Articles de revues : « Asymptotic emergence »

1

Percacci, Roberto, et Gian Paolo Vacca. « Asymptotic safety, emergence and minimal length ». Classical and Quantum Gravity 27, n^o 24 (29 novembre 2010) : 245026. http://dx.doi.org/10.1088/0264-9381/27/24/245026.

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Kumar, Ranjith R., S. Rahul, Y. R. Kartik et Sujit Sarkar. « Emergence of parity time symmetric quantum critical phenomena ». Journal of Physics : Conference Series 2038, n^o 1 (1 octobre 2021) : 012016. http://dx.doi.org/10.1088/1742-6596/2038/1/012016.

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Abstract Emergence of different interesting and insightful phenomena at different length scale is the heart of quantum many-body system. We show that the physics of parity-time (PT) symmetry is one new addition to them. We show explicitly that the emergence of different topological excitation at different length scale for the PT symmetry system through the analysis of renormalization group (RG) flow lines. We observe that the higher order RG process favour the emergence of asymptotic freedom like behaviour and also show the effect of strong correlation on the emergent phases. Interestingly, the asymptotic freedom like behaviour is favoured by PT symmetry phase of the system. Moreover, we also derive the scaling relation for the couplings in RG equations. These findings can be tested experimentally in ultracold atoms.

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Gross, D. D. « The discovery of asymptotic freedom and the emergence of QCD ». Uspekhi Fizicheskih Nauk 175, n^o 12 (2005) : 1306. http://dx.doi.org/10.3367/ufnr.0175.200512e.1306.

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GROSS, DAVID J. « THE DISCOVERY OF ASYMPTOTIC FREEDOM AND THE EMERGENCE OF QCD ». International Journal of Modern Physics A 20, n^o 25 (10 octobre 2005) : 5717–40. http://dx.doi.org/10.1142/s0217751x05029009.

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Gross, D. J. « The discovery of asymptotic freedom and the emergence of QCD ». Proceedings of the National Academy of Sciences 102, n^o 26 (20 juin 2005) : 9099–108. http://dx.doi.org/10.1073/pnas.0503831102.

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Cho, Junghee, Seung-Yeal Ha, Feimin Huang, Chunyin Jin et Dongnam Ko. « Emergence of bi-cluster flocking for the Cucker–Smale model ». Mathematical Models and Methods in Applied Sciences 26, n^o 06 (12 avril 2016) : 1191–218. http://dx.doi.org/10.1142/s0218202516500287.

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We present the mathematical analysis of bi-cluster flocking phenomenon for the short-ranged Cucker–Smale model with some well-prepared initial data. For this, we derive a system of differential inequalities for the functionals measuring the local spatial and velocity fluctuations and differences of local velocity averages, and then estimate the upper bound of spatial fluctuations and the lower bound of the difference between local velocity averages. We explicitly present an admissible class of initial configurations leading to the asymptotic emergence of bi-cluster flocking phenomenon. Unlike global flocking (a mono-cluster flocking configuration in velocity), where the convergence rate is always exponential, the asymptotic convergence to bi-cluster flocking configurations is affected by the far-field decay rate of communication weights so that it can be algebraic.

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Ha, Seung-Yeal, Kiseop Lee et Doron Levy. « Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system ». Communications in Mathematical Sciences 7, n^o 2 (2009) : 453–69. http://dx.doi.org/10.4310/cms.2009.v7.n2.a9.

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NINK, ANDREAS, et MARTIN REUTER. « ON QUANTUM GRAVITY, ASYMPTOTIC SAFETY AND PARAMAGNETIC DOMINANCE ». International Journal of Modern Physics D 22, n^o 05 (avril 2013) : 1330008. http://dx.doi.org/10.1142/s0218271813300085.

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We discuss the conceptual ideas underlying the Asymptotic Safety approach to the nonperturbative renormalization of gravity. By now numerous functional renormalization group (RG) studies predict the existence of a suitable nontrivial ultraviolet (UV) fixed point. We use an analogy to elementary magnetic systems to uncover the physical mechanism behind the emergence of this fixed point. It is seen to result from the dominance of certain paramagnetic-type interactions over diamagnetic ones. Furthermore, the spacetimes of quantum Einstein gravity (QEG) behave like a polarizable medium with a "paramagnetic" response to external perturbations. Similarities with the vacuum state of Yang–Mills theory are pointed out.

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Gross, David J. « Nobel Lecture : The discovery of asymptotic freedom and the emergence of QCD ». Reviews of Modern Physics 77, n^o 3 (7 septembre 2005) : 837–49. http://dx.doi.org/10.1103/revmodphys.77.837.

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Hernandez, X., et A. J. Lara-D I. « Asymptotic kinematics of globular clusters : The emergence of a Tully–Fisher relation ». Monthly Notices of the Royal Astronomical Society 491, n^o 1 (19 novembre 2019) : 272–80. http://dx.doi.org/10.1093/mnras/stz3038.

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ABSTRACT Using a recent homogeneous sample of 40 high-quality velocity dispersion profiles for Galactic globular clusters, we study the regime of low gravitational acceleration relevant to the outskirts of these systems. We find that a simple empirical profile having a central Gaussian component and a constant large-radius asymptote, σ∞, accurately describes the variety of observed velocity dispersion profiles. We use published population synthesis models, carefully tailored to each individual cluster, to estimate mass-to-light ratios from which total stellar masses, M, are inferred. We obtain a clear scaling, reminiscent of the galactic Tully–Fisher relation of $\sigma _{\infty }[\, \mathrm{km \, s}^{-1}]= 0.084^{+0.075}_{-0.040} (\mathrm{{\it M}/M}_{\odot })^{0.3 \pm 0.051}$, which is interesting to compare to the deep modified Newtonian dynamics (MOND) limit of $\sigma _{\infty } [\mathrm{km \, s}^{-1}]=0.2(\mathrm{{\it M}/M}_{\odot })^{0.25}$. Under a Newtonian interpretation, our results constitute a further restriction on models where initial conditions are crafted to yield the outer flattening observed today. Within a modified gravity scheme, because the globular clusters studied are not isolated objects in the deep MOND regime, the results obtained point towards a modified gravity where the external field effect of MOND does not appear, or is significantly suppressed.

