Heteropolymers in a Solvent at an Interface

Exact bounds are obtained for the quenched free energy of a polymer with random hydrophobicities in the presence of an interface separating a polar from a non polar solvent. The polymer may be ideal or have steric self-interactions. The bounds allow to prove that a ``neutral'' random polymer is localized near the interface at any temperature, whereas a ``non-neutral'' chain is shown to undergo a delocalization transition at a finite temperature. These results are valid for a quite general a priori probability distribution for both independent and correlated hydrophobic charges. As a particular case we consider random AB-copolymers and confirm recent numerical studies.Comment: 4 pages, no figure

Higgs Couplings in Composite Models

We study Higgs couplings in the composite Higgs model based on the coset SO(5)/SO(4). We show that the couplings to gluons and photons are insensitive to the elementary-composite mixings and thus not affected by light fermionic resonances. Moreover, at leading order in the mixings the Higgs couplings to tops and gluons, when normalized to the Standard Model (SM), are equal. These properties are shown to be direct consequences of the Goldstone symmetry and of the assumption of partial compositeness. In particular, they are independent of the details of the elementary-composite couplings and, under the further assumption of CP invariance, they are also insensitive to derivative interactions of the Higgs with the composite resonances. We support our conclusions with an explicit construction where the SM fermions are embedded in the 14 dimensional representation of SO(5).Comment: 13 pages, 3 figures, 2 tables; v2: small improvements in the discussion, results unchanged; typos corrected; one reference added. Matches version submitted to PR

Magnetic field dependence of the energy of negatively charged excitons in semiconductor quantum wells

A variational calculation of the spin-singlet and spin-triplet state of a negatively charged exciton (trion) confined to a single quantum well and in the presence of a perpendicular magnetic field is presented. We calculated the probability density and the pair correlation function of the singlet and triplet trion states. The dependence of the energy levels and of the binding energy on the well width and on the magnetic field strength was investigated. We compared our results with the available experimental data on GaAs/AlGaAs quantum wells and find that in the low magnetic field region (B<18 T) the observed transition are those of the singlet and the dark triplet trion (with angular momentum $L_z=-1$), while for high magnetic fields (B>25 T) the dark trion becomes optically inactive and possibly a transition to a bright triplet trion (angular momentum $L_z=0$) state is observed.Comment: 9 pages, 10 figures submitted to Phys. Rev.

Excitons and charged excitons in semiconductor quantum wells

A variational calculation of the ground-state energy of neutral excitons and of positively and negatively charged excitons (trions) confined in a single-quantum well is presented. We study the dependence of the correlation energy and of the binding energy on the well width and on the hole mass. The conditional probability distribution for positively and negatively charged excitons is obtained, providing information on the correlation and the charge distribution in the system. A comparison is made with available experimental data on trion binding energies in GaAs-, ZnSe-, and CdTe-based quantum well structures, which indicates that trions become localized with decreasing quantum well width.Comment: 9 pages, 11 figure

A Gaussian-Mixture based stochastic framework for the interpretation of spatial heterogeneity in multimodal fields

We provide theoretical formulations enabling characterization of spatial distributions of variables (such as, e.g., conductivity/permeability, porosity, vadose zone hydraulic parameters, and reaction rates) that are typical of hydrogeological and/or geochemical scenarios associated with randomly heterogeneous geomaterials and are organized on various scales of heterogeneity. Our approach and ensuing formulations embed the joint assessment of the probability distribution of a target variable and its associated spatial increments, DY, taken between locations separated by any given distance (or lag). The spatial distribution of Y is interpreted through a bimodal Gaussian mixture model. The modes of the latter correspond to an indicator random field which is in turn related to the occurrence of different processes and/or geomaterials within the domain of observation. The distribution of each component of the mixture is governed by a given length scale driving the strength of its spatial correlation. Our model embeds within a unique theoretical framework the main traits arising in a stochastic analysis of these systems. These include (i) a slight to moderate asymmetry in the distribution of Y and (ii) the occurrence of a dominant peak and secondary peaks in the distribution of DY whose importance changes with lag together with the moments of the distribution. This causes the probability distribution of increments to scale with lag in way that is consistent with observed experimental patterns. We analyze the main features of the modeling and parameter estimation framework through a set of synthetic scenarios. We then consider two experimental datasets associated with different processes and observation scales. We start with an original dataset comprising microscale reaction rate maps taken at various observation times. These are evaluated from AFM imaging of the surface of a calcite crystal in contact with a fluid and subject to dissolution. Such recent high resolution imaging techniques are key to enhance our knowledge of the processes driving the reaction. The second dataset is a well established collection of Darcy-scale air-permeability data acquired by Tidwell and Wilson (1999) [Water Resour Res, 35, 3375-3387] on a block of volcanic tuff through minipermeameters associated with various measurement scales

