Search

The analysis of the impact of the star polymer topology on depletion interaction potentials, depletion forces, and monomer density profiles is carried out analytically using field theory methods and techniques as well as molecular dynamic simulations. The dimensionless depletion interaction potentials and the dimensionless depletion forces for a dilute solution of ideal star polymers with three and five legs (arms) in a Θ -solvent confined in a slit between two parallel walls with repulsive surfaces and for the case where one of the surfaces is repulsive and the other inert are obtained. Furthermore, the dimensionless layer monomer density profiles for ideal star polymers with an odd number ( f ˜ = 3, 5) of arms immersed in a dilute solution of big colloidal particles with different adsorbing or repelling properties in respect of polymers are calculated, bearing in mind the Derjaguin approximation. Molecular dynamic simulations of a dilute solution of star-shaped polymers in a good solvent with N = 901 (3 × 300 + 1 -star polymer with three arms) and 1501 (5 × 300 + 1 -star polymer with five arms) beads accordingly confined in a slit with different boundary conditions are performed, and the results of the monomer density profiles for the above-mentioned cases are obtained. The numerical calculation of the radius of gyration for star polymers with f ˜ = 3, 5 arms and the ratio of the perpendicular to parallel components of the radius of gyration with respect to the wall orientation for the above-mentioned cases is performed. The obtained analytical and numerical results for star polymers with an odd number ( f ˜ = 3, 5) of arms are compared with our previous results for linear polymers in confined geometries. The acquired results show that a dilute solution of star polymer chains can be applied in the production of new functional materials, because the behavior of these solutions is strictly correlated with the topology of polymers and also with the nature and geometry of confined surfaces. The above-mentioned properties can find extensive practical application in materials engineering, as well as in biotechnology and medicine for drug and gene transmission. [ABSTRACT FROM AUTHOR]

We apply a real-space block renormalization group approach to study the critical properties of the random transverse-field Ising spin chain with multispin interactions. First, we recover the known properties of the traditional model with two-spin interactions by applying the renormalization approach for the arbitrary size of the block. For the model with three-spin couplings, we calculate the critical point and demonstrate that the phase transition is controlled by an infinite disorder fixed point. We have determined the typical correlation-length critical exponent, which seems to be different from that of the random transverse Ising chain with nearest-neighbor couplings. Thus, this model represents a new infinite disorder universality class. [ABSTRACT FROM AUTHOR]

The dynamic heterogeneities occurring just before the transition to the glassy phase have been named as the cause of amorphization in supercooled systems. Numerous studies conducted so far have confirmed this hypothesis, and based on it, a widely accepted solution to the puzzle of glass transition has been developed. This report focuses on verifying the existence of a strong pretransitional anomaly near the glass transition T g . For this purpose, supercooled liquid-crystalline systems with a strong rod-like structure were selected. Based on the obtained experimental data, we demonstrate in this article that the previously postulated dynamic heterogeneities exhibit a critical characteristic, meaning a strong pretransitional anomaly can be observed with the described critical exponent α = 0.5 . Due to this property, it can be concluded that these heterogeneities are critical fluctuations, and consequently, the transition to the glassy state can be described based on the theory of critical phenomena. To measure the pretransitional anomaly near T g in supercooled liquid-crystalline systems, broadband dielectric spectroscopy (BDS) and nonlinear dielectric effect (NDE) methods were applied. The exponent α provides insight into the nature and intensity of critical fluctuations in the system. A value of α = 0.5 suggests that the fluctuations become increasingly intense as the system approaches the critical point, contributing to the divergence in specific heat. Understanding the role of critical fluctuations in the glass transition is crucial for innovating and improving a wide range of materials for energy storage, materials design, biomedical applications, food preservation, and environmental sustainability. These advancements can lead to materials with superior properties, optimized manufacturing processes, and applications that meet the demands of modern technology and sustainability challenges. [ABSTRACT FROM AUTHOR]

Fluctuations are omnipresent; they exist in any matter, due either to its quantum nature or to its nonzero temperature. In the current review, we briefly cover the quantum electrodynamic Casimir (QED) force as well as the critical Casimir (CC) and Helmholtz (HF) forces. In the QED case, the medium is usually a vacuum and the massless excitations are photons, while in the CC and HF cases the medium is usually a critical or correlated fluid and the fluctuations of the order parameter are the cause of the force between the macroscopic or mesoscopic bodies immersed in it. We discuss the importance of the presented results for nanotechnology, especially for devising and assembling micro- or nano-scale systems. Several important problems for nanotechnology following from the currently available experimental findings are spelled out, and possible strategies for overcoming them are sketched. Regarding the example of HF, we explicitly demonstrate that when a given integral quantity characterizing the fluid is conserved, it has an essential influence on the behavior of the corresponding fluctuation-induced force. [ABSTRACT FROM AUTHOR]

We study the critical behaviors of systems undergoing fractal time processes above the upper critical dimension. We derive a set of novel critical exponents, irrespective of the order of the fractional time derivative or the particular form of interaction in the Hamiltonian. For fractal time processes, we not only discover new universality classes with a dimensional constant but also decompose the dangerous irrelevant variables to obtain corrections for critical dynamic behavior and static critical properties. This contrasts with the traditional theory of critical phenomena, which posits that static critical exponents are unrelated to the dynamical processes. Simulations of the Landau–Ginzburg model for fractal time processes and the Ising model with temporal long-range interactions both show good agreement with our set of critical exponents, verifying its universality. The discovery of this new universality class provides a method for examining whether a system is undergoing a fractal time process near the critical point. [ABSTRACT FROM AUTHOR]

