Abstract We consider N two-dimensional Ising models coupled in the presence of quenched disorder and use scale invariant scattering theory to exactly show the presence of a line of renormalization group fixed points for any fixed value of N other than 1. We show how this result relates to perturbative studies and sheds light on numerical simulations. We also observe that the limit N → 1 may be of interest for the Ising spin glass, and point out the potential relevance for nonuniversality in other contexts of random criticality.
Abstract We investigate a hiring process where a sequence of applicants is sequentially interviewed, and a decision on whether to hire an applicant is immediately made based on the applicant’s score. For the maximal and average improvement strategies, the decision depends on the applicant’s score and the scores of all employees, i.e. previous successful applicants. For local improvement strategies, an interviewing committee randomly chosen for each applicant makes the decision depending on the score of the applicant and the scores of the members of the committee. These idealized hiring strategies capture the challenges of decision-making under uncertainty. We probe the average score of the best employee, the probability of hiring all first N applicants, the fraction of superior companies in which, throughout the evolution, every hired applicant has a score above expected, etc.
Statistika adalah salah satu cabang ilmu matematika yang berkenaan dengan metode ilmiah yang mengumpulkan, mengorganisasi, meringkas, menyajikan, menganalisa data termasuk penarikan kesimpulan yang sah, dan membuat keputusan beralasan berdasarkan analisis tertentu. Statistika memiliki peran penting di segala bidang kehidupan, yaitu mulai dari bidang pemerintah, olahraga, pendididkan, kedokteran, dan lain sebagainya. Dalam penelitian ini peneliti menentukan untuk menggunakan distribusi Rayleigh karena distribusi Rayleigh ini sangat penting dalam statistika, dimana penerapannya di beberapa bidang seperti pertanian, kesehatan, biologi, fisika serta beragam ilmu lainnya. Penelitian ini bertujuan unuk mengetahui estimasi uji maksimum likelihood dan uji parameter distribusi Rayleigh, Mengetahui uji goodness of fit distribusi Rayleigh dengan menggunakan statistik uji Kolmogrov Smirnov, Mengetahui aplikasi inferensi parameter dan uji goodness of fit distribusi Rayleigh.Penelitian ini di laksanakan laboratorium penelitian jurusan matematika pada bulan juni 2023. Metode yang digunakan yaitu studi pustaka dengan tehnik analisis data yaitu statistic inferensia dengan estimasi parameter yaitu dengan estimasi titik metode likelihood. Untuk menetukan nilai kritis terhadap pengujian hipotesis H_0: θ= θ_0 vs H_1: θ≠ θ_0, dimana menolak H_0 pada berbagai tingkat signifikansi α=5%. Selanjutnya, dilakukan pengaplikasian statistik uji Kolmogorov-Smirnov untuk mengetahui apakah data pasien kemoterapi yang digunakan berasal dari populasi yang berdistribusi Rayleigh. Sehingga diperoleh kesimpulan hasil pengujian data H_0 ditolak dan disimpulkan data tidak berasal dari distribusi Rayleigh.
Abstract Dynamic space filling (DSF) is a stochastic process defined on any connected graph. Each vertex can host an arbitrary number of particles forming a pile, with every arriving particle landing on the top of the pile. Particles in a pile, except for the particle at the bottom, can hop to neighboring vertices. Eligible particles hop independently and stochastically, with the overall hopping rate set to unity. When the number of vertices in a graph is equal to the total number of particles, the evolution stops when a single particle occupies every vertex. We determine the halting time distribution on complete graphs. Using the mapping of the DSF into a two-species annihilation process, we argue that on d -dimensional tori with N ≫ 1 vertices, the average halting time scales with the number of vertices as N 4 / d when d ⩽ 4 and as N when d > 4.