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Yahalom, Asher, Meir Lewkowicz, Jacob Levitan, Gil Elgressy, Lawrence Horwitz et Yossi Ben-Zion. « Uncertainty relation for chaos ». International Journal of Geometric Methods in Modern Physics 12, n^o 09 (octobre 2015) : 1550093. http://dx.doi.org/10.1142/s0219887815500930.

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A necessary condition for the emergence of chaos is given. It is well known that the emergence of chaos requires a positive exponent which entails diverging trajectories. Here we show that this is not enough. An additional necessary condition for the emergence of chaos in the region where the trajectory of the system goes through, is that the product of the maximal positive exponent times, the duration in which the system configuration point stays in the unstable region should exceed unity. We give a theoretical analysis justifying this result and a few examples. We stress that the criterion suggested involves only local exponents and is not concerned with asymptotic defined exponents.

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Shinta, Arundati, Bimono . et Esti Listiari. « MEMBANGUN SITUASI KERJA YANG LEBIH MENYENANGKAN PADA KARYAWAN DENGAN PENGADAAN MINUMAN YANG BERGIZI TINGGI ». Jurnal Psikologi TALENTA 1, n^o 1 (20 septembre 2015) : 45. http://dx.doi.org/10.26858/talenta.v1i1.5226.

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Objective of this research is to verify the relationship between the availability of the free of charge of nutritious drink with the pleasing work situation. The second objective is to verify the relationship between the free of charge of nutritious drink with the pro-environment behavior emergence. Thirty (17 women, 13 men) employees participate in this research. They have consumed free of charge of nutrition drink. This research revealed that the free of charge of the nutrition drink enhance more the work situation, compare to the non-free of charge (chi-square = 7.778, asymptotic significance .005 or p <.01). The second result is that the free of charge of the nutritious drink supports more the pro-environment behavior emergence, compare to the non-free of charge (chi-square = 4.537, asymptotic significance .033 or p<.01). The pro-environment behavior is also sustained by their willingness to bring some household packaging waste.

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Voronkov, Sergey, Pavel Safronov, Alexander Dementiev, Olga Frolova et Tatiana Bugaeva. « ON THE TURBULENCE IN A VISCOUS HEAT-CONDUCTING GAS ». ENVIRONMENT. TECHNOLOGIES. RESOURCES. Proceedings of the International Scientific and Practical Conference 3 (16 juin 2021) : 382–86. http://dx.doi.org/10.17770/etr2021vol3.6527.

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The problem of the emergence of turbulence is one of the unsolved problems of physics and technology of the 20th century. It is noted that in order to understand the emergence of turbulence in a viscous heat-conducting gas, it is necessary to take into account the compressibility of the medium. A definition of turbulence in a viscous heat-conducting gas is given, which is a cyclically repeating process of the emergence and decay of coherent vortex structures described by a vector wave equation. The decay of vortex structures is accompanied by an explosive, asymptotic increase in pressure pulsations, which triggers a new cycle of turbulence generation. The emergence and decay of coherent vortex structures in the boundary layer on a plate and in a round jet is considered.

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HA, SEUNG-YEAL, EUNHEE JEONG, JEONG-HAN KANG et KYUNGKEUN KANG. « EMERGENCE OF MULTI-CLUSTER CONFIGURATIONS FROM ATTRACTIVE AND REPULSIVE INTERACTIONS ». Mathematical Models and Methods in Applied Sciences 22, n^o 08 (28 mai 2012) : 1250013. http://dx.doi.org/10.1142/s0218202512500133.

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We discuss a first-order Cucker–Smale-type consensus model with attractive and repulsive interactions and present upper and lower bound estimates on the number of asymptotic point-clusters depending on the relative ranges of interactions and coupling strength. When the number of agents approaches infinity, we introduce a scalar conservation law with a non-local flux for a macroscopic description. We show that the corresponding conservation law admits a classical solution for sufficiently smooth initial data, which illustrates the shock avoidance effect due to the non-locality of the interactions. We also study the dynamics of special Dirac-Comb-type solutions consisting of two and three point-clusters.

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Lebon, Frédéric, et Raffaella Rizzoni. « On the emergence of adhesion in asymptotic analysis of piecewise linear anisotropic elastic bonded joints ». European Journal of Mechanics - A/Solids 93 (mai 2022) : 104512. http://dx.doi.org/10.1016/j.euromechsol.2022.104512.

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ALEXANDRE, JEAN. « LIFSHITZ-TYPE QUANTUM FIELD THEORIES IN PARTICLE PHYSICS ». International Journal of Modern Physics A 26, n^o 26 (20 octobre 2011) : 4523–41. http://dx.doi.org/10.1142/s0217751x11054656.

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This introduction to Lifshitz-type field theories reviews some of its aspects in Particle Physics. Attractive features of these models are described with different examples, as the improvement of graphs convergence, the introduction of new renormalizable interactions, dynamical mass generation, asymptotic freedom, and other features related to more specific models. On the other hand, problems with the expected emergence of Lorentz symmetry in the IR are discussed, related to the different effective light cones seen by different particles when they interact.

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Liu, Zhisu, Yicheng Liu et Xiao Wang. « Emergence of time‐asymptotic flocking for a general Cucker–Smale‐type model with distributed time delays ». Mathematical Methods in the Applied Sciences 43, n^o 15 (18 juin 2020) : 8657–68. http://dx.doi.org/10.1002/mma.6525.

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Deguchi, Kengo, Philip Hall et Andrew Walton. « The emergence of localized vortex–wave interaction states in plane Couette flow ». Journal of Fluid Mechanics 721 (13 mars 2013) : 58–85. http://dx.doi.org/10.1017/jfm.2013.27.

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AbstractThe recently understood relationship between high-Reynolds-number vortex–wave interaction theory and computationally generated self-sustaining processes provides a possible route to an understanding of some of the underlying structures of fully turbulent flows. Here vortex–wave interaction (VWI) theory is used in the long streamwise wavelength limit to continue the development found at order-one wavelengths by Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). The asymptotic description given reduces the Navier–Stokes equations to the so-called boundary-region equations, for which we find equilibrium states describing the change in the VWI as the wavelength of the wave increases from $O(h)$ to $O(Rh)$, where $R$ is the Reynolds number and $2h$ is the depth of the channel. The reduced equations do not include the streamwise pressure gradient of the perturbation or the effect of streamwise diffusion of the wave–vortex states. The solutions we calculate have an asymptotic error proportional to ${R}^{- 2} $ when compared to the full Navier–Stokes equations. The results found correspond to the minimum drag configuration for VWI states and might therefore be of relevance to the control of turbulent flows. The key feature of the new states discussed here is the thickening of the critical layer structure associated with the wave part of the flow to completely fill the channel, so that the roll part of the flow is driven throughout the flow rather than as in Hall & Sherwin as a stress discontinuity across the critical layer. We identify a critical streamwise wavenumber scaling, which, when approached, causes the flow to localize and take on similarities with computationally generated or experimentally observed turbulent spots. In effect, the identification of this critical wavenumber for a given value of the assumed high Reynolds number fixes a minimum box length necessary for the emergence of localized structures. Whereas nonlinear equilibrium states of the Navier–Stokes equations are thought to form a backbone on which turbulent flows hang, our results suggest that the localized states found here might play a related role for turbulent spots.

