Resistivity at-bit (RAB) images and pressure cores reveal that gas-hydrates morphology in the clay-rich sediment varies from complex vein structures (grain-displacing) to invisible pore-filling material. The sizes of grain-displacing gas-hydrates vary from thin veins of a few microns in width to nodules of tens of centimetres or even meters in diameter. There is no quantitative treatment of grain-displacing morphology (vein structure) of gas-hydrates in literature. But saturation of gas-hydrates, estimated on assumption of pore-filling morphology, certainly misleads for fractured fine grained sediments. First time, we apply the differential **effective** **medium** **theory** to incorporate the grain-displacing (veins or fractures) morphology and estimate gas-hydrates saturation from velocities observed in the fractured Gas-hydrates reservoir.

The sequence adopted in this paper is as follows. For the sake of completeness, we start by writing the equivalent resistance (or conductance) of a network comprised of identical resistors forming an infinitely large regular ordered lattice. Because Kirchhoff’s laws on networks are expressed in terms of a Laplacian matrix, it is useful to solve this problem using Green Function (GF) methods. Indeed, writing it in terms of GF becomes extremely convenient when disorder is included since there is a vast body of knowledge on solving Laplacian-like equations[20] for disordered matrices[21, 22]. We then present the **effective** **medium** **theory** (EMT) that allows us to express the problem of calculating the conductance of a inhomogeneous disordered network in terms of an ordered regular network that has a homogeneous resistance[23]. Without any fitting parameter, we are able to demonstrate that this closed-form expression for the conductance provides an excellent match both with simulations and with experimental results. We conclude by illustrating how this approach can be useful in the study of NWNs as well as in other disordered materials.

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We have compared the velocity of traveling waves obtained by numerical simulations in heterogeneous ex- citable media with the predictions of an **effective** **medium** **theory**. The **effective** **medium** **theory** for reaction- diffusion systems predicts the value of the **effective** diffusion coefficient, which can be calculated from Eq. (5). This quantity permits the calculation of an **effective** velocity of the traveling waves which can be directly compared with the traveling wave obtained by numerical simulations in heterogeneous excitable media. The comparison of the **effective** **medium** **theory** with simulations shows a good agreement for large diffusion co- efficients D 1 and D 2 and small size of the domain of phases 1 and 2. To calculate the velocity we need the

In electromagnetic materials characterization, it is well known that the Maxwell-Garnett (MG) **effective** **medium** **theory** predicts the bulk **effective** permittivity of a composite in terms of the permittivities of the inclusion and host materials [7, 8]. The prediction can be quite accurate especially for the cases of low volume fractions of the inclusion inside the composites, such as the system of photonic crystals and functional fluids [9–12]. In the long wavelength regime, the electromagnetic properties of such composites are similar to homogeneous materials with the permittivity that can be tuned readily via the volume fraction of the inclusions, and can give rise to the realization of controllable dielectrics or even present the extraordinary electromagnetic properties [13, 14].

The method to evaluate density while using these tech- niques is generally based on **effective** **medium** **theory** [22– 24], in which wood is regarded as a mixture of pores (air in the cell lumina) and wood substance (cell wall) [3, 11] and responds to electromagnetic excitation as if it were homo- geneous [23]. This **theory**, however, has a lower wavelength limit and the following rule of thumb is often employed [23]: ‘‘the size of an inclusion in the mixture must not exceed a tenth of the wavelength in the **effective** **medium**’’. In gen- eral, wood has many pores of transverse sectional sizes ranging from about 10 to 200 lm, and thereby the lower wavelength limit for wood is to be about 100–2000 lm or 0.15–3 THz in frequency. Therefore, to correctly evaluate Part of this report was presented at the 72nd annual meeting of the

Abstract. The claim for multistandard operating handsets of small physical size as well as the ever increasing demand for higher data rates require new broadband operating an- tennas. Because of the widespread use of especially planar broadband antennas a lot of factors influencing the character- istic antenna parameters have to be regarded. Furthermore, aspects regarding the electromagnetic compatibility inside the handheld as well as the protection of biological systems, e.g. the user of a mobilephone, have to be payed attention to. An electromagnetic structure which allows for protection by means of shielding as well as enhances the antennas ef- ficiency by providing unique electromagnetic properties are the so called Sievenpiper High Impedance Surfaces (HIS) in- vented by Sievenpiper (1999). This paper will present the **theory** and the well known design equations for those struc- tures. An investigation by means of simulation tools and measurement setups will be done to approve the accuracy of the theoretical results. Here measurement results of the impedance and radiation properties of a planar log.-per. four- arm antenna equiped in conjunction with a fabricated proto- type Sievenpiper HIS will be presented.

single crystal is weak, and thus the anisotropy of ice poly- crystals is even weaker. On the other hand, ice along bore- holes is reasonably free of impurities when compared to most of the materials studied by similar sonic measurements. The recent sonic logging campaign performed at EPICA Dome C has revealed the feasibility of such measurements (Gus- meroli et al., 2012). Nowadays, commercial loggers measure precisely the velocity. In parallel, the characterization of the physical properties of the ice single crystal and of the de- pendences of these properties with pressure and temperature reaches precisions of the order of a few percents. This in- crease in the precision renders the inverse problem accessi- ble, from the measured velocities to the ice texture, but the inversion model still requires a high level of accuracy. With respect to this requirement, a rigorous model as the model based on the **effective** **medium** **theory** appears as a good can- didate and should be favored.