Can liquid-like and gas-like states be distinguished beyond the critical point, where the liquid--gas phase transition no longer exists and conventionally only a single supercritical fluid phase is defined? Recent experiments and simulations report strong evidence of dynamical crossovers above the critical temperature and pressure. Despite using different criteria, many existing theoretical explanations consider a single crossover line separating liquid-like and gas-like states in the supercritical fluid phase. We argue that such a single-line scenario is inconsistent with the supercritical behavior of the Ising model, which has two crossover lines due to its symmetry, violating the universality principle of critical phenomena. To reconcile the inconsistency, we define two thermodynamic crossover lines in supercritical fluids as boundaries of liquid-like, indistinguishable, and gas-like states. Near the critical point, the two crossover lines follow critical scalings with exponents of the Ising universality class, supported by calculations of theoretical models and analyses of experimental data from the standard database. The upper line agrees with crossovers independently estimated from the inelastic X-ray scattering data of supercritical argon, and from the small-angle neutron scattering data of supercritical carbon dioxide. The lower line is verified by the equation of states for the compressibility factor. This work provides a fundamental framework for understanding supercritical physics in general phase transitions. [ABSTRACT FROM AUTHOR]

The report presents static, low-frequency, and dynamic dielectric properties in the isotropic liquid, nematic, and solid phases of MBBA and related nanocolloids with paraelectric BaTiO3 nanoparticles (spherical, d = 50 nm). MBBA (4-methoxybenzylidene-4′–butylaniline) is a liquid crystalline compound with a permanent dipole moment transverse to the long molecular axis. The distortions-sensitive analysis of the dielectric constant revealed its hidden pretransitional anomaly, strongly influenced by the addition of nanoparticles. The evolution of the dielectric constant in the nematic phase shows the split into two regions, with the crossover coinciding with the standard melting temperature. The 'universal' exponential-type behavior of the low-frequency contribution to the real part of the dielectric permittivity is found. The critical-like pretransitional behavior in the solid phase is also evidenced. This is explained by linking the Lipovsky model to the Mossotti catastrophe concept under quasi-negative pressure conditions. The explicit preference for the 'critical-like' evolution of the apparent activation enthalpy is worth stressing for dynamics. Finally, the long-range, 'critical-like' behavior of the dissipation factor (D = tgδ), covering the isotropic liquid and nematic phases, is shown. [ABSTRACT FROM AUTHOR]

We pursue the analysis of nesting statistics in the O.n/loop model on random maps, initiated for maps with the topology of disks and cylinders by Borot, Bouttier and Duplantier (2016), here for arbitrary topologies. For this purpose, we rely on the topological recursion results by Borot, Eynard and Orantin (2011, 2015) for the enumeration of maps in the O.n/model. We characterize the generating series of maps of genus g with k boundaries and k0 marked points which realize a fixed nesting graph. These generating series are amenable to explicit computations in the loop model with bending energy on triangulations, and we characterize their behavior at criticality in the dense and in the dilute phase. [ABSTRACT FROM AUTHOR]

The long-range supercritical changes of dielectric constant, resembling ones observed in the isotropic liquid phase of liquid crystalline compounds, are evidenced for linseed oil—although in the given case, the phenomenon is associated with the liquid–solid melting/freezing discontinuous phase transitions. This ‘supercriticality’ can be an additional factor supporting the unique pro-health properties of linseed oil. Broadband dielectric spectroscopy studies also revealed the ‘glassy’ changes of relaxation times, well portrayed by the ‘activated and critical’ equation recently introduced. In the solid phase, the premelting effect characteristic for the canonic melting/freezing discontinuous transition, i.e., without any pretransitional effect in the liquid phase, has been detected. It is interpreted within the grain model, and its parameterization is possible using the Lipovsky model and the ‘reversed’ Mossotti catastrophe concept. For the premelting effect in the solid state, the singular ‘critical’ temperature correlates with the bulk discontinuous melting and freezing temperatures. Consequently, the report shows that linseed oil, despite its ‘natural and complex’ origins, can be considered a unique model system for two fundamental problems: (i) pretransitional (supercritical) effects in the liquid state associated with a weakly discontinuous phase transition, and (ii) the premelting behavior in the solid side of the discontinuous melting/freezing discontinuous transition.

The long-range supercritical changes of dielectric constant, resembling ones observed in the isotropic liquid phase of liquid crystalline compounds, are evidenced for linseed oil—although in the given case, the phenomenon is associated with the liquid–solid melting/freezing discontinuous phase transitions. This 'supercriticality' can be an additional factor supporting the unique pro-health properties of linseed oil. Broadband dielectric spectroscopy studies also revealed the 'glassy' changes of relaxation times, well portrayed by the 'activated and critical' equation recently introduced. In the solid phase, the premelting effect characteristic for the canonic melting/freezing discontinuous transition, i.e., without any pretransitional effect in the liquid phase, has been detected. It is interpreted within the grain model, and its parameterization is possible using the Lipovsky model and the 'reversed' Mossotti catastrophe concept. For the premelting effect in the solid state, the singular 'critical' temperature correlates with the bulk discontinuous melting and freezing temperatures. Consequently, the report shows that linseed oil, despite its 'natural and complex' origins, can be considered a unique model system for two fundamental problems: (i) pretransitional (supercritical) effects in the liquid state associated with a weakly discontinuous phase transition, and (ii) the premelting behavior in the solid side of the discontinuous melting/freezing discontinuous transition. [ABSTRACT FROM AUTHOR]