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RADKO, TIMOUR. « On the generation of large-scale structures in a homogeneous eddy field ». Journal of Fluid Mechanics 668 (16 novembre 2010) : 76–99. http://dx.doi.org/10.1017/s0022112010004568.

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An analytical theory is developed which illustrates dynamics of the spontaneous generation of large-scale structures in the unforced two-dimensional eddying flows. The eddy field is represented by the closely packed array of standing coherent vortices whose intensity is weakly modulated by the long-wavelength perturbations introduced into the system. The asymptotic multiscale analysis makes it possible to identify instabilities resulting from the positive feedback of the background eddies on large-scale perturbations. Initially, these instabilities amplify at a rate proportional to the square root of their wavenumber. Linear growth is arrested when the amplitude of the long-wavelength perturbations reaches the level of background eddies. The subsequent evolutionary pattern is characterized by the emergence of relatively sharp features in the large-scale streamfunction field – features suggestive of the coherent jets commonly observed in eddying geophysical flows. The proposed solutions differ substantially from their counterparts in forced-dissipative systems, exemplified by the canonical model of Kolmogorov flow. The asymptotic model is successfully tested against numerical simulations.

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Bridges, Thomas J. « Emergence of unsteady dark solitary waves from coalescing spatially periodic patterns ». Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences 468, n^o 2148 (15 août 2012) : 3784–803. http://dx.doi.org/10.1098/rspa.2012.0315.

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A dark solitary wave, in one space dimension and time, is a wave that is bi-asymptotic to a periodic state, with a phase shift, and with localized modulation in between. The most well-known case of dark solitary waves is the exact solution of the defocusing nonlinear Schrödinger equation. In this paper, our interest is in developing a mechanism for the emergence of dark solitary waves in general, and not necessarily integrable, Hamiltonian PDEs. The focus is on the periodic state at infinity as the generator. It is shown that a natural mechanism for the emergence is a transition between one periodic state that is (spatially) elliptic and another one that is (spatially) hyperbolic. It is shown that the emergence is governed by a Korteweg–de Vries (KdV) equation for the perturbation wavenumber on a periodic background. A novelty in the result is that the three coefficients in the KdV equation are determined by the Krein signature of the elliptic periodic orbit, the curvature of the wave action flux and the slope of the wave action, with the last two evaluated at the critical periodic state.

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Zhang, Shan-Shan, Tao Xu, Min Li et Xue-Feng Zhang. « Higher-order algebraic soliton solutions of the Gerdjikov–Ivanov equation : Asymptotic analysis and emergence of rogue waves ». Physica D : Nonlinear Phenomena 432 (avril 2022) : 133128. http://dx.doi.org/10.1016/j.physd.2021.133128.

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MEUNIER, N., et E. SANCHEZ-PALENCIA. « SENSITIVE VERSUS CLASSICAL SINGULAR PERTURBATION PROBLEM VIA FOURIER TRANSFORM ». Mathematical Models and Methods in Applied Sciences 16, n^o 11 (novembre 2006) : 1783–816. http://dx.doi.org/10.1142/s0218202506001716.

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We consider a class of singular perturbation elliptic boundary value problems depending on a parameter ε which are classical for ε > 0 but highly ill-posed for ε = 0 as the boundary condition does not satisfy the Shapiro–Lopatinskii condition. This kind of problems is motivated by certain situations in thin shell theory, but we only deal here with model problems and geometries allowing a Fourier transform treatment. We consider more general loadings and more singular perturbation terms than in previous works on the subject. The asymptotic process exhibits a complexification phenomenon: in some sense, the solution becomes more and more complicated as ε decreases, and the limit does not exist in classical distribution theory (it may only be described in spaces of analytical functionals not enjoying localization properties). This phenomenon is associated with the emergence of the new characteristic parameter |log ε|. Numerical experiments based on a formal asymptotics are presented, exhibiting features which are unusual in classical elliptic equations theory. We also give a Fourier transform treatment of classical singular perturbations in order to exhibit the drastic differences with the present situation.

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GARBA, MICHAEL T., et HORACIO GONZÁLEZ–VÉLEZ. « ASYMPTOTIC PEAK UTILISATION IN HETEROGENEOUS PARALLEL CPU/GPU PIPELINES : A DECENTRALISED QUEUE MONITORING STRATEGY ». Parallel Processing Letters 22, n^o 02 (16 mai 2012) : 1240008. http://dx.doi.org/10.1142/s0129626412400087.

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Widespread heterogeneous parallelism is unavoidable given the emergence of General-Purpose computing on graphics processing units (GPGPU). The characteristics of a Graphics Processing Unit (GPU)—including significant memory transfer latency and complex performance characteristics—demand new approaches to ensuring that all available computational resources are efficiently utilised. This paper considers the simple case of a divisible workload based on widely-used numerical linear algebra routines and the challenges that prevent efficient use of all resources available to a naive SPMD application using the GPU as an accelerator. We suggest a possible queue monitoring strategy that facilitates resource usage with a view to balancing the CPU/GPU utilisation for applications that fit the pipeline parallel architectural pattern on heterogeneous multicore/multi-node CPU and GPU systems. We propose a stochastic allocation technique that may serve as a foundation for heuristic approaches to balancing CPU/GPU workloads.

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Boi, S., A. Mazzino et G. Lacorata. « Explicit expressions for eddy-diffusivity fields and effective large-scale advection in turbulent transport ». Journal of Fluid Mechanics 795 (19 avril 2016) : 524–48. http://dx.doi.org/10.1017/jfm.2016.220.