Inspired by recent experiments on fluctuations of the flagellar beating in sperms and C. reinhardtii, we investigate the precision of phase fluctuations in a system of nearest-neighbour-coupled molecular motors. We model the system as a Kuramoto chain of oscillators with coupling constant $k$ and noisy driving. The precision $p$ is a Fano-factor-like observable which obeys the Thermodynamic Uncertainty Relation (TUR), that is an upper bound related to dissipation. We first consider independent motor noises with diffusivity $D$: in this case the precision goes as $k/D$, coherently with the behavior of spatial order. The minimum observed precision is that of the uncoupled oscillator $p_{unc}$, the maximum observed one is $Np_{unc}$, saturating the TUR bound. Then we consider driving noises which are spatially correlated, as it may happen in the presence of some direct coupling between adjacent motors. Such a spatial correlation in the noise does not reduce evidently the degree of spatial correlation in the chain, but sensibly reduces the maximum attainable precision $p$, coherently with experimental observations. The limiting behaviors of the precision, in the two opposite cases of negligible interaction and strong interaction, are well reproduced by the precision of the single chain site $p_{unc}$ and the precision of the center of mass of the chain $N_{eff} p_{unc}$ with $N_{eff}<N$: both do not depend on the degree of interaction in the chain, but $N_{eff}$ decreases with the correlation length of the motor noises.
Abstract In random sequential covering, identical objects are deposited randomly, irreversibly, and sequentially; only attempts increasing the coverage are accepted. A finite system eventually gets congested, and we study the statistics of congested configurations. For the covering of an interval by dimers, we determine the average number of deposited dimers, compute all higher cumulants, and establish the probabilities of reaching minimally and maximally congested configurations. We also investigate random covering by segments with ℓ sites and sticks. Covering an infinite substrate continues indefinitely, and we analyze the dynamics of random sequential covering of Z and R d .
Aritra Ghosh, Malay Bandyopadhyay, Sushanta Dattagupta
et al.
This review provides a brief and quick introduction to the quantum Langevin equation for an oscillator, while focusing on the steady-state thermodynamic aspects. A derivation of the quantum Langevin equation is carefully outlined based on the microscopic model of the heat bath as a collection of a large number of independent quantum oscillators, the so-called independent-oscillator model. This is followed by a discussion on the relevant `weak-coupling' limit. In the steady state, we analyze the quantum counterpart of energy equipartition theorem which has generated a considerable amount of interest in recent literature. The free energy, entropy, specific heat, and third law of thermodynamics are discussed for one-dimensional quantum Brownian motion in a harmonic well. Following this, we explore some aspects of dissipative diamagnetism in the context of quantum Brownian oscillators, emphasizing upon the role of confining potentials and also upon the environment-induced classical-quantum crossover. We discuss situations where the system-bath coupling is via the momentum variables by focusing on a gauge-invariant model of momentum-momentum coupling in the presence of a vector potential; for this problem, we derive the quantum Langevin equation and discuss quantum thermodynamic functions. Finally, the topic of fluctuation theorems is discussed (albeit, briefly) in the context of classical and quantum cyclotron motion of a particle coupled to a heat bath.
We consider an Erdos-Renyi random graph consisting of N vertices connected by randomly and independently drawing an edge between every pair of them with probability c/N so that at N->infinity one obtains a graph of finite mean degree c. In this regime, we study the distribution of resistance distances between the vertices of this graph and develop an auxiliary field representation for this quantity in the spirit of statistical field theory. Using this representation, a saddle point evaluation of the resistance distance distribution is possible at N->infinity in terms of an 1/c expansion. The leading order of this expansion captures the results of numerical simulations very well down to rather small values of c; for example, it recovers the empirical distribution at c=4 or 6 with an overlap of around 90%. At large values of c, the distribution tends to a Gaussian of mean 2/c and standard deviation sqrt{2/c^3}. At small values of c, the distribution is skewed toward larger values, as captured by our saddle point analysis, and many fine features appear in addition to the main peak, including subleading peaks that can be traced back to resistance distances between vertices of specific low degrees and the rest of the graph. We develop a more refined saddle point scheme that extracts the corresponding degree-differentiated resistance distance distributions. We then use this approach to recover analytically the most apparent of the subleading peaks that originates from vertices of degree 1. Rather intuitively, this subleading peak turns out to be a copy of the main peak, shifted by one unit of resistance distance and scaled down by the probability for a vertex to have degree 1. We comment on a possible lack of smoothness in the true N->infinity distribution suggested by the numerics.