During cell division, precise and regulated distribution of cellular material between daughter cells is a critical step and is governed by complex biochemical and biophysical mechanisms. To achieve this, membraneless organelles and condensates often require complete disassembly during mitosis. The biophysical principles governing the disassembly of condensates remain poorly understood. Here, we used a physical biology approach to study how physical and material properties of the nucleolus, a prominent nuclear membraneless organelle in eukaryotic cells, change during mitosis and across different scales. We found that nucleolus disassembly proceeds continuously through two distinct phases with a slow and reversible preparatory phase followed by a rapid irreversible phase that was concurrent with the nuclear envelope breakdown. We measured microscopic properties of nucleolar material including effective diffusion rates and binding affinities as well as key macroscopic properties of surface tension and bending rigidity. By incorporating these measurements into the framework of critical phenomena, we found evidence that near mitosis surface tension displays a power-law behavior as a function of biochemically modulated interaction strength. This two-step disassembly mechanism maintains structural and functional stability of nucleolus while enabling its rapid and efficient disassembly in response to cell cycle cues. [ABSTRACT FROM AUTHOR]

Selma Lagerlöf said that culture is what remains when one has forgotten everything we had learned. Without any warranty, through ongoing research tasks, that I will ever attain this high level of wisdom, I simply share here reminiscences that have played, during my life, an important role in my incursions in science, mainly in theoretical physics. I end by presenting some perspectives for future developments. [ABSTRACT FROM AUTHOR]

Large, open‐gate transistors made from metal nanoparticle arrays offer possibilities to build new electronic devices, such as sensors. A nanoparticle necklace network (N3) of Au particles from 300 K to cryogenic temperatures exhibit a nonohmic I–Vd behavior, I ≈ (Vd–VT)ζ, where VT is a conduction gap and ζ is a constant critical exponent. The conduction gap in N3, made from disordered networks of 1D chains of 10 nm diameter Au particles exhibits room temperature (RT) gating. Although the I–Vd behavior at RT is identical to Coulomb blockade, the conduction is modulated by field‐assisted tunneling exhibiting classical critical behavior. In this study, based on three results, invariance of VT on gating, invariance of VT on temperature, and zero–bias conductance, a sharp transition temperature at ≈140 K is discovered where the conduction mechanism switches from Coulomb blockade to classical critical percolation behavior. The N3 architecture allows the reconciliation of the Coulomb blockade versus activation process as a sharp thermal transition to serve as a model system to study the exotic behavior in nanogranular‐metallic materials. The novel global critical behavior to local Coulomb blockade governed transition in these N3 architectures may potentially lead to novel sensors and biosensors. [ABSTRACT FROM AUTHOR]

The analysis of the impact of the star polymer topology on depletion interaction potentials, depletion forces, and monomer density profiles is carried out analytically using field theory methods and techniques as well as molecular dynamic simulations. The dimensionless depletion interaction potentials and the dimensionless depletion forces for a dilute solution of ideal star polymers with three and five legs (arms) in a Θ-solvent confined in a slit between two parallel walls with repulsive surfaces and for the case where one of the surfaces is repulsive and the other inert are obtained. Furthermore, the dimensionless layer monomer density profiles for ideal star polymers with an odd number (f˜ = 3, 5) of arms immersed in a dilute solution of big colloidal particles with different adsorbing or repelling properties in respect of polymers are calculated, bearing in mind the Derjaguin approximation. Molecular dynamic simulations of a dilute solution of star-shaped polymers in a good solvent with N = 901 (3 × 300 + 1 -star polymer with three arms) and 1501 (5 × 300 + 1 -star polymer with five arms) beads accordingly confined in a slit with different boundary conditions are performed, and the results of the monomer density profiles for the above-mentioned cases are obtained. The numerical calculation of the radius of gyration for star polymers with f˜ = 3, 5 arms and the ratio of the perpendicular to parallel components of the radius of gyration with respect to the wall orientation for the above-mentioned cases is performed. The obtained analytical and numerical results for star polymers with an odd number (f˜ = 3, 5) of arms are compared with our previous results for linear polymers in confined geometries. The acquired results show that a dilute solution of star polymer chains can be applied in the production of new functional materials, because the behavior of these solutions is strictly correlated with the topology of polymers and also with the nature and geometry of confined surfaces. The above-mentioned properties can find extensive practical application in materials engineering, as well as in biotechnology and medicine for drug and gene transmission.

We apply a real-space block renormalization group approach to study the critical properties of the random transverse-field Ising spin chain with multispin interactions. First, we recover the known properties of the traditional model with two-spin interactions by applying the renormalization approach for the arbitrary size of the block. For the model with three-spin couplings, we calculate the critical point and demonstrate that the phase transition is controlled by an infinite disorder fixed point. We have determined the typical correlation-length critical exponent, which seems to be different from that of the random transverse Ising chain with nearest-neighbor couplings. Thus, this model represents a new infinite disorder universality class.

