Energy relaxation in disordered lattice φ4 system:The combined effects of disorder and nonlinearity

We address the issue of how disorder together with nonlinearity affect energy relaxation in the latticeφ~4 system.The absence of nonlinearity leads such a model to only supporting fully localized Anderson modes whose energies will not relax.However,through exploring the time decay behavior of each Anderson mode’s energy–energy correlation,we find that adding nonlinearity,three distinct relaxation details can occur.(i)A small amount of nonlinearity causes a rapid exponential decay of the correlation for all modes.(ii)In the intermediate value of nonlinearity,this exponential decay will turn to power-law with a large scaling exponent close to-1.(iii)Finally,all Anderson modes’energies decay in a power-law manner but with a quite small exponent,indicating a slow long-time tail decay.Obviously,the last two relaxation details support a new localization mechanism.As an application,we show that these are relevant to the nonmonotonous nonlinearity dependence of thermal conductivity.Our results thus provide new information for understanding the combined effects of disorder and nonlinearity on energy relaxation.

Nitric oxide synergizes minoxidil delivered by transdermal hyaluronic acid liposomes for multimodal androgenetic-alopecia therapy

Androgenetic alopecia(AGA)is a common clinical condition,affecting over 200 million people globally each year.For decades,Minoxidil(Mi)tincture has been the primary treatment for this disease,but its low utilization rate and significant side effects necessitate new therapeutic strategies.Nitric oxide(NO)is a signaling molecule in various physiological processes,including vasodilation,immune responses,and cell proliferation.Herein,we constructed a hyaluronic acid liposome(HL)complex as a novel transdermal delivery system(HL@Mi/NONOate)for NO and Mi,which displayed promising transdermal and hair-regrowth effects.In-depth mechanistic studies revealed three potential pathways of the synergistic AGA therapy.First,NO promoted capillary dilation and accelerated blood flow,thus achieving efficient penetration of Mi.Due to the structural advantage of liposomes,the residence time of the Mi in the skin was prolonged.Moreover,HL@Mi/NONOate promoted cell proliferation and angiogenesis,and upregulated the expression of regulatory factors involved in follicle stem cell differentiation.In the AGA model,HL@Mi/NONOate down-regulated the expression of inflammatory factors,inhibiting the inflammation of follicle and improving the microenvironment of hair regrowth.Concurrently,HL@Mi/NONOate upregulated the expression of Ki67 and PCNA proteins in follicle tissues,inducing follicle regeneration and development,ultimately achieving the synergistic multimodal AGA therapy.