and cavity generation [4,5]). While there are well-known equations governing poroelasticity at the so-called macroscopic lengthscale (i.e. a lengthscale much greater than that of the pores) [6–9], these laws typically require ab initio a statement of the constitutive laws describing the bulk properties of the solid and fluid components that are averaged volumetrically, irrespective of any underlying structure. As a result, any **effective** coefficients are meaningful only at the macroscopic scale and models must be parametrized via macroscopic experiments. Given these deficiencies, a model that explicitly accounts for pore-scale physics provides numerous benefits. In general, however, the underlying fluid–structure interaction (FSI) problems are highly complex, multiphysical and nonlinear coupled processes, for which direct simulation on complicated pore structures over multiple lengthscales is practically impossible. As such, **effective** models that explicitly incorporate pore-scale physics into a macroscopic model provide theoretical and computational benefits at the expense of a mathematically challenging homogenization process. It is beyond the scope of this work to present a comprehensive review and comparison of upscaling techniques that may be employed in the field of poroelasticity. However, in addition to multiscale homogenization, we wish to highlight other applicable techniques such as **effective** **medium** **theory** [10,11], mixture **theory** [12–14] and volume averaging [15,16]. For a more complete discussion we refer the reader to review articles that discuss upscaling in the wider fields of poroelasticity [17], flow in porous media [18,19] and solute transport [20].

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The laws of quantum mechanics were found to be successful in describing single particles and atoms. However, when particles and atoms accumulate them self to from a bulk matter, quantum laws suffers from some long standing problems [5,6].One of them is known as many body problem[7].The behavior of superconductors(Sc) at high temperature, till know, have no well defined simple full quantum **theory** to describe them [8,9]. **Theory** that can describe the early universe and unify gravity with other forces [10, 11].This may be attributed to the fact that, when particles ender a **medium**, quantum equations accounts for the effect of potential only, does not account for the effect of friction anther particles. Some attempts were made by the first authore do consider the friction effect. This work is concerned with alternative derivations based on Maxwell's and classical oscillator equations. The derivations were done in sections 2,3 and 4.The new equation is applied to oscillators in sec 5. Discussion and conclusion. The new equation is applied to oscillators in sections 6 and 7.

Eringen (1966a, 1990) developed the theories of 'micropolar continua' and 'microstructures continua' which are special cases of the **theory** of 'micromorphic continua' earlier developed by Eringen and his coworkers (1964). Thus,theEringen's '3M' theories (Micromorphic, Microstretch, Micropolar) are the generalization the classical **theory** of elasticity. In classical continuum, each particle of a continuum is represented by a geometrical point and can have three degree of freedom of translation during the process of deformation.

In these cases other theories, like quantum mechanics and relativity, can be used to make better predictions. In the realm of classical mechanics then these the- ories, in their approximate form, return to the original Newtonian formulation. We can see then that Newtonian mechanics takes the role of what is called an **effective** **theory**: a **theory** that has validity only in a certain regime of parameters or in certain length scales. As one moves outside of these limits the predictions given by the **effective** **theory** become less and less correct, moving away from the observed values. Then another **theory** can take its place, effectively creating a chain of **effective** theories, each one becoming more and more "fundamental" of the former, able to predict a larger and larger number of events and observa- tions.

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Structural Identification (St-Id) is the process of constructing and calibrating a physics-based model based on the measured static and/or dynamic response of the structure. Over the last two decades, although the St-Id methods have become increasingly popular amongst civil- structural engineering communities, most complete and successful applications are often found with flexible structures such as long-span bridges and towers. Very few comprehensive studies were reported on building structures, especially those with **medium**-rise characteristics which are often associated with complicated analytical modelling and different degrees of parameter uncertainties. To address this need, this paper presents an in-depth study on St-Id of a benchmark **medium**-rise building firstly demonstrating the importance of developing appropriate initial analytical models that can be used for the automated model calibration techniques. Then, a novel parametric study based sensitivity analysis approach is introduced to identify tuning parameters as well as their appropriate ranges to maximise the correlation of the calibrated model whilst preserving the physical relevance of the calibrated model. Modal data of the first few modes measured under ambient vibration conditions are used in this study.

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It is clear that the eﬀective ﬁeld **theory** is renormalizable: all necessary counterterms are presented in the Lagrangian by construction. This fact, however, does not make life easier because one needs to formulate an inﬁnite number of renormalization prescriptions (RP’s) in order to ﬁx the ﬁnite parts of relevant counterterms. This (so-called "problem of couplings") is the main obstacle on the way of constructing the physically meaningful **theory** of S matrix.

successfully tested on some nonlinear models such as model of diffusion and reaction in porous catalysts [14, 15]. In the present paper, we demonstrate the whole **theory** behind this technique and apply it on a model treated by A Nakayama and H Koyama [16] namely a kind of the problem of combined free and forced convection over a plane or axisymmetric body of arbitrary shape which is embedded in a fluid-saturated porous **medium**. This model accepts multiple (dual) solutions that is why it has been chosen for examining the proposed method.