The dynamic heterogeneities occurring just before the transition to the glassy phase have been named as the cause of amorphization in supercooled systems. Numerous studies conducted so far have confirmed this hypothesis, and based on it, a widely accepted solution to the puzzle of glass transition has been developed. This report focuses on verifying the existence of a strong pretransitional anomaly near the glass transition Tg. For this purpose, supercooled liquid-crystalline systems with a strong rod-like structure were selected. Based on the obtained experimental data, we demonstrate in this article that the previously postulated dynamic heterogeneities exhibit a critical characteristic, meaning a strong pretransitional anomaly can be observed with the described critical exponent α=0.5. Due to this property, it can be concluded that these heterogeneities are critical fluctuations, and consequently, the transition to the glassy state can be described based on the theory of critical phenomena. To measure the pretransitional anomaly near Tg in supercooled liquid-crystalline systems, broadband dielectric spectroscopy (BDS) and nonlinear dielectric effect (NDE) methods were applied. The exponent α provides insight into the nature and intensity of critical fluctuations in the system. A value of α=0.5 suggests that the fluctuations become increasingly intense as the system approaches the critical point, contributing to the divergence in specific heat. Understanding the role of critical fluctuations in the glass transition is crucial for innovating and improving a wide range of materials for energy storage, materials design, biomedical applications, food preservation, and environmental sustainability. These advancements can lead to materials with superior properties, optimized manufacturing processes, and applications that meet the demands of modern technology and sustainability challenges.

This model discussion focuses on links between the unique properties of relaxor ceramics and the basics of Critical Phenomena Physics and Glass Transition Physics. It indicates the significance of uniaxiality for the appearance of mean-field type features near the paraelectric-to-ferroelectric phase transition. Pretransitional fluctuations, that are increasing up to the size of a grain and leading to inter-grain, random, local electric fields are responsible for relaxor ceramics characteristics. Their impact yields the pseudospinodal behavior associated with "weakly discontinuous" local phase transitions. The emerging model redefines the meaning of the Burns temperature and polar nanoregions (PNRs). It offers a coherent explanation of "dielectric constant" changes with the "diffused maximum" near the paraelectric-to-ferroelectric transition, the sensitivity to moderate electric fields (tunability), and the "glassy" dynamics. These considerations are challenged by the experimental results of complex dielectric permittivity studies in a Ba0.65Sr0.35TiO3 relaxor ceramic, covering ca. 250 K, from the paraelectric to the "deep" ferroelectric phase. The distortion-sensitive and derivative-based analysis in the paraelectric phase and the surrounding paraelectric-to-ferroelectric transition reveal a preference for the exponential scaling pattern for ε(T) changes. This may suggest that Griffith-phase behavior is associated with mean-field criticality disturbed by random local impacts. The preference for the universalistic "critical & activated" evolution of the primary relaxation time is shown for dynamics. The discussion is supplemented by a coupled energy loss analysis. The electric field-related tunability studies lead to scaling relationships describing their temperature changes. [ABSTRACT FROM AUTHOR]

The commonly quoted bistable Higgs potential is not a proper description of the Higgs field because, among other technical reasons, one of its stable states acquires a negative expectation value in vacuum. We rely on formal catastrophe theory to derive the form of the Higgs potential that admits only one positive mean value in vacuum. No symmetry is broken during the ensuing phase transition that assigns mass to the Higgs field; only gauge redundancy is "broken" by the appearance of phase in the massive state, but this redundancy is not a true symmetry of the massless field. Furthermore, a secondary, certainly amusing conclusion, is that, in its high-energy state, the field oscillates about its potential minimum between positive and negative masses, but it is doubtful that such evanescent states can survive below the critical temperature of 159.5 GeV, where the known particles were actually created. [ABSTRACT FROM AUTHOR]

To understand how the temporal non-locality («memory») properties of a process affect its critical regimes, the power-law compound and time-fractional Poisson process is presented as a universal hereditary model of criticality. Seismicity is considered as an application of the theory of criticality. On the basis of the proposed hereditarian criticality model, the critical regimes of seismicity are investigated. It is shown that the seismic process has the property of «memory» (non-locality over time) and statistical time-dependence of events. With a decrease in the fractional exponent of the Poisson process, the relaxation slows down, which can be associated with the hardening of the medium and the accumulation of elastic energy. Delayed relaxation is accompanied by an abnormal increase in fluctuations, which is caused by the non-local correlations of random events over time. According to the found criticality indices, the seismic process is in subcritical regimes for the zero and first moments and in supercritical regimes for the second statistical moment of events' reoccurrence frequencies distribution. The supercritical regimes indicate the instability of the deformation changes that can go into a non-stationary regime of a seismic process. [ABSTRACT FROM AUTHOR]

Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics. This review paper discusses a fundamental question: how can entanglement be effectively and indirectly (e.g., through intermediate nodes) distributed between distant nodes in an imperfect quantum network, where the connections are only partially entangled and subject to quantum noise? We survey recent studies addressing this issue by drawing exact or approximate mappings to percolation theory, a branch of statistical physics centered on network connectivity. Notably, we show that the classical percolation frameworks do not uniquely define the network's indirect connectivity. This realization leads to the emergence of an alternative theory called "concurrence percolation", which uncovers a previously unrecognized quantum advantage that emerges at large scales, suggesting that quantum networks are more resilient than initially assumed within classical percolation contexts, offering refreshing insights into future quantum network design. [ABSTRACT FROM AUTHOR]

Abstract Large, open‐gate transistors made from metal nanoparticle arrays offer possibilities to build new electronic devices, such as sensors. A nanoparticle necklace network (N3) of Au particles from 300 K to cryogenic temperatures exhibit a nonohmic I–Vd behavior, I ≈ (Vd–VT)ζ, where VT is a conduction gap and ζ is a constant critical exponent. The conduction gap in N3, made from disordered networks of 1D chains of 10 nm diameter Au particles exhibits room temperature (RT) gating. Although the I–Vd behavior at RT is identical to Coulomb blockade, the conduction is modulated by field‐assisted tunneling exhibiting classical critical behavior. In this study, based on three results, invariance of VT on gating, invariance of VT on temperature, and zero–bias conductance, a sharp transition temperature at ≈140 K is discovered where the conduction mechanism switches from Coulomb blockade to classical critical percolation behavior. The N3 architecture allows the reconciliation of the Coulomb blockade versus activation process as a sharp thermal transition to serve as a model system to study the exotic behavior in nanogranular‐metallic materials. The novel global critical behavior to local Coulomb blockade governed transition in these N3 architectures may potentially lead to novel sensors and biosensors.