Abstract We consider stationary driven systems in contact with a thermal equilibrium bath. There is a constant (Joule) heat dissipated from the steady system to the environment as long as all parameters are unchanged. As a natural generalization from equilibrium thermodynamics, the nonequilibrium heat capacity measures the excess in that dissipated heat when the temperature of the thermal bath is changed. To improve experimental accessibility we show how the heat capacity can also be obtained from the response of the instantaneous heat flux to small periodic temperature variations.
Abstract Numerous models in opinion dynamics focus on the temporal dynamics within a single electoral unit (e.g. country). The empirical observations, on the other hand, are often made across multiple electoral units (e.g. polling stations) at a single point in time (e.g. elections). Aggregates of these observations, while quite useful in many applications, neglect the underlying heterogeneity in opinions. To address this issue we build a simple agent–based model in which all agents have fixed opinions, but are able to change their electoral units. We demonstrate that this model is able to generate rank–size distributions consistent with the empirical data.
The statistical properties of spectra of quantum systems within the framework of random matrix theory is widely used in many areas of physics. These properties are affected, if two or more sets of spectra are superposed, resulting from the discrete symmetries present in the system. Superposition of spectra of $m$ such circular orthogonal, unitary and symplectic ensembles are studied numerically using higher-order spacing ratios. For given $m$ and the Dyson index $β$, the modified index $β'$ is tabulated whose nearest neighbor spacing distribution is identical to that of $k$-th order spacing ratio. For the case of $m=2$ ($m=3$) in COE (CUE) a scaling relation between $β'$ and $k$ is given. For COE, it is conjectured that for $k=m+1$ ($m\geq2$) and $k=m-3$-th ($m\geq5$) order spacing ratio distribution the $β'$ is $m+2$ and $m-4$ respectively. Whereas in the case of CSE, for $k=m+1$ ($m\geq2$) and $k=m-1$-th ($m\geq3$) the $β'$ is $2m+3$ and $2(m-2)$ respectively. We also conjecture that for given $m$ ($k$) and $β$, the sequence of $β'$ as a function of $k$ ($m$) is unique. Strong numerical evidence in support of these results is presented. These results are tested on complex systems like the measured nuclear resonances, quantum chaotic kicked top and spin chains.
Abstract Brownian motors and Feymann ratchets have been intensively studied in the past decades due to their significance to the foundation of statistical physics. In this work, we propose a new type of Brownian motor, i.e. a self-driven motor that only utilizes the temperature differences inside and outside the motor. The motor is a container with asymmetric geometry. When filling gas, directional motion occurs when the temperature is different from the environment. This new mechanism is about the asymmetric geometry of the container, which induces anisotropic thermalization, and results in a density gradient and propels the motor. The directional motion ceases until the density gradient disappears as the inside temperature approaches the environment temperature. The same mechanism is also applied to design self-driven rotators. Additionally, possible experimental realizations are discussed.
Mohammad Yaghoubi, M. Ebrahim Foulaadvand, Antoine Bérut
et al.
We provide insights into energetics of a Brownian oscillator in contact with a heat bath and driven by an external unbiased time-periodic force that takes the system out of thermodynamic equilibrium. Solving the corresponding Langevin equation, we compute average kinetic and potential energies in the long-time stationary state. We also derive the energy balance equation and study the energy flow in the system. In particular, we identify the energy delivered by the external force, the energy dissipated by a thermal bath and the energy provided by thermal equilibrium fluctuations. Next, we illustrate Jarzynski work-fluctuation relation and consider the stationary state fluctuation theorem for the total work done on the system by the external force. Finally, by determining time scales in the system, we analyze the strong damping regime and discuss the problem of overdamped dynamics when inertial effects can be neglected.
Raffaele Pastore, Antonio de Candia, Anallisa Fierro
et al.
The dynamical arrest of gels is the consequence of a well defined structural phase transition, leading to the formation of a spanning cluster of bonded particles. The dynamical glass transition, instead, is not accompanied by any clear structural signature. Nevertheless, both transitions are characterized by the emergence of dynamical heterogeneities. Reviewing recent results from numerical simulations, we discuss the behavior of dynamical heterogeneities in different systems and show that a clear connection with the structure exists in the case of gels. The emerging picture may be also relevant for the more elusive case of glasses. We show, as an example, that the relaxation process of a simple glass-forming model can be related to a reverse percolation transition and discuss further perspective in this direction.