Can Homes Affect Well-Being? A Scoping Review among Housing Conditions, Indoor Environmental Quality, and Mental Health Outcomes

The purpose of the scoping review is to explore the relationship between housing conditions, indoor environmental quality (IEQ), and mental health implications on human well-being. In fact, time spent at home increased due to the recent COVID-19 lockdown period, and social-sanitary emergencies are expected to grow due to the urbanization phenomenon. Thus, the role of the physical environment in which we live, study, and work, has become of crucial importance, as the literature has recently highlighted. This scoping review, conducted on the electronic database Scopus, led to the identification of 366 articles. This, after the screening processes based on the inclusion criteria, led to the final inclusion of 31 papers related specifically to the OECD area. The review allowed the identification of five housing conditions [house type, age, and floor level; housing qualities; household composition; neighborhood; green spaces] that, by influencing the IEQ parameters, had impacts on the mental health outcomes addressed. By synthesizing the contributions of the review, a list of design recommendations has been provided. These will serve as a basis for future researchers, from which to develop measures to reduce inequalities in housing by making them healthier, more resilient, and salutogenic

On the identification of Dragon Kings among extreme-valued outliers

Abstract. Extreme values of earth, environmental, ecological, physical, biological, financial and other variables often form outliers to heavy tails of empirical frequency distributions. Quite commonly such tails are approximated by stretched exponential, log-normal or power functions. Recently there has been an interest in distinguishing between extreme-valued outliers that belong to the parent population of most data in a sample and those that do not. The first type, called Gray Swans by Nassim Nicholas Taleb (often confused in the literature with Taleb's totally unknowable Black Swans), is drawn from a known distribution of the tails which can thus be extrapolated beyond the range of sampled values. However, the magnitudes and/or space–time locations of unsampled Gray Swans cannot be foretold. The second type of extreme-valued outliers, termed Dragon Kings by Didier Sornette, may in his view be sometimes predicted based on how other data in the sample behave. This intriguing prospect has recently motivated some authors to propose statistical tests capable of identifying Dragon Kings in a given random sample. Here we apply three such tests to log air permeability data measured on the faces of a Berea sandstone block and to synthetic data generated in a manner statistically consistent with these measurements. We interpret the measurements to be, and generate synthetic data that are, samples from α-stable sub-Gaussian random fields subordinated to truncated fractional Gaussian noise (tfGn). All these data have frequency distributions characterized by power-law tails with extreme-valued outliers about the tail edges

Extended power-law scaling of heavy-tailed random air-permeability fields in fractured and sedimentary rocks