Fluctuations are omnipresent; they exist in any matter, due either to its quantum nature or to its nonzero temperature. In the current review, we briefly cover the quantum electrodynamic Casimir (QED) force as well as the critical Casimir (CC) and Helmholtz (HF) forces. In the QED case, the medium is usually a vacuum and the massless excitations are photons, while in the CC and HF cases the medium is usually a critical or correlated fluid and the fluctuations of the order parameter are the cause of the force between the macroscopic or mesoscopic bodies immersed in it. We discuss the importance of the presented results for nanotechnology, especially for devising and assembling micro- or nano-scale systems. Several important problems for nanotechnology following from the currently available experimental findings are spelled out, and possible strategies for overcoming them are sketched. Regarding the example of HF, we explicitly demonstrate that when a given integral quantity characterizing the fluid is conserved, it has an essential influence on the behavior of the corresponding fluctuation-induced force.

We study the critical behaviors of systems undergoing fractal time processes above the upper critical dimension. We derive a set of novel critical exponents, irrespective of the order of the fractional time derivative or the particular form of interaction in the Hamiltonian. For fractal time processes, we not only discover new universality classes with a dimensional constant but also decompose the dangerous irrelevant variables to obtain corrections for critical dynamic behavior and static critical properties. This contrasts with the traditional theory of critical phenomena, which posits that static critical exponents are unrelated to the dynamical processes. Simulations of the Landau–Ginzburg model for fractal time processes and the Ising model with temporal long-range interactions both show good agreement with our set of critical exponents, verifying its universality. The discovery of this new universality class provides a method for examining whether a system is undergoing a fractal time process near the critical point.

The report presents static, low-frequency, and dynamic dielectric properties in the isotropic liquid, nematic, and solid phases of MBBA and related nanocolloids with paraelectric BaTiO3 nanoparticles (spherical, d = 50 nm). MBBA (4-methoxybenzylidene-4′–butylaniline) is a liquid crystalline compound with a permanent dipole moment transverse to the long molecular axis. The distortions-sensitive analysis of the dielectric constant revealed its hidden pretransitional anomaly, strongly influenced by the addition of nanoparticles. The evolution of the dielectric constant in the nematic phase shows the split into two regions, with the crossover coinciding with the standard melting temperature. The ‘universal’ exponential-type behavior of the low-frequency contribution to the real part of the dielectric permittivity is found. The critical-like pretransitional behavior in the solid phase is also evidenced. This is explained by linking the Lipovsky model to the Mossotti catastrophe concept under quasi-negative pressure conditions. The explicit preference for the ‘critical-like’ evolution of the apparent activation enthalpy is worth stressing for dynamics. Finally, the long-range, ‘critical-like’ behavior of the dissipation factor (D = tgδ), covering the isotropic liquid and nematic phases, is shown.

Selma Lagerlöf said that culture is what remains when one has forgotten everything we had learned. Without any warranty, through ongoing research tasks, that I will ever attain this high level of wisdom, I simply share here reminiscences that have played, during my life, an important role in my incursions in science, mainly in theoretical physics. I end by presenting some perspectives for future developments.

It has recently become appreciated that cells self-organize their interiors through the formation of biomolecular condensates. These condensates, typically formed through liquid-liquid phase separation of proteins, nucleic acids, and other biopolymers, exhibit reversible assembly/disassembly in response to changing conditions. Condensates play many functional roles, aiding in biochemical reactions, signal transduction, and sequestration of certain components. Ultimately, these functions depend on the physical properties of condensates, which are encoded in the microscopic features of the constituent biomolecules. In general, the mapping from microscopic features to macroscopic properties is complex, but it is known that near a critical point, macroscopic properties follow power laws with only a small number of parameters, making it easier to identify underlying principles. How far does this critical region extend for biomolecular condensates and what principles govern condensate properties in the critical regime? Using coarse-grained molecular-dynamics simulations of a representative class of biomolecular condensates, we found that the critical regime can be wide enough to cover the full physiological range of temperatures. Within this critical regime, we identified that polymer sequence influences surface tension predominately via shifting the critical temperature. Finally, we show that condensate surface tension over a wide range of temperatures can be calculated from the critical temperature and a single measurement of the interface width. [ABSTRACT FROM AUTHOR]

Carnot cycles of samples of harmonically confined ultracold 87 Rb fluids, near and across Bose–Einstein condensation (BEC), are analyzed. This is achieved through the experimental determination of the corresponding equation of state in terms of the appropriate global thermodynamics for non-uniform confined fluids. We focus our attention on the efficiency of the Carnot engine when the cycle occurs for temperatures either above or below the critical temperature and when BEC is crossed during the cycle. The measurement of the cycle efficiency reveals a perfect agreement with the theoretical prediction (1 − T L / T H) , with T H and T L serving as the temperatures of the hot and cold heat exchange reservoirs. Other cycles are also considered for comparison. [ABSTRACT FROM AUTHOR]