Abstract—The problem of ambiguity in deﬁning eﬀective dielectric permittivity is studied theoretically in application to a plane layered heterogeneous **medium**, compounded by two and more alternating homogeneous layers with diﬀerent dielectric permittivities (water and glass), for the range of wavelengths from 1 to 10 cm. The eﬀective permittivity for such a heterogeneous **medium** is usually determined by the phenomenological semi-empirical Braggeman’s power rule, and the aim of the given investigation is validation of this rule by means of rigorous model of plane wave transmission and reﬂection. It is shown that the complex values of eﬀective dielectric permittivity for a layered dielectric, determined by measuring its transmission and reﬂection coeﬃcients, diﬀer noticeably from one to another. It is also shown that in a wide frequency range, the Braggeman’s formula gets as a close approximation only for such an eﬀective dielectric permittivity, which is determined by a transmission coeﬃcient.

Cerning [27] stated that carbon source along with nitrogen source and other ion sources are important composition of media that enhance EPS production. Yeast extract was reported to greatly influence EPS yield by L. plantarum MTCC9510 and Paeniacillus polymyca EJS-3 [28,29]. Likewise study by Shankar and others showed that yeast extract was more efficient nitrogen substrate than other nitrogen sources for growth and production of EPS by S. phocae. The nitrogen substrates in this study were compared, though the maximum cell growth cell biomass was observed by urea containing **medium** but highest EPS yield was formed by yeast extract **medium**. This may be due to

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To illustrate how one obtains the eﬀective ﬁeld **theory** from the underlying funda- mental **theory**, a brief description of how to construct the pion-nucleon Lagrangian is outlined. An eﬀective ﬁeld **theory** has two main features: it maintains the sym- metry properties of the underlying fundamental **theory**, and it has an expansion parameter, typically a small momentum or small mass scale, which permits cal- culation to a given order in the **theory** to be performed in a systematic way. In EFT, the small expansion parameter arises from the separation of scales between the small momenta and masses involved and the characteristic scale of the EFT. In the case of QCD the characteristic mass for chiral symmetry is Λ χ 1GeV , and we immediately note that m π << Λ χ . Thus, if the external momenta (p) involved in the process are small, both ratios m π /Λ χ and p/Λ χ are small, and provide the small expansion parameter that an EFT requires.

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Previous studies have shown the benefits of VR as a training **medium** in existing industries and practices. Alfalah et al. (2017) identified VR’s capability of enhancing trainee satisfaction rates versus traditional teaching methods, creating a more efficient and dynamic form of learning [8]. Work carried out by Seymour et al. (2002) explored the benefits of virtual reality for surgical training and found that users made fewer errors throughout a simulated surgery, in some cases by a significant margin [9]. These studies suggest that professional trainings can be fruitfully enhanced by VR. Few studies have, however, directly compared the differences in learners’ performance with traditional trainings, and where this has happened they have mostly focused on student samples or tested VR against low-fidelity alternatives such as written manuals or safety cards [10], [11], [12]. Our study aimed to investigate the effectiveness of virtual reality trainings compared to traditional training methods in a professional setting, where the traditional training consists of intensive practical, hands-on exercises. We further included ‘mixed’ training settings to investigate potential cross-over and sequence effects of training methods. Our study * jonathan.saunders@shu.ac.uk

3) In this work, focusing in the **medium** is proposed by creating a radial inhomogeneity of the refractive index n r E ( ) , 2 . this, radiation with a nonuniform cross section of the beam is used due to the use of films with nonlinear parameters. In this case, the dependence of the refractive index of the film material n r E ( , 2 ) on the intensity level of the radiation incident on the film, which is generally inhomogeneous in the cross section, is used. In the case of Kerr type nonlinearity, the refractive index has the form (1). Relation (3), taking into account (1), can be used to calculate the field distribution E(r) which ensures beam focusing. The field distribution function, providing the condition of phase matching of the rays for the first-order Kerr nonlinearity, is determined by the expression:

The nuclear problem is pathologically complicated: on one hand, the inter-nucleon interaction is non-central, non- local and unconstrained at short distances, and on the other hand, the complexity of solving the many-body Schr¨odinger equation increases dramatically with the number of nucle- ons. Phenomenological and one-boson exchange models have provided guidance and have proved successful in ap- plications to light nuclei; but a deeper understanding of the interactions between nucleons has been achieved us- ing **effective** field theories (EFTs) [1–3], which provide in- teractions consistent with the symmetries of the underly- ing **theory** of the strong interactions, QCD. Moreover, EFT eliminates the model dependence (e.g., there are an infinite number of nucleon-nucleon interactions which are phase- shift equivalent), explains naturally the hierarchy of the nu- clear interactions, and can mitigate shortcomings with the description of low-momentum observables, such as qua- drupole transitions.

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