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Large-scale transport is investigated in terms of new explicit expressions for eddy diffusivities and effective advection obtained from asymptotic perturbative methods. The carrier flow is formed by a large-scale component plus a small-scale contribution mimicking a turbulent flow. The scalar dynamics is observed in its pre-asymptotic regimes (i.e. on scales comparable to those of the large-scale velocity). The resulting eddy diffusivity is thus a tensor field which explicitly depends on the large-scale velocity. Small-scale interactions also cause the emergence of an effective large-scale (compressible) advection field which, as a result of the present study however, turns out to be of negligible importance. Two issues are addressed by means of Lagrangian simulations: quantifying the possible deterioration of the eddy-diffusivity/effective advection description by reducing to zero the spectral gap separating the large-scale velocity component from the small-scale component; comparing the accuracy of our closure against other simple, reasonable, options. Answering these questions is important in view of possible applications of our closure to tracer dispersion in environmental flows.

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Duchemin, Laurent. « Self-focusing of thin liquid jets ». Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences 464, n^o 2089 (23 octobre 2007) : 197–206. http://dx.doi.org/10.1098/rspa.2007.0068.

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The nonlinear evolution of an initially perturbed free surface perpendicularly accelerated, or of an initially flat free surface subject to a perturbed velocity profile, gives rise to the emergence of thin spikes of fluid. We are investigating the long-time evolution of a thin inviscid jet of this kind, subject or not to a body force acting in the direction of the jet itself. A fully nonlinear theory for the long-time evolution of the jet is given. In two dimensions, the curvature of the tip scales like t 3 , where t is time, and the peak undergoes an overshoot in acceleration which evolves like t −5 . In three dimensions, the jet evolves towards an axisymmetric shape, and the curvature and the overshoot in acceleration obey asymptotic laws in t 2 and t −4 , respectively. The asymptotic self-similar shape of the spike is found to be a hyperbola in two dimensions, a hyperboloid in three dimensions. Scaling laws and self-similarity are confronted with two-dimensional computations of the Richtmyer–Meshkov instability.

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Weis, I. Michael, et Luise A. Hermanutz. « The population biology of the arctic dwarf birch, Betula glandulosa : seed rain and the germinable seed bank ». Canadian Journal of Botany 66, n^o 10 (1 octobre 1988) : 2055–61. http://dx.doi.org/10.1139/b88-281.

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The seed rain and seed bank of arctic dwarf birch, Betula glandulosa, were studied at Kuujjuaq, Que., and Tarr Inlet, near Iqaluit, N.W.T. At each site dispersing seeds were captured in sticky traps in three adjacent plots having locally high and low birch densities; soil cores were collected in parallel. Trap data indicate that birch samaras disperse principally during late fall and early spring. The number of samaras dispersed was significantly greater at Kuujjuaq than near Iqaluit and was greater in high- than in low-density areas. Samaras collected at Kuujjuaq were significantly heavier (x = 0.19 mg) than those from Tarr Inlet (x = 0.10 mg). Germination showed an asymptotic exponential weight dependence. From the weight distribution of samaras, we expected germination of 69.7% of samaras from Kuujjuaq. Few viable propagules were found in collections from the Iqaluit area; from their weight distribution 0.38% were expected to germinate. We predicted emergence from soil cores, using seed-trap and germination data, and tested predictions under greenhouse conditions. Observations and predictions agreed for low-density areas. At Kuujjuaq 248 emergences/m2 were predicted and 229 observed; at Iqaluit no emergences were predicted and none observed. In high-density plots at Kuujjuaq 9292 emergences/m2 were predicted and 2164 observed. Corresponding rates for Iqaluit were 2 and 17 emergences/m2, respectively. Differences in seed banks and recruitment indicate differences in the structure, dynamics, and reproductive biology of populations at the two sites.

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Li, Zhuchun, Seung-Yeal Ha et Xiaoping Xue. « Emergent phenomena in an ensemble of Cucker–Smale particles under joint rooted leadership ». Mathematical Models and Methods in Applied Sciences 24, n^o 07 (14 avril 2014) : 1389–419. http://dx.doi.org/10.1142/s0218202514500043.

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We present an emergent flocking estimate in a group of interacting Cucker–Smale particles under the joint rooted leadership via the discrete-time Cucker–Smale model. It is well known that the network topology regulates the emergence of flocking, and the rooted leadership topology is the most general topology with a leader–follower structure. When the network topology satisfies a weaker rooted leadership, in which the union of neighbor graphs on infinite time-blocks is under rooted leadership, we show that the asymptotic flocking can be achieved from some class of initial configurations by generalizing the earlier result of Li and Xue using the (sp) matrix theory in Ref. 36.

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Chaumont, Loïc, et Thi Ngoc Anh Nguyen. « On mutations in the branching model for multitype populations ». Advances in Applied Probability 50, n^o 2 (juin 2018) : 543–64. http://dx.doi.org/10.1017/apr.2018.24.

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AbstractThe forest of mutations associated to a multitype branching forest is obtained by merging together all vertices in each of its clusters and by preserving connections between them. (Here, by cluster, we mean a maximal connected component of the forest in which all vertices have the same type.) We first show that the forest of mutations of any multitype branching forest is itself a branching forest. Then we give its progeny distribution and we describe some of its crucial properties in terms of the initial progeny distribution. We also obtain the limiting behaviour of the number of mutations both when the total number of individuals tends to ∞ and when the number of roots tends to ∞. The continuous-time case is then investigated by considering multitype branching forests with edge lengths. When mutations are nonreversible, we give a representation of their emergence times which allows us to describe the asymptotic behaviour of the latter, under certain conditions on the mutation rates. These results have potential relevance for emergence of mutations in population cells, particularly for genetic evolution of cancer or development of infectious diseases.

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Garcke, Harald, Johannes Kampmann, Andreas Rätz et Matthias Röger. « A coupled surface-Cahn–Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes ». Mathematical Models and Methods in Applied Sciences 26, n^o 06 (12 avril 2016) : 1149–89. http://dx.doi.org/10.1142/s0218202516500275.