The majority-voter model is studied by Monte Carlo simulations on hypercubic lattices of dimension 𝑑 = 2 to 7 with periodic boundary conditions. The critical exponents associated to the finite-size scaling of the magnetic susceptibility are shown to be compatible with those of the Ising model. At dimension 𝑑 = 4, the numerical data are compatible with the presence of multiplicative logarithmic corrections. For 𝑑 > 5, the estimates of the exponents are close to the prediction 𝑑2 when taking into account the dangerous irrelevant variable at the Gaussian fixed point. Moreover, the universal values of the Binder cumulant are also compatible with those of the Ising model. This indicates that the upper critical dimension of the majority-voter model is not 𝑑𝑐 = 6 as claimed in the literature, but 𝑑𝑐 = 4 like the equilibrium Ising model. [ABSTRACT FROM AUTHOR]

The main task of the article is to define the critical minimum number of tests for the dynamics of a traffic node in autonomous driving based on critical phenomena, i.e. the percolation theory. The critical (minimum) number of tests of a node means how we can represent the traffic dynamics of a node with critical, percolating path using a "state-following state" system on the graph. The test cases along the percolation path, i.e., those involved in the formation of the new phase, represent the entire test system and are minimal. In the article we show that only less than 10 of the 640 tests to be performed have to be realized and are representative for release processes. [ABSTRACT FROM AUTHOR]

To understand how the temporal non-locality («memory») properties of a process affect its critical regimes, the power-law compound and time-fractional Poisson process is presented as a universal hereditary model of criticality. Seismicity is considered as an application of the theory of criticality. On the basis of the proposed hereditarian criticality model, the critical regimes of seismicity are investigated. It is shown that the seismic process has the property of «memory» (non-locality over time) and statistical time-dependence of events. With a decrease in the fractional exponent of the Poisson process, the relaxation slows down, which can be associated with the hardening of the medium and the accumulation of elastic energy. Delayed relaxation is accompanied by an abnormal increase in fluctuations, which is caused by the non-local correlations of random events over time. According to the found criticality indices, the seismic process is in subcritical regimes for the zero and first moments and in supercritical regimes for the second statistical moment of events’ reoccurrence frequencies distribution. The supercritical regimes indicate the instability of the deformation changes that can go into a non-stationary regime of a seismic process.

This model discussion focuses on links between the unique properties of relaxor ceramics and the basics of Critical Phenomena Physics and Glass Transition Physics. It indicates the significance of uniaxiality for the appearance of mean-field type features near the paraelectric-to-ferroelectric phase transition. Pretransitional fluctuations, that are increasing up to the size of a grain and leading to inter-grain, random, local electric fields are responsible for relaxor ceramics characteristics. Their impact yields the pseudospinodal behavior associated with “weakly discontinuous” local phase transitions. The emerging model redefines the meaning of the Burns temperature and polar nanoregions (PNRs). It offers a coherent explanation of “dielectric constant” changes with the “diffused maximum” near the paraelectric-to-ferroelectric transition, the sensitivity to moderate electric fields (tunability), and the “glassy” dynamics. These considerations are challenged by the experimental results of complex dielectric permittivity studies in a Ba0.65Sr0.35TiO3 relaxor ceramic, covering ca. 250 K, from the paraelectric to the “deep” ferroelectric phase. The distortion-sensitive and derivative-based analysis in the paraelectric phase and the surrounding paraelectric-to-ferroelectric transition reveal a preference for the exponential scaling pattern for ε(T) changes. This may suggest that Griffith-phase behavior is associated with mean-field criticality disturbed by random local impacts. The preference for the universalistic “critical & activated” evolution of the primary relaxation time is shown for dynamics. The discussion is supplemented by a coupled energy loss analysis. The electric field-related tunability studies lead to scaling relationships describing their temperature changes.

The commonly quoted bistable Higgs potential is not a proper description of the Higgs field because, among other technical reasons, one of its stable states acquires a negative expectation value in vacuum. We rely on formal catastrophe theory to derive the form of the Higgs potential that admits only one positive mean value in vacuum. No symmetry is broken during the ensuing phase transition that assigns mass to the Higgs field; only gauge redundancy is “broken” by the appearance of phase in the massive state, but this redundancy is not a true symmetry of the massless field. Furthermore, a secondary, certainly amusing conclusion, is that, in its high-energy state, the field oscillates about its potential minimum between positive and negative masses, but it is doubtful that such evanescent states can survive below the critical temperature of 159.5 GeV, where the known particles were actually created.

Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics. This review paper discusses a fundamental question: how can entanglement be effectively and indirectly (e.g., through intermediate nodes) distributed between distant nodes in an imperfect quantum network, where the connections are only partially entangled and subject to quantum noise? We survey recent studies addressing this issue by drawing exact or approximate mappings to percolation theory, a branch of statistical physics centered on network connectivity. Notably, we show that the classical percolation frameworks do not uniquely define the network’s indirect connectivity. This realization leads to the emergence of an alternative theory called “concurrence percolation”, which uncovers a previously unrecognized quantum advantage that emerges at large scales, suggesting that quantum networks are more resilient than initially assumed within classical percolation contexts, offering refreshing insights into future quantum network design.

