Abstract:
The effect of finiteness in degree number is analyzed on a growing network. The dynamics is governed by a rule where the degree number increases under a scheme similar to the Malthus-Verhulst model in the context of population growth. One notices that the second moment of degree is closely related to the linking probability of this growing network. The degree distribution is analyzed in both stationary and time-dependent regimes through some exact results and simulations, and a scaling behaviour is found in asymptotically large time.

Abstract:
The nonequilibrium stationary state of an irreversible spherical model is investigated on hypercubic lattices. The model is defined by Langevin equations similar to the reversible case, but with asymmetric transition rates. In spite of being irreversible, we have succeeded in finding an explicit form for the stationary probability distribution, which turns out to be of the Boltzmann-Gibbs type. This enables one to evaluate the exact form of the entropy production rate at the stationary state, which is non-zero if the dynamical rules of the transition rates are asymmetric.

Abstract:
The Langevin dynamics of a $d$-dimensional mean spherical model with competing interactions along $m\leq d$ directions of a hypercubic lattice is analysed. After a quench at high temperatures, the dynamical behaviour is characterized by two distinct time scales associated with stationary and aging regimes. The asymptotic expressions for the autocorrelation and response functions, in supercritical, critical, and subcritical cases, were calculated. Aging effects, which are known to be present in the ferromagnetic version of this model system, are not affected by the introduction of competing interactions.

Abstract:
The question of robustness of a network under random ``attacks'' is treated in the framework of critical phenomena. The persistence of spontaneous magnetization of a ferromagnetic system to the random inclusion of antiferromagnetic interactions is investigated. After examing the static properties of the quenched version (in respect to the random antiferromagnetic interactions) of the model, the persistence of the magnetization is analysed also in the annealed approximation, and the difference in the results are discussed.

Abstract:
Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen to be embedded in a metric arrangement, where the geographic distance between vertices plays a crucial role. The present work proposes a model for growing network that takes into account the geographic distance between vertices: the probability that they are connected is higher if they are located nearer than farther. In this framework, the mean degree of vertices, degree distribution and shortest path length between two randomly chosen vertices are analysed.

Abstract:
A generalized version of the nonequilibrium linear Glauber model with $q$ states in $d$ dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the $q$ states. Exact expressions for the two-time autocorrelation and response functions on a $d$-dimensional lattice are obtained. In the stationary regime, the fluctuation-dissipation theorem holds, while in the transient the aging is observed with the fluctuation-dissipation ratio leading to the value predicted for the linear Glauber model.

Abstract:
We analyse a non-equilibrium exclusion process in which particles are created and annihilated in pairs and hop to the the right or to the left with different transition rates, $p$ and $q$, respectively. We have studied the dynamics of a single particle, and exactly determined the entropy, entropy production rate and entropy flux as functions of time. In the system of many particles, we have characterised the system by its probability distribution, as well as the entropy production rate in close forms, provided that $p+q$ equals the sum of dimers creation and annihilation rates. The general case, where this constraint is absent, was considered at pair approximation level; the time-dependent behaviour of the system was analysed, and the stationary entropy production was determined. In all cases, in the stationary regime, we showed that the entropy production rate is a bilinear form in the current of particles and the force $\ln(p/q)$.

Abstract:
We show that the near infrared solar absorption spectra recorded in the framework of the Total Carbon Column Observing Network (TCCON) can be used to derive the vertical distribution of tropospheric water vapour. Using spectral H2O signatures in the 4500–4700 cm 1 region one can well distinguish lower from middle/upper tropospheric water vapour concentrations. The vertical resolution is about 3 and 6 km, for the lower and middle/upper troposphere, respectively. We document the quality of the remotely-sensed profiles by comparisons with coincident in-situ Vaisala RS92 radiosonde measurements. The agreement of both techniques is very satisfactory. Due to the long-term strategy of the network and the high measurement frequency, the TCCON water vapour profile data offer novel opportunities for estimating the water vapour variability at different time scales and altitudes.

Abstract:
We obtain exact expressions for the two-time autocorrelation and response functions of the $d$-dimensional linear Glauber model. Although this linear model does not obey detailed balance in dimensions $d\geq 2$, we show that the usual form of the fluctuation-dissipation ratio still holds in the stationary regime. In the transient regime, we show the occurence of aging, with a special limit of the fluctuation-dissipation ratio, $X_{\infty}=1/2$, for a quench at the critical point.

Abstract:
We show that the near infrared solar absorption spectra recorded in the framework of the Total Carbon Column Observing Network (TCCON) can be used to derive the vertical distribution of tropospheric water vapour. The resolution of the TCCON spectra of 0.02 cm 1 is sufficient for retrieving lower and middle/upper tropospheric water vapour concentrations with a vertical resolution of about 3 and 8 km, respectively. We document the good quality of the remotely-sensed profiles by comparisons with coincident in-situ Vaisala RS92 radiosonde measurements. Due to the high measurement frequency, the TCCON water vapour profile data offer novel opportunities for estimating the water vapour variability at different timescales and altitudes.