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We propose and investigate a model for lipid raft formation and dynamics in biological membranes. The model describes the lipid composition of the membrane and an interaction with cholesterol. To account for cholesterol exchange between cytosol and cell membrane we couple a bulk-diffusion to an evolution equation on the membrane. The latter describes the relaxation dynamics for an energy which takes lipid–phase separation and lipid–cholesterol interaction energy into account. It takes the form of an (extended) Cahn–Hilliard equation. Different laws for the exchange term represent equilibrium and nonequilibrium models. We present a thermodynamic justification, analyze the respective qualitative behavior and derive asymptotic reductions of the model. In particular we present a formal asymptotic expansion near the sharp interface limit, where the membrane is separated into two pure phases of saturated and unsaturated lipids, respectively. Finally we perform numerical simulations and investigate the long-time behavior of the model and its parameter dependence. Both the mathematical analysis and the numerical simulations show the emergence of raft-like structures in the nonequilibrium case whereas in the equilibrium case only macrodomains survive in the long-time evolution.

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HAMED, MOHAMMAD ABU, et EHUD YARIV. « Induced-charge electrokinetic flows about polarizable nano-particles : the thick-Debye-layer limit ». Journal of Fluid Mechanics 627 (25 mai 2009) : 341–60. http://dx.doi.org/10.1017/s0022112009005965.

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Using the standard weak-field approximation, we analyse the steady-state electrokinetic flow about an uncharged ideally polarizable spherical particle for the case of a Debye thickness which is large compared with the particle size. The dimensionless problem is governed by two parameters: β, the applied field magnitude (normalized with the thermal scale), and λ, the Debye thickness (normalized with particle size). The double limit β ≪ 1 and λ ≫ 1 is singular, and the resolution of the flow field requires the use of inner–outer asymptotic expansions in the spirit of Proudman & Pearson (J. Fluid Mech., vol. 2, 1957, p. 237). Two asymptotic limits are identified: the ‘moderately thick’ limit βλ ≪ 1, in which the outer domain is characterized by the Debye thickness, and the ‘super-thick’ limit βλ ≫ 1, in which the outer domain represents the emergence of electro-migration in the leading-order ionic-transport process. The singularity is stronger in the comparable two-dimensional flow about a circular cylinder, where a switchback mechanism in the moderately thick limit modifies the familiar O(β2) leading-order flow to O(β2 ln λ).

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Friedrich, Manuel, Leonard Kreutz et Bernd Schmidt. « Emergence of Rigid Polycrystals from Atomistic Systems with Heitmann–Radin Sticky Disk Energy ». Archive for Rational Mechanics and Analysis 240, n^o 2 (12 mars 2021) : 627–98. http://dx.doi.org/10.1007/s00205-021-01615-w.

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AbstractWe investigate the emergence of rigid polycrystalline structures from atomistic particle systems. The atomic interaction is governed by a suitably normalized pair interaction energy, where the ‘sticky disk’ interaction potential models the atoms as hard spheres that interact when they are tangential. The discrete energy is frame invariant and no underlying reference lattice on the atomistic configurations is assumed. By means of $$\Gamma $$ Γ -convergence, we characterize the asymptotic behavior of configurations with finite surface energy scaling in the infinite particle limit. The effective continuum theory is described in terms of a piecewise constant field delineating the local orientation and micro-translation of the configuration. The limiting energy is local and concentrated on the grain boundaries, that is, on the boundaries of the zones where the underlying microscopic configuration has constant parameters. The corresponding surface energy density depends on the relative orientation of the two grains, their microscopic translation misfit, and the normal to the interface. We further provide a fine analysis of the surface energies at grain boundaries both for vacuum–solid and solid–solid phase transitions. The latter relies fundamentally on a structure result for grain boundaries showing that, due to the extremely brittle setup, interpolating boundary layers near cracks are energetically not favorable.

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Kakin, Polina I., Mikhail A. Reiter, Maria M. Tumakova, Nikolay M. Gulitskiy et Nikolay V. Antonov. « Stirred Kardar-Parisi-Zhang Equation with Quenched Random Noise : Emergence of Induced Nonlinearity ». Universe 8, n^o 2 (26 janvier 2022) : 72. http://dx.doi.org/10.3390/universe8020072.

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We study the stochastic Kardar-Parisi-Zhang equation for kinetic roughening where the time-independent (columnar or spatially quenched) Gaussian random noise f(t,x) is specified by the pair correlation function ⟨f(t,x)f(t′,x′)⟩∝δ(d)(x−x′), d being the dimension of space. The field-theoretic renormalization group analysis shows that the effect of turbulent motion of the environment (modelled by the coupling with the velocity field described by the Kazantsev-Kraichnan statistical ensemble for an incompressible fluid) gives rise to a new nonlinear term, quadratic in the velocity field. It turns out that this “induced” nonlinearity strongly affects the scaling behaviour in several universality classes (types of long-time, large-scale asymptotic regimes) even when the turbulent advection appears irrelevant in itself. Practical calculation of the critical exponents (that determine the universality classes) is performed to the first order of the double expansion in ε=4−d and the velocity exponent ξ (one-loop approximation). As is the case with most “descendants” of the Kardar-Parisi-Zhang model, some relevant fixed points of the renormalization group equations lie in “forbidden zones”, i.e., in those corresponding to negative kinetic coefficients or complex couplings. This persistent phenomenon in stochastic non-equilibrium models requires careful and inventive physical interpretation.

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Sautbekov, Seil S., Sotirios Bourgiotis, Ariadni Chrysostomou et Panayiotis V. Frangos. « A NOVEL ASYMPTOTIC SOLUTION TO THE SOMMERFELD RADIATION PROBLEM : ANALYTIC FIELD EXPRESSIONS AND THE EMERGENCE OF THE SURFACE WAVES ». Progress In Electromagnetics Research M 64 (2018) : 9–22. http://dx.doi.org/10.2528/pierm17082806.

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NAGASAWA, Sumio, et Katsumi YAMADA. « An Asymptotic Regression Curve for Describing the Emergence Pattern of the Azuki Bean Weevil, Callosobruchus chinensis L. (Coleoptera : Bruchidae) ». Applied Entomology and Zoology 23, n^o 2 (1988) : 181–85. http://dx.doi.org/10.1303/aez.23.181.

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Wang, Jing, et Jianqiang Sun. « Two types of scale effects on the nonlinear forced vibration of axially moving nanobeams ». International Journal of Modern Physics B 34, n^o 10 (20 avril 2020) : 2050095. http://dx.doi.org/10.1142/s0217979220500952.