The double exponential WJ distribution has been shown to competently describe extreme events and critical phenomena, while the Gaussian function has celebrated rich applications in many other fields. Here we present the analysis that the WJ distribution may be properly treated as an extended Gaussian function. Based on the Taylor expansion, we propose three methods to formulate the WJ distribution in the form of Gaussian functions, with Method I and Method III being accurate and self-consistent, and elaborate the relationship among the parameters of the functions. Moreover, we derive the parameter scaling formula of the WJ distribution to express a general Gaussian function, with the work illustrated by a classical case of extreme events and critical phenomena and application to topical medical image processing to prove the effectiveness of the WJ distribution rather than the Gaussian function. Our results sturdily advocate that the WJ distribution can elegantly represent a Gaussian function of arbitrary parameters, whereas the latter usually is not able to satisfactorily describe the former except for specific parameter sets. Thus, it is conclusive that the WJ distribution offers applicability in extreme events and critical phenomena as well as processes describable by the Gaussian function, namely, implying plausibly a unifying approach to the pertinent data processing of those quite distinct areas and establishing a link between relevant extreme value theories and Gaussian processes. [ABSTRACT FROM AUTHOR]

Recent progress in studies on quantum chromodynamics (QCD) phase transition and related critical phenomena within the functional renormalization group (fRG) approach were reviewed, including the nonperturbative critical exponents and baryon number fluctuations, which are pertinent to the critical end point (CEP) in the QCD phase diagram. The fRG is a nonperturbative continuum field approach, in which quantum thermal fluctuations are successively integrated with the evolution of the renormalization group (RG) scale. Different methods of finding solutions to the flow or fixed-point equations of a nonperturbative effective potential have been discussed, for example, the Taylor expansion, expansion of the spatial dimension ε=4-d, and the recently proposed direct solution of the global potential. Furthermore, the baryon number of fluctuations is relevant to the critical phenomena of the CEP. Both have been discussed, and one explores the underlying reasons for the observed non-monotonic dependence of the kurtosis of the net proton number of distributions on collision energy in experiments.

A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature of the key processes like gene expression and cell differentiation give rise to fluctuations (noise) at the levels of the biomolecules, and this combined with nonlinear interactions gives rise to a number of emergent phenomena. In this review, we describe and discuss some of these phenomena which have the character of phase transitions in physical systems. We specifically focus on noise-induced transitions in a stochastic model of gene expression and in a population genetics model which have no analogs when the dynamics are solely deterministic in nature. Some of these transitions exhibit critical-point phenomena belonging to the mean-field Ising universality class of equilibrium phase transitions. A number of other examples, ranging from biofilms to homeostasis in adult tissues, are also discussed, which exhibit behaviour similar to critical phenomena in equilibrium and nonequilbrium phase transitions. The examples illustrate how the subject of statistical mechanics provides a bridge between theoretical models and experimental observations. [ABSTRACT FROM AUTHOR]

Recently acoustic signature of dislocation avalanches in HCP materials was found to be long tailed in size and energy, suggesting critical dynamics. Moreover, the intermittent plastic response was found to be generic for micro- and nano-sized systems independently of their crystallographic symmetry. These rather remarkable discoveries are reviewed in this paper in the perspective of the recent studies performed in our group. We discuss the physical origin and the scaling properties of plastic fluctuations and address the nature of their dependence on crystalline symmetry, system size, and disorder content. A particular emphasis is placed on the formation of dislocation structures, and on our ability to temper plastic fluctuations by alloying. We also discuss the “smaller is wilder” size effect that culminates in a paradoxical crack-free brittle behavior of very small, initially dislocation free crystals. We argue that the implied transition between different rheological behaviors is regulated by the ratio of length scales $R=L/l$, where $L$ is the system size and $l$ is the internal length. We link this size effect with size dependence of strength (“smaller is stronger”) and the size-induced switch between different hardening mechanisms. We show that the task of taming the intermittency of plastic flow at ultra-small scales can be accomplished by generating tailored quenched disorder which allows one to control micro- and nano-forming and opens new perspectives in micro-metallurgy and structural engineering of miniature load-carrying elements. These insights were beyond the reach of conventional theoretical approaches that do not explicitly account for the stochastic nature of collective dislocation dynamics.

While swarming behavior is regarded as a critical phenomenon in phase transition and frequently shows the properties of a critical state such as Lévy walk, a general mechanism to explain the critical property in swarming behavior has not yet been found. Here, we address this problem with a simple swarm model, the Self-Propelled Particle (SPP) model, and propose a way to explain this critical behavior by introducing agents making decisions via the data-hypothesis interaction in Bayesian inference, namely, Bayesian and inverse Bayesian inference (BIB). We compare three SPP models, namely, the simple SPP, the SPP with Bayesian-only inference (BO) and the SPP with BIB models. We show that only the BIB model entails coexisting tornado, splash and translation behaviors, and the Lévy walk pattern.

The majority-voter model is studied by Monte Carlo simulations on hypercubic lattices of dimension d = 2 to 7 with periodic boundary conditions. The critical exponents associated to the finite-size scaling of the magnetic susceptibility are shown to be compatible with those of the Ising model. At dimension d = 4, the numerical data are compatible with the presence of multiplicative logarithmic corrections. For d ≥ 5, the estimates of the exponents are close to the prediction d/2 when taking into account the dangerous irrelevant variable at the Gaussian fixed point. Moreover, the universal values of the Binder cumulant are also compatible with those of the Ising model. This indicates that the upper critical dimension of the majority-voter model is not d_c = 6 as claimed in the literature, but d_c = 4 like the equilibrium Ising model.

