Laplacian Distribution and Domination

Let $m_G(I)$ denote the number of Laplacian eigenvalues of a graph $G$ in an interval $I$, and let $\gamma(G)$ denote its domination number. We extend the recent result $m_G[0,1) \leq \gamma(G)$, and show that isolate-free graphs also satisfy $\gamma(G) \leq m_G[2,n]$. In pursuit of better understanding Laplacian eigenvalue distribution, we find applications for these inequalities. We relate these spectral parameters with the approximability of $\gamma(G)$, showing that $\frac{\gamma(G)}{m_G[0,1)} \not\in O(\log n)$. However, $\gamma(G) \leq m_G[2, n] \leq (c + 1) \gamma(G)$ for $c$-cyclic graphs, $c \geq 1$. For trees $T$, $\gamma(T) \leq m_T[2, n] \leq 2 \gamma(G)$

Stochastic Dynamical Model of Intermittency in Fully Developed Turbulence

A novel model of intermittency is presented in which the dynamics of the rates of energy transfer between successive steps in the energy cascade is described by a hierarchy of stochastic differential equations. The probability distribution of velocity increments is calculated explicitly and expressed in terms of generalized hypergeometric functions of the type ${_n}F_0$, which exhibit power-law tails. The model predictions are found to be in good agreement with experiments on a low temperature gaseous helium jet. It is argued that distributions based on the functions ${_n}F_0$ might be relevant also for other physical systems with multiscale dynamics.Comment: 10 pages, 2 figures. To appear in Physical Review

Exactly solvable nonequilibrium Langevin relaxation of a trapped nanoparticle

In this work, we study the nonequilibrium statistical properties of the relaxation dynamics of a nanoparticle trapped in a harmonic potential. We report an exact time-dependent analytical solution to the Langevin dynamics that arises from the stochastic differential equation of our system's energy in the underdamped regime. By utilizing this stochastic thermodynamics approach, we are able to completely describe the heat exchange process between the nanoparticle and the surrounding environment. As an important consequence of our results, we observe the validity of the heat exchange fluctuation theorem (XFT) in our setup, which holds for systems arbitrarily far from equilibrium conditions. By extending our results for the case of $N$ noninterating nanoparticles, we perform analytical asymptotic limits and direct numerical simulations that corroborate our analytical predictions.Comment: 11 pages, 6 figure

A maximum entropy approach to H-theory: Statistical mechanics of hierarchical systems

A novel formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small subsystem---representing the region where the measurements are made---in contact with a set of `nested heat reservoirs' corresponding to the hierarchical structure of the system. The probability distribution function (pdf) of the fluctuating temperatures at each reservoir, conditioned on the temperature of the reservoir above it, is determined from a maximum entropy principle subject to appropriate constraints that describe the thermal equilibrium properties of the system. The marginal temperature distribution of the innermost reservoir is obtained by integrating over the conditional distributions of all larger scales, and the resulting pdf is written in analytical form in terms of certain special transcendental functions, known as the Fox $H$-functions. The distribution of states of the small subsystem is then computed by averaging the quasi-equilibrium Boltzmann distribution over the temperature of the innermost reservoir. This distribution can also be written in terms of $H$-functions. The general family of distributions reported here recovers, as particular cases, the stationary distributions recently obtained by Mac\^edo {\it et al.} [Phys.~Rev.~E {\bf 95}, 032315 (2017)] from a stochastic dynamical approach to the problem.Comment: 20 pages, 2 figure

Multicanonical distribution: Statistical equilibrium of multiscale systems

A multicanonical formalism is introduced to describe statistical equilibrium of complex systems exhibiting a hierarchy of time and length scales, where the hierarchical structure is described as a set of nested "internal heat reservoirs" with fluctuating "temperatures." The probability distribution of states at small scales is written as an appropriate averaging of the large-scale distribution (the Boltzmann-Gibbs distribution) over these effective internal degrees of freedom. For a large class of systems the multicanonical distribution is given explicitly in terms of generalized hypergeometric functions. As a concrete example, it is shown that generalized hypergeometric distributions describe remarkably well the statistics of acceleration measurements in Lagrangian turbulence.Comment: 11 pages, 1 figur

Perubahan Fungsi Ruang Domestik di Sekitar Kampus Unpaz (Universidade Da Paz), Dili, Timor Leste

Universidade da Paz (UNPAZ) didirikan oleh Fundação Neon Metin (FNM) pada 9 Maret 2004, dan juga merupakan universitas swasta terbesar yang ada di Timor Leste saat ini. UNPAZ sangat berkembang dari segi pengembangan kampus (infrastruktur) maupun meningkatnya jumlah mahasiswa. Perkembangan kampus ini menyebabkan terjadinya Perubahan fungsi ruang pada Kampus UNPAZ. Selain kampus Perubahan fisik dan fungsi ruang domestik terjadi pada kampung sekitarnya, terutama Kampung Osindo I Manleuana. Kampung Osindo I Manleuana secara geografis terletak di Kelurahan Fatuhada, Kecamatan Dom-Aleixo, Kotamadya Dili, Timor Leste. Kampung ini mula-mula penduduknya bermata pencaharian sebagai petani. Letak kampung dekat jalur akses utama menuju Kampus UNPAZ menyebabkan kegiatan ekonomi penduduk menjadi berubah. Perubahan ini menyebabkan terjadinya Perubahan fungsi ruang domestik pada rumah tinggal maupun halamannya. Untuk meneliti lebih jauh lagi tentang proses Perubahan fungsi ruang domestik dengan kehadirannya Kampus UNPAZ, digunakan pendekatan penelitian kualitatif, dengan teknik pengumpulan data melalui observasi, wawancara, dokumentasi dan pembagian kuesioner pada masyarakat setempat. Perubahan-Perubahan fungsi ruang domestik di atas dianalisis dengan teori-teori yang relevan yaitu Perubahan fisik, ruang, bentuk ruang, dan pola organisasi ruang