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Various non-classical continuum mechanics models appearing in previous studies cannot perfectly explain the mechanical properties of micro- and nanomaterials. Establishing a reasonable continuum mechanics model that comprehensively reflects the scale effect on material deformation is of great practical significance for objectively explaining the variation law of mechanical properties of micro- and nanomaterials under the combined action of different scale effects. Based on nonlocal strain gradient theory, a new scale-dependent model is proposed for axially moving nanobeams. In this study, an asymptotic expansion is performed using the multiscale time method to obtain the amplitude-frequency response curve of the equilibrium solutions for the forced vibration problem. Afterwards, the effects of various system parameters, especially the scale parameters, on the resonance curve are examined. Finally, the effects of nonlocal parameters and material characteristic length parameters on the amplitude-frequency response curves are investigated through typical numerical examples. The numerical results show that the nonlocal parameters promote the emergence of the main resonance, whereas the material characteristic length parameters suppress the emergence of the main resonance. Moreover, these parameters also affect the response amplitude and the skewness and jumping point of the amplitude-frequency characteristic curve.

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Lucibello, C., et F. Ricci-Tersenghi. « The Statistical Mechanics of Random Set Packing and a Generalization of the Karp-Sipser Algorithm ». International Journal of Statistical Mechanics 2014 (10 mars 2014) : 1–13. http://dx.doi.org/10.1155/2014/136829.

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We analyse the asymptotic behaviour of random instances of the maximum set packing (MSP) optimization problem, also known as maximum matching or maximum strong independent set on hypergraphs. We give an analytic prediction of the MSPs size using the 1RSB cavity method from statistical mechanics of disordered systems. We also propose a heuristic algorithm, a generalization of the celebrated Karp-Sipser one, which allows us to rigorously prove that the replica symmetric cavity method prediction is exact for certain problem ensembles and breaks down when a core survives the leaf removal process. The e-phenomena threshold discovered by Karp and Sipser, marking the onset of core emergence and of replica symmetry breaking, is elegantly generalized to Cs=e/(d-1) for one of the ensembles considered, where d is the size of the sets.

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Ibrahimi, Muhamet, Arda Güçlü, Naide Jahangirov, Mecit Yaman, Oguz Gülseren et Seymur Jahangirov. « Operator Representation and Class Transitions in Elementary Cellular Automata ». Complex Systems 31, n^o 4 (15 décembre 2022) : 415–32. http://dx.doi.org/10.25088/complexsystems.31.4.415.

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We exploit the mirror and complementary symmetries of elementary cellular automata (ECAs) to rewrite their rules in terms of logical operators. The operator representation based on these fundamental symmetries enables us to construct a periodic table of ECAs that maps all unique rules in clusters of similar asymptotic behavior. We also expand the elementary cellular automaton (ECA) dynamics by introducing a parameter that scales the pace with which operators iterate the system. While tuning this parameter continuously, further emergent behavior in ECAs is unveiled as several rules undergo multiple phase transitions between periodic, chaotic and complex (class 4) behavior. This extension provides an environment for studying class transitions and complex behavior in ECAs. Moreover, the emergence of class 4 structures can potentially enlarge the capacity of many ECA rules for universal computation.

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Fang, A., Z. Q. Zhang, Steven G. Louie et C. T. Chan. « Anomalous Anderson localization behaviors in disordered pseudospin systems ». Proceedings of the National Academy of Sciences 114, n^o 16 (4 avril 2017) : 4087–92. http://dx.doi.org/10.1073/pnas.1620313114.

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We discovered unique Anderson localization behaviors of pseudospin systems in a 1D disordered potential. For a pseudospin-1 system, due to the absence of backscattering under normal incidence and the presence of a conical band structure, the wave localization behaviors are entirely different from those of conventional disordered systems. We show that there exists a critical strength of random potential (Wc), which is equal to the incident energy (E), below which the localization length ξ decreases with the random strength W for a fixed incident angle θ. But the localization length drops abruptly to a minimum at W=Wc and rises immediately afterward. The incident angle dependence of the localization length has different asymptotic behaviors in the two regions of random strength, with ξ∝sin−4θ when W<Wc and ξ∝sin−2θ when W>Wc. The existence of a sharp transition at W=Wc is due to the emergence of evanescent waves in the systems when W>Wc. Such localization behavior is unique to pseudospin-1 systems. For pseudospin-1/2 systems, there is also a minimum localization length as randomness increases, but the transition from decreasing to increasing localization length at the minimum is smooth rather than abrupt. In both decreasing and increasing regions, the θ dependence of the localization length has the same asymptotic behavior ξ∝sin−2θ.

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Dong, Jiu-Gang, Seung-Yeal Ha et Doheon Kim. « Emergent behaviors of continuous and discrete thermomechanical Cucker–Smale models on general digraphs ». Mathematical Models and Methods in Applied Sciences 29, n^o 04 (avril 2019) : 589–632. http://dx.doi.org/10.1142/s0218202519400013.

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We present emergent dynamics of continuous and discrete thermomechanical Cucker–Smale (TCS) models equipped with temperature as an extra observable on general digraph. In previous literature, the emergent behaviors of the TCS models were mainly studied on a complete graph, or symmetric connected graphs. Under this symmetric setting, the total momentum is a conserved quantity. This determines the asymptotic velocity and temperature a priori using the initial data only. Moreover, this conservation law plays a crucial role in the flocking analysis based on the elementary [Formula: see text] energy estimates. In this paper, we consider a more general connection topology which is registered by a general digraph, and the weights between particles are given to be inversely proportional to the metric distance between them. Due to this possible symmetry breaking in communication, the total momentum is not a conserved quantity, and this lack of conservation law makes the asymptotic velocity and temperature depend on the whole history of solutions. To circumvent this lack of conservation laws, we instead employ some tools from matrix theory on the scrambling matrices and some detailed analysis on the state-transition matrices. We present two sufficient frameworks for the emergence of mono-cluster flockings on a digraph for the continuous and discrete models. Our sufficient frameworks are given in terms of system parameters and initial data.

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Deppman, Airton, et Evandro Oliveira Andrade-II. « Emergency of Tsallis statistics in fractal networks ». PLOS ONE 16, n^o 9 (29 septembre 2021) : e0257855. http://dx.doi.org/10.1371/journal.pone.0257855.