Carnot cycles of samples of harmonically confined ultracold 87Rb fluids, near and across Bose–Einstein condensation (BEC), are analyzed. This is achieved through the experimental determination of the corresponding equation of state in terms of the appropriate global thermodynamics for non-uniform confined fluids. We focus our attention on the efficiency of the Carnot engine when the cycle occurs for temperatures either above or below the critical temperature and when BEC is crossed during the cycle. The measurement of the cycle efficiency reveals a perfect agreement with the theoretical prediction (1−TL/TH), with TH and TL serving as the temperatures of the hot and cold heat exchange reservoirs. Other cycles are also considered for comparison.

The review presents the development of an approach of constructing approximate solutions to complicated physics problems, starting from asymptotic series, through optimized perturbation theory, to self-similar approximation theory. The close interrelation of underlying ideas of these theories is emphasized. Applications of the developed approach are illustrated by typical examples demonstrating that it combines simplicity with good accuracy. [ABSTRACT FROM AUTHOR]

Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it pertains to those geometric clusters (defined as connected sets of nearest-neighbor aligned spins) in the context of Ising models. We show how data from surface probes can be used to distinguish whether electronic patterns observed at the surface of a material are confined to the surface, or whether the patterns originate in the bulk. Whereas thermodynamic critical exponents are derived from the behavior of Fortuin–Kasteleyn (FK) clusters, critical exponents can be similarly defined for geometric clusters. We find that these geometric critical exponents are not only distinct numerically from the thermodynamic and uncorrelated percolation exponents, but that they separately satisfy scaling relations at the critical fixed points discussed in the text. We furthermore find that the two-dimensional (2D) cross-sections of geometric clusters in the three-dimensional (3D) Ising model display critical scaling behavior at the bulk phase transition temperature. In particular, we show that when considered on a 2D slice of a 3D system, the pair connectivity function familiar from percolation theory displays more robust critical behavior than the spin-spin correlation function, and we calculate the corresponding critical exponent. We discuss the implications of these two distinct length scales in Ising models. We also calculate the pair connectivity exponent in the clean 2D case. These results extend the theory of geometric criticality in the clean Ising universality classes, and facilitate the broad application of geometric cluster analysis techniques to maximize the information that can be extracted from scanning image probe data in condensed matter systems. [ABSTRACT FROM AUTHOR]

Abstract We have investigated the predictability of precipitation using a new configuration of the superparameterized Community Atmosphere Model (SP‐CAM). The new configuration, called the multiple‐instance SP‐CAM, or MP‐CAM, uses the average heating and drying rates from 10 independent two‐dimensional cloud‐permitting models (CPMs) in each grid column of the global model, instead of a single CPM. The 10 CPMs start from slightly different initial conditions and simulate alternative realizations of the convective cloud systems. By analyzing the ensemble of possible realizations, we can study the predictability of the cloud systems and identify the weather regimes and physical mechanisms associated with chaotic convection. We explore alternative methods for quantifying the predictability of precipitation. Our results show that unpredictable precipitation occurs when the simulated atmospheric state is close to critical points as defined by Peters and Neelin (2006, https://doi.org/10.1038/nphys314). The predictability of precipitation is also influenced by the convective available potential energy and the degree of mesoscale organization. It is strongly controlled by the large‐scale circulation. A companion paper compares the global atmospheric circulations simulated by SP‐CAM and MP‐CAM.

We present a theoretical and experimental investigation of drainage in porous media. The study is limited to stabilized fluid fronts at moderate injection rates, but it takes into account capillary, viscous, and gravitational forces. In the theoretical framework presented, the work applied on the system, the energy dissipation, the final saturation and the width of the stabilized fluid front can all be calculated if we know the dimensionless fluctuation number, the wetting properties, the surface tension between the fluids, the fractal dimensions of the invading structure and its boundary, and the exponent describing the divergence of the correlation length in percolation. Furthermore, our theoretical description explains how the Haines jumps’ local activity and dissipation relate to dissipation on larger scales.

We consider critical branching Brownian motion with absorption, in which there is initially a single particle at x > 0, particles move according to independent one-dimensional Brownian motions with the critical drift of -√2, and particles are absorbed when they reach zero. Here we obtain asymptotic results concerning the behavior of the process before the extinction time, as the position x of the initial particle tends to infinity. We estimate the number of particles in the system at a given time and the position of the right-most particle. We also obtain asymptotic results for the configuration of particles at a typical time.

We consider critical branching Brownian motion with absorption, in which there is initially a single particle at x > 0, particles move according to independent one-dimensional Brownian motions with the critical drift of -√2, and particles are absorbed when they reach zero. Here we obtain asymptotic results concerning the behavior of the process before the extinction time, as the position x of the initial particle tends to infinity. We estimate the number of particles in the system at a given time and the position of the right-most particle. We also obtain asymptotic results for the configuration of particles at a typical time.

We consider branching Brownian motion on the real line with absorption at zero, in which particles move according to independent Brownian motions with the critical drift of -√2. Kesten (Stoch Process 7:9–47, 1978) showed that almost surely this process eventually dies out. Here we obtain upper and lower bounds on the probability that the process survives until some large time t. These bounds improve upon results of Kesten (Stoch Process 7:9–47, 1978), and partially confirm nonrigorous predictions of Derrida and Simon (EPL 78:60006, 2007).