process. We review the several options available for the use of ultrasound in this context, either to induce a direct physical effect (LIPUS, shock waves), to deliver bioactive molecules such as growth factors, or to transfect cells with osteogenic plasmids; with a main focus on LIPUS (or Low Intensity Pulsed Ultrasound) as it is the most widespread and studied technique. The biological response to LIPUS is complex as numerous cell types respond to this stimulus involving several pathways. Known to-date mechanotransduction pathways involved in cell responses include MAPK and other kinases signaling pathways, gap-junctional intercellular communication, up-regulation and clustering of integrins, involvement of the COX-2/PGE2, iNOS/NO pathways and activation of ATI mechanoreceptor. The mechanisms by which ultrasound can trigger these effects remain intriguing. Possible mechanisms include direct and indirect mechanical effects like acoustic radiation force, acoustic streaming, and propagation of surface waves, fluid-flow induced circulation and redistribution of nutrients, oxygen and signaling molecules. Effects caused by the transformation of acoustic wave energy into heat can usually be neglected, but heating of the transducer may have a potential impact on the stimulation in some in-vitro systems, depending on the coupling conditions. Cavitation cannot occur at the pressure levels delivered by LIPUS. In-vitro studies, although not appropriate to identify the overall biological effects, are of great interest to study specific mechanisms of action. The diversity of current experimental set-ups however renders this analysis very complex, as phenomena such as transducer heating, inhomogeneities of the sound intensity in the near field, resonances in the transmission and reflection through the culture dish walls and the formation of standing waves will greatly affect the local type and amplitude of the stimulus exerted on the cells. A future engineering challenge is therefore the design of dedicated experimental set-ups, in which the different mechanical phenomena induced by ultrasound can be controlled. This is a prerequisite to evaluate the biological effects of the different phenomena with respect to particular parameters, like intensity, frequency, or duty cycle. By relating the variations of these parameters to the induced physical effects and to the biological responses, it will become possible to derive an ‘acoustic dose’ and propose a quantification and cross-calibration of the different experimental systems. Improvements in bone healing management will probably also come from a combination of ultrasound with a ‘biologic’ components, e.g. growth factors, scaffolds, gene therapies, or drug delivery vehicles, the effects of which being potentiated by the ultrasound.     

A theoretical study on various models for the domain boundaries in epitaxial GaN films

Various domain boundaries that are found in epitaxial Wurtzite GaN films were studied by molecular dynamics simulation. The Ewald summation algorithm and Keating potential model are adopted to calculate the long-range Coulomb interaction and the short-range bonding force in the semiconductor system, respectively. The research results show that the domain formation energies of (100) and (110) boundaries are significantly different. The latter ones have general quite higher formation energies than the formers. The like-atom (i.e. atoms of the same kind) bonding domain boundaries (LABDB) have higher formation energies than their counterparts of unlike-atom (i.e. atoms of different kinds) bonding domain boundaries (UABDB) in all GaN (100) and (110) interfaces. The UABDB structures are all stable while most of the LABDB are unstable. The advantage and the limitation of Keating potential model in Molecular Dynamics simulation for covalent crystal are discussed. Received: 7 April 1999 / Accepted: 1 November 1999 / Published online: 8 March 2000     

A brief review of continuous models for ionic solutions: the Poisson-Boltzmann and related theories

The Poisson–Boltzmann (PB) theory is one of the most important theoretical models describing charged systems continuously. However, it suffers from neglecting ion correlations, which hinders its applicability to more general charged systems other than extremely dilute ones. Therefore, some modified versions of the PB theory are developed to effectively include ion correlations. Focused on their applications to ionic solutions, the original PB theory and its variances, including the field-theoretic approach, the correlation-enhanced PB model, the Outhwaite–Bhuiyan modified PB theory and the mean field theories, are briefly reviewed in this paper with the diagnosis of their advantages and limitations.     

Mathematical models for dengue fever epidemiology: A 10-year systematic review

Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading.Mathematical models describing dengue fever epidemiological dynamics are found back from 1970. Dengue fever is a viral mosquito-borne infection caused by four antigenically related but distinct serotypes (DENV-1 to DENV-4). With 2.5 billion people at risk of acquiring the infection, it is a major international public health concern. Although most of the cases are asymptomatic or mild, the disease immunological response is complex, with severe disease linked to the antibody-dependent enhancement (ADE) - a disease augmentation phenomenon where pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection. Here, we present a 10-year systematic review on mathematical models for dengue fever epidemiology. Specifically, we review multi-strain frameworks describing host-to-host and vector-host transmission models and within-host models describing viral replication and the respective immune response.Following a detailed literature search in standard scientific databases, different mathematical models in terms of their scope, analytical approach and structural form, including model validation and parameter estimation using empirical data, are described and analyzed.Aiming to identify a consensus on infectious diseases modeling aspects that can contribute to public health authorities for disease control, we revise the current understanding of epidemiological and immunological factors influencing the transmission dynamics of dengue. This review provide insights on general features to be considered to model aspects of real-world public health problems, such as the current epidemiological scenario we are living in.     

受激散射过程理论模型的发展与应用

在激光间接驱动的惯性约束聚变（ICF）中,高强度激光与低密度等离子体发生相互作用,会激发两种受激散射过程：受激布里渊散射和受激拉曼散射。它们会损失激光能量、破坏辐射场对称性、产生超热电子,从而危害聚变点火过程。因此,理解受激散射的物理过程并找到抑制其发展的有效方法,是ICF研究中重点关注的问题。介绍了中国激光聚变研究团队为研究受激散射过程而发展的多个理论模型,以及这些模型在实验数据分析中的具体应用。这些理论模型与实验研究一起,为提升受激散射过程的物理理解发挥了重要作用。     

A theoretical investigation of adsorbate-induced surface relaxation effects using cluster models: Al on Si(111)

Differently sized cluster calculations are used to investigate theoretically the preferred adsorption site for an Al adatom on the Si(111) surface. By performing partial geometry optimizations at the Hartree-Fock level on AlSi_n subclusters around the site of interest we find significant Al adatom-induced surface relaxation effects distorting the Si atoms from their bulk lattice positions. The largest relaxation effects take place at the T₄ site resulting in Al adsorption at the T₄ site to be 5 kcal/mol more stable than at the H₃ site and considerably more stable than adsorption at the T₁ site. However, we only have confidence in this result after performing for the T₄ site a partial geometry optimization on the AlSi₅ subcluster in the AlSi₂₆H₂₄ cluster and by including appropriate correlation corrections.     

A new Monte Carlo simulation for two models of self-avoiding lattice trees in two dimensions

By means of a new Monte Carlo sampling of a grand canonical ensemble, we verify universality for the critical exponents and of two models of lattice trees constrained to be self-avoiding on sites or on bonds. The attrition constants are also obtained. This algorithm, a generalization of that recently proposed by Berretti and Sokal for random walks, appears to optimize the critical slowing down in the scaling region. Systematic and statistical errors are carefully estimated.     

The theoretical analysis of the lattice hydrodynamic models for traffic flow theory

The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but also connected with the microscopic car following model closely. The modified Korteweg-de Vries (mKdV) equation related to the density wave in a congested traffic region has been derived near the critical point since Nagatani first proposed it. But the Korteweg-de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail for the car following model. We devote ourselves to obtaining the KdV equation from the original lattice hydrodynamic models and the KdV soliton solution to describe the traffic jam. Especially, we obtain the general soliton solution of the KdV equation and the mKdV equation. We review several lattice hydrodynamic models, which were proposed recently. We compare the modified models and carry out some analysis. Numerical simulations are conducted to demonstrate the nonlinear analysis results.