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Scale-free networks constitute a fast-developing field that has already provided us with important tools to understand natural and social phenomena. From biological systems to environmental modifications, from quantum fields to high energy collisions, or from the number of contacts one person has, on average, to the flux of vehicles in the streets of urban centres, all these complex, non-linear problems are better understood under the light of the scale-free network’s properties. A few mechanisms have been found to explain the emergence of scale invariance in complex networks, and here we discuss a mechanism based on the way information is locally spread among agents in a scale-free network. We show that the correct description of the information dynamics is given in terms of the q-exponential function, with the power-law behaviour arising in the asymptotic limit. This result shows that the best statistical approach to the information dynamics is given by Tsallis Statistics. We discuss the main properties of the information spreading process in the network and analyse the role and behaviour of some of the parameters as the number of agents increases. The different mechanisms for optimization of the information spread are discussed.

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Junior, David R., Luis E. Oxman et Gustavo M. Simões. « From Center-Vortex Ensembles to the Confining Flux Tube ». Universe 7, n^o 8 (21 juillet 2021) : 253. http://dx.doi.org/10.3390/universe7080253.

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In this review, we discuss the present status of the description of confining flux tubes in SU(N) pure Yang–Mills theory in terms of ensembles of percolating center vortices. This is based on three main pillars: modeling in the continuum the ensemble components detected in the lattice, the derivation of effective field representations, and contrasting the associated properties with Monte Carlo lattice results. The integration of the present knowledge about these points is essential to get closer to a unified physical picture for confinement. Here, we shall emphasize the last advances, which point to the importance of including the non-oriented center-vortex component and non-Abelian degrees of freedom when modeling the center-vortex ensemble measure. These inputs are responsible for the emergence of topological solitons and the possibility of accommodating the asymptotic scaling properties of the confining string tension.

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Yang, Huizhen, et Di Wang. « The Integrated Design of Underwater Interceptor Guidance Control Based on Adaptive Global Sliding Mode ». Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 36, n^o 3 (juin 2018) : 502–8. http://dx.doi.org/10.1051/jnwpu/20183630502.

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The underwater interceptor’s target have the characteristics of small size, fast speed and strong maneuverability, which requires the underwater interceptor guidance system to have fast and stable response capability. Aiming at the design requirement, this paper proposes a global sliding mode controller of integrated guidance and control(IGC). The integrated guidance and control mathematical model of the underwater interceptor’s lateral channel is established, and the global sliding mode control based on the adaptive regulation law is designed aiming to the problem of uncertainty about the emergence of an integrated system for the target maneuver. The asymptotic stability is proved by applying the Lyapunov theorem. Then the high-gain continuing method is adopted to restrain the buffeting for the IGC system. The proposed controller compensates the uncertain information and improves the robustness and fastness of the system. The simulation results show the effectiveness.

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Ackerman, Phillip L., et Christopher E. Sager. « Cognitive/Intellectual Abilities as Predictors of Skilled Performance : Answering the Which, When, and How Questions ». Proceedings of the Human Factors Society Annual Meeting 32, n^o 16 (octobre 1988) : 1006–10. http://dx.doi.org/10.1177/154193128803201603.

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Recently, there has been a re-emergence of interest in the cognitive ability determinants of individual differences in skill acquisition and skilled performance. First we review some basic characteristics of individual differences in skill acquisition. We next consider the current evidence for the emergent “task-specific” factor, a matter that may have important implications for the utility of ability measures as predictors of individual differences in asymptotic skilled performance. We also review two major factors in determining the relations between abilities and individual differences in skill acquisition, advances in theory and the enlargement of the data base for discussion of the topic. We address these factors, in the context of a discussion of “which” abilities predict individual differences in skilled performance, “when” such predictors are maximally effective, and “how” abilities and information processing demands interact to determine ability-performance associations.

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RIORDAN, OLIVER. « Thek-Core and Branching Processes ». Combinatorics, Probability and Computing 17, n^o 1 (janvier 2008) : 111–36. http://dx.doi.org/10.1017/s0963548307008589.

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Thek-coreof a graphGis the maximal subgraph ofGhaving minimum degree at leastk. In 1996, Pittel, Spencer and Wormald found the threshold λcfor the emergence of a non-trivialk-core in the random graphG(n, λ/n), and the asymptotic size of thek-core above the threshold. We give a new proof of this result using a local coupling of the graph to a suitable branching process. This proof extends to a general model of inhomogeneous random graphs with independence between the edges. As an example, we study thek-core in a certain power-law or ‘scale-free’ graph with a parameterccontrolling the overall density of edges. For eachk≥ 3, we find the threshold value ofcat which thek-core emerges, and the fraction of vertices in thek-core whencis ϵ above the threshold. In contrast toG(n, λ/n), this fraction tends to 0 as ϵ→0.

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Rahman, A., T. K. James, J. M. Mellsop et N. Grbavac. « Predicting broadleaf weed populations in maize from the soil seedbank ». New Zealand Plant Protection 57 (1 août 2004) : 281–85. http://dx.doi.org/10.30843/nzpp.2004.57.6973.

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Investigations over three years studied the relationship between weed seeds in the soil seedbank and the resultant populations of broadleaf weeds in maize fields Plots were protected from preemergence herbicide after which soil samples (100 mm) were collected and weed seeds therein enumerated Emerged weed seedlings in field plots were counted over the following 8 weeks Up to 67 broadleaf weed species were identified although not all were found at every site and some were specific to a region or soil type On average 2182 of the seed in the soil seedbank emerged For most weeds strong linear relationships were noted between seedling numbers and the seed numbers in the soil although for some like white clover (Trifolium repens) only a weak relationship was observed In the case of fathen (Chenopodium album) which had the largest seedbank there was evidence of asymptotic behaviour with seedling emergence levelling off at high seed numbers

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Meldi, Marcello, Hugo Lejemble et Pierre Sagaut. « On the emergence of non-classical decay regimes in multiscale/fractal generated isotropic turbulence ». Journal of Fluid Mechanics 756 (5 septembre 2014) : 816–43. http://dx.doi.org/10.1017/jfm.2014.476.