Abstract. We analyze the scaling behaviors of two field-scale log permeability data sets showing heavy-tailed frequency distributions in three and two spatial dimensions, respectively. One set consists of 1-m scale pneumatic packer test data from six vertical and inclined boreholes spanning a decameters scale block of unsaturated fractured tuffs near Superior, Arizona, the other of pneumatic minipermeameter data measured at a spacing of 15 cm along three horizontal transects on a 21 m long and 6 m high outcrop of the Upper Cretaceous Straight Cliffs Formation, including lower-shoreface bioturbated and cross-bedded sandstone near Escalante, Utah. Order q sample structure functions of each data set scale as a power ξ(q) of separation scale or lag, s, over limited ranges of s. A procedure known as extended self-similarity (ESS) extends this range to all lags and yields a nonlinear (concave) functional relationship between ξ(q) and q. Whereas the literature tends to associate extended and nonlinear power-law scaling with multifractals or fractional Laplace motions, we have shown elsewhere that (a) ESS of data having a normal frequency distribution is theoretically consistent with (Gaussian) truncated (additive, self-affine, monofractal) fractional Brownian motion (tfBm), the latter being unique in predicting a breakdown in power-law scaling at small and large lags, and (b) nonlinear power-law scaling of data having either normal or heavy-tailed frequency distributions is consistent with samples from sub-Gaussian random fields or processes subordinated to tfBm or truncated fractional Gaussian noise (tfGn), stemming from lack of ergodicity which causes sample moments to scale differently than do their ensemble counterparts. Here we (i) demonstrate that the above two data sets are consistent with sub-Gaussian random fields subordinated to tfBm or tfGn and (ii) provide maximum likelihood estimates of parameters characterizing the corresponding Lévy stable subordinators and tfBm or tfGn functions

Postseismic deformation and body forces shaping the Apennines and adjacent sedimentary basins in Umbria-Marche

The geodynamic complexity of the Apennines and adjacent sedimentary basins in Umbria-Marche (North-Central Italy) makes the dynamics of the present day deformation and its relationships with the seismicity less well understood. In this paper, we argue that, further to buoyancy forces, postseismic deformation of earthquakes taking place on the Apennines contributes to the regional deformation. We investigate the interaction between the normal faulting system responsible of the 1997 Umbria-Marche earthquake sequence (Colfiorito fault) and the low angle normal faulting system bordering the sedimentary basins, namely the Altotiberina fault. We set-up a 2D finite element model of the lithosphere-asthenosphere accounting for lateral heterogeneities and investigate how this heterogeneous structure is capable of localizing strain under the Umbria-Marche sedimentary basins, providing a way for the Colfiorito fault to influence the evolution of the Altotiberina fault. We show how the two different length and time scale processes, namely postseismic deformation and buoyancy, are complementary in shaping the Apennines and adjacent sedimentary basins. The high resolution deformation patterns modeled in this study can hardly be reproduced by a model accounting only for external forces such as a rotating or subducting or retreating Adria

Extended power-law scaling of air permeabilities measured on a block of tuff

Abstract. We use three methods to identify power-law scaling of multi-scale log air permeability data collected by Tidwell and Wilson on the faces of a laboratory-scale block of Topopah Spring tuff: method of moments (M), Extended Self-Similarity (ESS) and a generalized version thereof (G-ESS). All three methods focus on q-th-order sample structure functions of absolute increments. Most such functions exhibit power-law scaling at best over a limited midrange of experimental separation scales, or lags, which are sometimes difficult to identify unambiguously by means of M. ESS and G-ESS extend this range in a way that renders power-law scaling easier to characterize. Our analysis confirms the superiority of ESS and G-ESS over M in identifying the scaling exponents, ξ(q), of corresponding structure functions of orders q, suggesting further that ESS is more reliable than G-ESS. The exponents vary in a nonlinear fashion with q as is typical of real or apparent multifractals. Our estimates of the Hurst scaling coefficient increase with support scale, implying a reduction in roughness (anti-persistence) of the log permeability field with measurement volume. The finding by Tidwell and Wilson that log permeabilities associated with all tip sizes can be characterized by stationary variogram models, coupled with our findings that log permeability increments associated with the smallest tip size are approximately Gaussian and those associated with all tip sizes scale show nonlinear variations in ξ(q) with q, are consistent with a view of these data as a sample from a truncated version (tfBm) of self-affine fractional Brownian motion (fBm). Since in theory the scaling exponents, ξ(q), of tfBm vary linearly with q we conclude that nonlinear scaling in our case is not an indication of multifractality but an artifact of sampling from tfBm. This allows us to explain theoretically how power-law scaling of our data, as well as of non-Gaussian heavy-tailed signals subordinated to tfBm, are extended by ESS. It further allows us to identify the functional form and estimate all parameters of the corresponding tfBm based on sample structure functions of first and second orders