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AbstractThe present paper addresses the issue of finding key parameters that may lead to the occurrence of non-classical decay regimes for fractal/multiscale generated grid turbulence. To this aim, a database of numerical simulations has been generated by the use of the eddy-damped quasi-normal Markovian (EDQNM) model. The turbulence production in the wake of the fractal/multiscale grid is modelled via a turbulence production term based on the forcing term developed for direct numerical simulations (DNS) purposes and the dynamics of self-similar wakes. The sensitivity of the numerical results to the simulation parameters has been investigated successively. The analysis is based on the observation of both the time evolution of the turbulent energy spectrum $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}E(k,t)$ and the decay of the flow statistical quantities, such as the turbulent kinetic energy $\mathcal{K}(t)$ and the energy dissipation rate $\varepsilon (t)$. A satisfactory agreement with existing experimental data published by different research teams is observed. In particular, it is observed that the key parameter that governs the nature of turbulence decay is $\alpha ={d/U_{\infty }}\, {(\varepsilon (0)/\mathcal{K}(0))}={d/L(0)} \, {(\sqrt{\mathcal{K}(0)}/U_{\infty })}$ (with $d$ the bar diameter and $U_{\infty }$ the upstream uniform velocity), which measures the ratio of the time scale largest grid bar $d/U_{\infty }$ to the turbulent time scale $\mathcal{K}(0)/\varepsilon (0)$. Two asymptotic behaviours for $\alpha \rightarrow + \infty $ and $\alpha \rightarrow 0$ are identified: (i) a fast algebraic decay law regime for rapidly decaying production terms, due to strongly modified initial kinetic energy spectrum and (ii) a real exponential decay regime associated with strong, very slowly decaying production terms. The present observations are in full agreement with conclusions drawn from recent fractal grid experiments, and it provides a physical scenario for occurrence of anomalous decay regime which encompasses previous hypotheses.

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Marani, Marco, Gabriel G. Katul, William K. Pan et Anthony J. Parolari. « Intensity and frequency of extreme novel epidemics ». Proceedings of the National Academy of Sciences 118, n^o 35 (23 août 2021) : e2105482118. http://dx.doi.org/10.1073/pnas.2105482118.

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Observational knowledge of the epidemic intensity, defined as the number of deaths divided by global population and epidemic duration, and of the rate of emergence of infectious disease outbreaks is necessary to test theory and models and to inform public health risk assessment by quantifying the probability of extreme pandemics such as COVID-19. Despite its significance, assembling and analyzing a comprehensive global historical record spanning a variety of diseases remains an unexplored task. A global dataset of historical epidemics from 1600 to present is here compiled and examined using novel statistical methods to estimate the yearly probability of occurrence of extreme epidemics. Historical observations covering four orders of magnitude of epidemic intensity follow a common probability distribution with a slowly decaying power-law tail (generalized Pareto distribution, asymptotic exponent = −0.71). The yearly number of epidemics varies ninefold and shows systematic trends. Yearly occurrence probabilities of extreme epidemics, Py, vary widely: Py of an event with the intensity of the “Spanish influenza” (1918 to 1920) varies between 0.27 and 1.9% from 1600 to present, while its mean recurrence time today is 400 y (95% CI: 332 to 489 y). The slow decay of probability with epidemic intensity implies that extreme epidemics are relatively likely, a property previously undetected due to short observational records and stationary analysis methods. Using recent estimates of the rate of increase in disease emergence from zoonotic reservoirs associated with environmental change, we estimate that the yearly probability of occurrence of extreme epidemics can increase up to threefold in the coming decades.

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Ryan, Matthew R., Sandra Wayman, Christopher J. Pelzer, Caitlin A. Peterson, Uriel D. Menalled et Terry J. Rose. « Winter Wheat (Triticum aestivum L.) Tolerance to Mulch ». Plants 10, n^o 10 (29 septembre 2021) : 2047. http://dx.doi.org/10.3390/plants10102047.

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Mulch from cover crops can effectively suppress weeds in organic corn (Zea mays L.) and soybean (Glycine max L.) as part of cover crop-based rotational no-till systems, but little is known about the feasibility of using mulch to suppress weeds in organic winter small grain crops. A field experiment was conducted in central NY, USA, to quantify winter wheat (Triticum aestivum L.) seedling emergence, weed and crop biomass production, and wheat grain yield across a gradient of mulch biomass. Winter wheat seedling density showed an asymptotic relationship with mulch biomass, with no effect at low rates and a gradual decrease from moderate to high rates of mulch. Selective suppression of weed biomass but not wheat biomass was observed, and wheat grain yield was not reduced at the highest level of mulch (9000 kg ha−1). Results indicate that organic winter wheat can be no-till planted in systems that use mulch for weed suppression. Future research should explore wheat tolerance to mulch under different conditions, and the potential of no-till planting wheat directly into rolled-crimped cover crops.

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Radko, Timour. « On the generation of large-scale eddy-driven patterns : the average eddy model ». Journal of Fluid Mechanics 809 (9 novembre 2016) : 316–44. http://dx.doi.org/10.1017/jfm.2016.668.

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A theoretical model is developed which illustrates the dynamics of the spontaneous generation of large-scale structures in baroclinically unstable eddying flows. Techniques of asymptotic multiscale analysis are used to identify instabilities resulting from the positive feedback of the background eddies on large-scale perturbations. The novelty of the proposed approach lies in the choice of a dynamically consistent time-dependent background eddy field, which is taken from simulations of baroclinic instability in the Phillips two-layer system. The resulting solutions differ considerably from those of traditional multiscale models, in which the background eddy field is represented by steady analytical patterns. The present formulation makes it possible to (i) test the multiscale theory against the corresponding numerical simulations, (ii) unambiguously interpret the key physical processes at play and (iii) rationalize the emergence of large-scale patterns for certain background parameters. While the proposed approach to multiscale modelling is illustrated on a particular example of the Phillips baroclinic instability model, it is our belief that the presented technique is readily adaptable to a wide range of applications.

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Pudjaprasetya, S. R. « Modelling and simulation of waves in three-layer porous media ». Nonlinear Processes in Geophysics 20, n^o 6 (25 novembre 2013) : 1023–30. http://dx.doi.org/10.5194/npg-20-1023-2013.

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Abstract. The propagation of gravity waves in an emerged three-layer porous medium is considered in this paper. Based on the assumption that the flow can be described by Darcy's Law, an asymptotic theory is developed for small-amplitude long waves. This leads to a weakly nonlinear Boussinesq-type diffusion equation for the wave height, with coefficients dependent on the conductivities and depths of each layer. In the limit of equal conductivities of all layers, the equation reduces to the single-layer result recorded in the literature. The model equations are numerically integrated in the case of an incident monochromatic wave hitting the layers. The results exhibit dissipation and also a downstream net height rise at infinity. Wave transmission coefficient in three-layer porous media with conductivity of mangrove is discussed. Numerically, propagation of an initial solitary wave through a porous medium shows the emergence of wave reflection and transmission that both evolve as permanent waves. Additionally we examine the impact of a solitary gravity wave on a porous medium breakwater.

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